**2. Teleportation of CdSe/ZnS QDs in the classical space**

#### **2.1 Quantum entanglement**

Quantum entanglement is a new resource of quantum physics, the same as, for example, energy [12]. New resources make it possible to discover new potentials and implement fundamentally new processes of quantum physics. The modern representation of quantum states is based on the statement that, in quantum mechanics, any physical system is described completely by a state vector |Ψ〉 in the Hilbert space *H*. A system with a two-dimensional Hilbert space is called a qubit (quantum bit). For several Hilbert spaces, for example, for *H*A and *H*B, the complete Hilbert space is the tensor product of the subsystem spaces: *H*AB = *H*<sup>A</sup> ⊗ *H*B. Any quantum system that is described by a single state vector is a pure state. Next, the density operator and other mathematical transformations are introduced. Everything, all Physics is over! Mathematics on paper remained only!

A real qubit is a quantum object that has two stable quantum states, which, as a rule, have different easily measured classical characteristics. For example, a

**51**

In essence, |*α*|

2 and |*β*| 2

*Quantum Dots CdSe/ZnS as a Source Array of Entangled States*

quantum of light in the "*o*" and "*e*" states of polarization, or a neutral atom and a charged ion of this atom. And these characteristics are measured easily using classic devices. The modern representation of quantum entanglement is based on the modern representation of quantum states. A quantum state |Ψ〉 is entangled if it cannot be written as a tensor product, i.e., |Φ〉 ≠ |*a*〉 ⊗ |*b*〉. And, here, if the quantum state

*<sup>N</sup>*(|*a*1〉 <sup>⊗</sup> |*b*1〉 + |*a*2〉 <sup>⊗</sup> |*b*2〉) (1)

(|01〉 − |10〉) (2)

2 + |*β*| 2 = 1.

is written as the sum of tensor products, then this state is entanglement.

<sup>|</sup>Φ〉 <sup>=</sup> \_1 √ \_ 2

The term "entanglement" was introduced by Schrödinger for the first time in 1935 [13]. Schrödinger introduced this term to describe the specific relationship between quantum systems, which have correlations between their dynamic quantities: position and momentum. And this relationship is expressed in an infinite set of dynamic values of two particles. Thus, Schrödinger justified one of the key properties of quantum entanglement—the complete uncertainty of the values of classical dynamic quantities such as the position and momentum of a particle. And what do we see in Eq. (2)? Here, the quantum state |Φ〉 of a quantum superposition of one object in two basic states is written, |0〉 and |1〉 decoherence of which will give an equiprobable (1/2) result to find this object, both in the state |01〉 and in the state |10〉. Where is the uncertainty here? Complete uncertainty reflects the form of

∣ Ψ〉 = α ∣ 0〉 + β ∣ 1〉, (3)

Thus, we conclude that the quantum state |*Ψ*〉 in the entry form (3) is a quantum superposition, and it is an entangled quantum state. The principle of quantum superposition states that the linear combination of quantum states of all quantum objects of the participants of this superposition is also a quantum state. The linear combination provides an exponential growth of quantum states of quantum objects with two basic states (qubit) with a linear increase in the number of these qubits. This means that *N* quits provide 2*<sup>N</sup>* entangled quantum states of quantum superposition. And if we return to physics, this means that the wave function of the state |*Ψ*〉 contains 2*<sup>N</sup>* entangled wave functions. If *N* qubits occupy a macroscopic volume, then the wave function of state |*Ψ*〉 is macroscopic. This is a fundamental conclusion, since the macroscopic wave function is the basis of all quantum processes as a result of Bose-Einstein condensation. The way to create a Bose-Einstein condensate regardless of temperature opens up fantastic prospects for practical devices based on quantum

are probabilities of obtaining a state of |0〉 or |1〉 in clas-

where *α* and *β* are complex numbers, the sum of squares of which |*α*|

states, but to be in an uncertain state, there are no problems here.

effects. This is one of the physical resources of quantum entangled states.

sical space as a result of decoherence. To feel that there is entanglement you can simply imagine the coin that was thrown up, and it falls and rotates. While the coin is rotate, it is impossible to say what condition it is in. The coin is in a completely indefinite state, but it is exact in some of the states |0〉 or |1〉. The coin fell to the ground and here it can be said, determined or measured in which particular state and in which particular place on the earth. Some people write in their articles that a quantum object in a state of quantum superposition is simultaneously in all its basic states. But this is nonsense. A quantum object cannot be simultaneously in its two

<sup>|</sup>Φ〉 <sup>=</sup> \_1

As an example, a type of state is usually given

writing a quantum state |*Ψ*〉 quantum superposition.

*DOI: http://dx.doi.org/10.5772/intechopen.88558*

*Quantum Dots - Fundamental and Applications*

The typical relaxation time of exciton luminescence is the nanosecond time range. Consequently, relaxation of all excited quantum states of QDs takes place in the nanosecond range, whereas relaxation of metastable excitons takes place in the millisecond range, which is six orders of magnitude greater than the lifetime of all other quantum states of QDs. In other words, QDs with a metastable exciton are a quasistable quantum state, and can play the role of a second stable state |1〉 of QDs, as a qubit. The first stable state of such a qubit |0〉 is QD in the ground quantum state. The irradiation of a colloid QDs is a simple and practically free way to continuously generate an array of qubits in two stable quantum states, naturally, when

Obviously, we must receive the result of any quantum process, for example, quantum computing or teleportation in the classical space, in the space where we all function. For example, a digital computer operates in its "digital space." We will need it only when it "produces" a result that is understandable to us, for example, a graph or a picture, but not as a set of numbers. QDs with a metastable exciton, as a qubits in the quantum state |1〉, have unique nonlinear optical characteristics. The fact is that the electron capture by the surface trap separates the charge carriers by a distance that coincides with the size of the QD, which are several nanometers. Such a large separation of charge carriers is the source of a very large light-induced dipole moment *p* of an individual QD with a metastable exciton. The dipole moment *p* is responsible for the value of light-induced change in the refractive index [11]. Therefore, a large value of *p* makes it possible to record the distribution of the concentration of individual QDs with a metastable exciton using conventional interferometry. It is this distribution of the concentration of QDs in the quantum state that is the result of the quantum process in the quantum space, which is the "quantum box" by definition of the founding fathers of quantum mechanics. We see that quantum dots can be in two stable quantum states, which allows them to be used as a qubit in all modern quantum technologies. One of these quantum states has a significantly different classical refractive index. This property makes it possible to register individual QDs in this quantum state |1〉 by interferometry methods and, thus, to register the results of quantum processes in classical space. The experimental results of this chapter substantiate and realize this possibility, which opens up new areas for the use of quantum dots in fundamental and

the energy of the optical beam quanta exceeds the QD bandgap.

**2. Teleportation of CdSe/ZnS QDs in the classical space**

Physics is over! Mathematics on paper remained only!

Quantum entanglement is a new resource of quantum physics, the same as, for example, energy [12]. New resources make it possible to discover new potentials and implement fundamentally new processes of quantum physics. The modern representation of quantum states is based on the statement that, in quantum mechanics, any physical system is described completely by a state vector |Ψ〉 in the Hilbert space *H*. A system with a two-dimensional Hilbert space is called a qubit (quantum bit). For several Hilbert spaces, for example, for *H*A and *H*B, the complete Hilbert space is the tensor product of the subsystem spaces: *H*AB = *H*<sup>A</sup> ⊗ *H*B. Any quantum system that is described by a single state vector is a pure state. Next, the density operator and other mathematical transformations are introduced. Everything, all

A real qubit is a quantum object that has two stable quantum states, which, as a rule, have different easily measured classical characteristics. For example, a

**50**

applied physics.

**2.1 Quantum entanglement**

quantum of light in the "*o*" and "*e*" states of polarization, or a neutral atom and a charged ion of this atom. And these characteristics are measured easily using classic devices. The modern representation of quantum entanglement is based on the modern representation of quantum states. A quantum state |Ψ〉 is entangled if it cannot be written as a tensor product, i.e., |Φ〉 ≠ |*a*〉 ⊗ |*b*〉. And, here, if the quantum state is written as the sum of tensor products, then this state is entanglement.

$$|\Phi\rangle = \frac{1}{N} (|a\_1\rangle \otimes |b\_1\rangle + |a\_2\rangle \otimes |b\_2\rangle) \tag{1}$$

As an example, a type of state is usually given

$$|\spadesuit\rangle = \frac{1}{\sqrt{2}}(|01\rangle - |10\rangle) \tag{2}$$

The term "entanglement" was introduced by Schrödinger for the first time in 1935 [13]. Schrödinger introduced this term to describe the specific relationship between quantum systems, which have correlations between their dynamic quantities: position and momentum. And this relationship is expressed in an infinite set of dynamic values of two particles. Thus, Schrödinger justified one of the key properties of quantum entanglement—the complete uncertainty of the values of classical dynamic quantities such as the position and momentum of a particle. And what do we see in Eq. (2)? Here, the quantum state |Φ〉 of a quantum superposition of one object in two basic states is written, |0〉 and |1〉 decoherence of which will give an equiprobable (1/2) result to find this object, both in the state |01〉 and in the state |10〉. Where is the uncertainty here? Complete uncertainty reflects the form of writing a quantum state |*Ψ*〉 quantum superposition.

$$
\mid \Psi \rangle = \mathfrak{a} \mid \mathbb{O} \rangle + \mathfrak{b} \mid \mathfrak{1} \rangle,\tag{3}
$$

where *α* and *β* are complex numbers, the sum of squares of which |*α*| 2 + |*β*| 2 = 1. In essence, |*α*| 2 and |*β*| 2 are probabilities of obtaining a state of |0〉 or |1〉 in classical space as a result of decoherence. To feel that there is entanglement you can simply imagine the coin that was thrown up, and it falls and rotates. While the coin is rotate, it is impossible to say what condition it is in. The coin is in a completely indefinite state, but it is exact in some of the states |0〉 or |1〉. The coin fell to the ground and here it can be said, determined or measured in which particular state and in which particular place on the earth. Some people write in their articles that a quantum object in a state of quantum superposition is simultaneously in all its basic states. But this is nonsense. A quantum object cannot be simultaneously in its two states, but to be in an uncertain state, there are no problems here.

Thus, we conclude that the quantum state |*Ψ*〉 in the entry form (3) is a quantum superposition, and it is an entangled quantum state. The principle of quantum superposition states that the linear combination of quantum states of all quantum objects of the participants of this superposition is also a quantum state. The linear combination provides an exponential growth of quantum states of quantum objects with two basic states (qubit) with a linear increase in the number of these qubits. This means that *N* quits provide 2*<sup>N</sup>* entangled quantum states of quantum superposition. And if we return to physics, this means that the wave function of the state |*Ψ*〉 contains 2*<sup>N</sup>* entangled wave functions. If *N* qubits occupy a macroscopic volume, then the wave function of state |*Ψ*〉 is macroscopic. This is a fundamental conclusion, since the macroscopic wave function is the basis of all quantum processes as a result of Bose-Einstein condensation. The way to create a Bose-Einstein condensate regardless of temperature opens up fantastic prospects for practical devices based on quantum effects. This is one of the physical resources of quantum entangled states.

### **2.2 Experimental implementation of multi-particle quantum superposition**

Obviously, practical applications make sense with an array of entangled quantum states, the source of which is quantum superposition. Qbits are quantum objects in two basic states, the dynamic characteristics of which, for example, their location, can be easily measured in classical space. It is these qubits, more precisely, their quantum states |0〉 and |1〉 that form the quantum state of many-particle quantum superposition |*Ψ*〉 in the self-assembly mode. Self-assembly is a typical process of quantum physics, a typical example is Bose-Einstein condensate. Another typical example is the self-assembly of nanoscale quantum objects with a large quantum confinement [14]. Practical devices require qubits cheap and easily accessible. In addition, such qubits must function under normal conditions: they do not require ultrahigh vacuum or ultralow temperatures.

The semiconductor quantum dots (QDs) of CdSe/ZnS were used in this work as such qubits. The modern concept of quantum entanglement asserts that quantum entanglement is a consequence of some nonlocality of quantum mechanics, which cannot be explained from the standpoint of classical physics [15]. This concept is the basis for research on quantum communications, quantum cryptography and quantum networks. Let us leave the question of nonlocality "for later," and let's discuss the obvious property of quantum entanglement, which is it's decoherence. An array of tossed and rotating coins will fall to the ground. Each coin will fall on one of its sides. This particular side of the coin is the result of the interaction of all the coins, both among themselves and with external and internal forces, as they rotate. Decoherence of quantum superposition unravels all entangled quantum states into concrete quantum states |0〉 and |1〉 of each qubit in classical space and, thus, makes it possible to record the result of the interaction of forces in quantum superposition or quantum entanglement.

The dynamic principle of quantum superposition states that the quantum state of quantum superposition can occur again after decoherence, if conditions for this exist. Therefore, the continuous functioning of the states of quantum superposition according to the scheme "self-assembly of quantum superposition—decoherence under the influence of external and internal forces—self-assembly of quantum superposition again—decoherence again, etc." can occur only with continuous generation of the qubit. The quantum state of the qubit |0〉 is the ground unexcited state, which does not require external influence for its existence. The quantum state of the qubit |1〉 is a QD with a metastable exciton. Therefore, the continuous generation of this state is a necessary condition for the continuous functioning of the quantum state of quantum superposition. An optical beam with quantum energy greater than the bandgap is the driving force that is able to generate the state |1〉 continuously.

An optical beam with a wavelength of *λ* = 437 nm was used for this in experiments. A CW-laser was used as a source of this beam with a power of 30 mW. The scheme and methodology of the experiment are presented in detail in [16]. Here, we will focus on key phenomena that characterize quantum entanglement as a truly new resource with fundamentally different possibilities of practical application. In short, the experiment consisted in observing and registering the trace profile of an optical beam that spread through a suspension of CdSe/ZnS quantum dots. The fact is that the pattern of the beam trace profile is a pattern of wave aberrations of a light-induced lens [17, 18], which occurs in a QDs suspension, as a result of the self-action of an optical beam, which generates a |1〉 quantum state with a different refractive index compared to the refractive index quantum state |0〉. The dynamic pattern of wave aberrations of a light-induced lens reflects the dynamics of the space-time redistribution of the wave surface of a light-induced change

**53**

illumination.

*Quantum Dots CdSe/ZnS as a Source Array of Entangled States*

in the refractive index. The wave surface of the light-induced refractive index is the space-time distribution of the concentration of QDs in the quantum state |1〉. Thus, registration of the redistribution of the refractive index makes it possible to measure the redistribution of the concentration of the quantum state |1〉 (QD with a metastable exciton), including as a result of the presence of such QDs in the quantum state of quantum superposition. This is the "highlight" of the experiment. The fact is that decoherence of an array of entangled quantum states in quantum space, which is a "quantum box," as defined by the founding fathers of quantum mechanics, occurs under the influence of all forces, internal and external. Including those forces, the existence of which we do not know. Thereby, the registration of the result of decoherence of quantum superposition makes it possible to detect these

*DOI: http://dx.doi.org/10.5772/intechopen.88558*

forces and understand their physical nature.

*w*0 = *λ*/*πθ* = 28 μm; *I*0 = 2*Pl*/*πw*<sup>2</sup>

ness of the cuvette with colloid was 5 mm.

**2.3 Experimental implementation of teleporting CT CdSe/ZnS**

All the experimental results were obtained in a simple experiment, the scheme of which is shown in **Figure 1a**. This graphic also shows a typical beam trace profile pattern on a remote screen. **Figure 1b** shows a typical transformation of the pattern of the beam trace profile after the start of illumination. Here, the time of 0 ms is the beginning of the illumination of the QDs suspension, and the intensity distribution is the input beam profile without a cuvette with a suspension with QDs in the beam. The input beam parameters were: beam convergence angle *θ* = 5.45 10<sup>−</sup><sup>3</sup>

Quantum teleportation is the concept of quantum physics, which is being studied in a large number of recent published works. The main research topics are quantum communication, quantum computing and quantum networks. The term teleportation means the process by which bodies and objects are transferred from one place to another without moving along any path. The "quantum teleportation" boom begins with article [19], in which an unknown quantum state is first measured and then reconstructed at a remote place. The implementation of this information protocol requires a classical communication channel [19], and quantum entanglement [12]. The conceptual basis of such a quantum teleportation is the assertion that two quantum particles in an entangled state have some non-locality so that changes in the state of one particle immediately correlate with changes in the remote system regardless of the signal passing time between them [15]. If this concept is accepted as a physical reality, then one should assume the existence of some otherworldly forces, which, and only they, provide such a speculative correlation between remote quantum objects. This article substantiates another concept of quantum teleportation, which is really a physical reality, since this concept is the result of an experiment. The meaning of the experiment was to look the transformation of the pattern of the beam trace profile when moving the cuvette with the QDs colloid on a rough surface, as a result of which, the QDs colloid was subjected to micro-shaking. **Figure 2** contains information about how the dimensions of the pattern of the beam trace profile change in the process of establishing a steady state and after the beginning of the movement of the cuvette with the colloid QDs. These data were obtained at the position of the cuvette along the axis *Z* = −15*z*0. Here *D*hor, *R*dw *R*up is the horizontal diameter, the radius of the lower half and the radius of the upper half of the pattern of the beam trace profile. The time *τ* is the characteristic time of exponential relaxation of processes that control the pattern of the beam trace profile during the accumulation of QDs and the establishment of a steady state. The beginning of the movement of the cuvette with colloid took place after 3 seconds of

; *z*0 = *πw*<sup>0</sup>

2

= 2436 W/cm2

;

/*λ* = 5.2 = 5.2 mm. The thick-

*Quantum Dots CdSe/ZnS as a Source Array of Entangled States DOI: http://dx.doi.org/10.5772/intechopen.88558*

*Quantum Dots - Fundamental and Applications*

ultrahigh vacuum or ultralow temperatures.

or quantum entanglement.


**2.2 Experimental implementation of multi-particle quantum superposition**

Obviously, practical applications make sense with an array of entangled quantum states, the source of which is quantum superposition. Qbits are quantum objects in two basic states, the dynamic characteristics of which, for example, their location, can be easily measured in classical space. It is these qubits, more precisely, their quantum states |0〉 and |1〉 that form the quantum state of many-particle quantum superposition |*Ψ*〉 in the self-assembly mode. Self-assembly is a typical process of quantum physics, a typical example is Bose-Einstein condensate. Another typical example is the self-assembly of nanoscale quantum objects with a large quantum confinement [14]. Practical devices require qubits cheap and easily accessible. In addition, such qubits must function under normal conditions: they do not require

The semiconductor quantum dots (QDs) of CdSe/ZnS were used in this work as such qubits. The modern concept of quantum entanglement asserts that quantum entanglement is a consequence of some nonlocality of quantum mechanics, which cannot be explained from the standpoint of classical physics [15]. This concept is the basis for research on quantum communications, quantum cryptography and quantum networks. Let us leave the question of nonlocality "for later," and let's discuss the obvious property of quantum entanglement, which is it's decoherence. An array of tossed and rotating coins will fall to the ground. Each coin will fall on one of its sides. This particular side of the coin is the result of the interaction of all the coins, both among themselves and with external and internal forces, as they rotate. Decoherence of quantum superposition unravels all entangled quantum states into concrete quantum states |0〉 and |1〉 of each qubit in classical space and, thus, makes it possible to record the result of the interaction of forces in quantum superposition

The dynamic principle of quantum superposition states that the quantum state of quantum superposition can occur again after decoherence, if conditions for this exist. Therefore, the continuous functioning of the states of quantum superposition according to the scheme "self-assembly of quantum superposition—decoherence under the influence of external and internal forces—self-assembly of quantum superposition again—decoherence again, etc." can occur only with continuous generation of the qubit. The quantum state of the qubit |0〉 is the ground unexcited state, which does not require external influence for its existence. The quantum state of the qubit |1〉 is a QD with a metastable exciton. Therefore, the continuous generation of this state is a necessary condition for the continuous functioning of the quantum state of quantum superposition. An optical beam with quantum energy greater than the bandgap is the driving force that is able to generate the state

An optical beam with a wavelength of *λ* = 437 nm was used for this in experiments. A CW-laser was used as a source of this beam with a power of 30 mW. The scheme and methodology of the experiment are presented in detail in [16]. Here, we will focus on key phenomena that characterize quantum entanglement as a truly new resource with fundamentally different possibilities of practical application. In short, the experiment consisted in observing and registering the trace profile of an optical beam that spread through a suspension of CdSe/ZnS quantum dots. The fact is that the pattern of the beam trace profile is a pattern of wave aberrations of a light-induced lens [17, 18], which occurs in a QDs suspension, as a result of the self-action of an optical beam, which generates a |1〉 quantum state with a different refractive index compared to the refractive index quantum state |0〉. The dynamic pattern of wave aberrations of a light-induced lens reflects the dynamics of the space-time redistribution of the wave surface of a light-induced change

**52**

in the refractive index. The wave surface of the light-induced refractive index is the space-time distribution of the concentration of QDs in the quantum state |1〉. Thus, registration of the redistribution of the refractive index makes it possible to measure the redistribution of the concentration of the quantum state |1〉 (QD with a metastable exciton), including as a result of the presence of such QDs in the quantum state of quantum superposition. This is the "highlight" of the experiment. The fact is that decoherence of an array of entangled quantum states in quantum space, which is a "quantum box," as defined by the founding fathers of quantum mechanics, occurs under the influence of all forces, internal and external. Including those forces, the existence of which we do not know. Thereby, the registration of the result of decoherence of quantum superposition makes it possible to detect these forces and understand their physical nature.

### **2.3 Experimental implementation of teleporting CT CdSe/ZnS**

All the experimental results were obtained in a simple experiment, the scheme of which is shown in **Figure 1a**. This graphic also shows a typical beam trace profile pattern on a remote screen. **Figure 1b** shows a typical transformation of the pattern of the beam trace profile after the start of illumination. Here, the time of 0 ms is the beginning of the illumination of the QDs suspension, and the intensity distribution is the input beam profile without a cuvette with a suspension with QDs in the beam. The input beam parameters were: beam convergence angle *θ* = 5.45 10<sup>−</sup><sup>3</sup> ; *w*0 = *λ*/*πθ* = 28 μm; *I*0 = 2*Pl*/*πw*<sup>2</sup> = 2436 W/cm2 ; *z*0 = *πw*<sup>0</sup> 2 /*λ* = 5.2 = 5.2 mm. The thickness of the cuvette with colloid was 5 mm.

Quantum teleportation is the concept of quantum physics, which is being studied in a large number of recent published works. The main research topics are quantum communication, quantum computing and quantum networks. The term teleportation means the process by which bodies and objects are transferred from one place to another without moving along any path. The "quantum teleportation" boom begins with article [19], in which an unknown quantum state is first measured and then reconstructed at a remote place. The implementation of this information protocol requires a classical communication channel [19], and quantum entanglement [12]. The conceptual basis of such a quantum teleportation is the assertion that two quantum particles in an entangled state have some non-locality so that changes in the state of one particle immediately correlate with changes in the remote system regardless of the signal passing time between them [15]. If this concept is accepted as a physical reality, then one should assume the existence of some otherworldly forces, which, and only they, provide such a speculative correlation between remote quantum objects. This article substantiates another concept of quantum teleportation, which is really a physical reality, since this concept is the result of an experiment.

The meaning of the experiment was to look the transformation of the pattern of the beam trace profile when moving the cuvette with the QDs colloid on a rough surface, as a result of which, the QDs colloid was subjected to micro-shaking. **Figure 2** contains information about how the dimensions of the pattern of the beam trace profile change in the process of establishing a steady state and after the beginning of the movement of the cuvette with the colloid QDs. These data were obtained at the position of the cuvette along the axis *Z* = −15*z*0. Here *D*hor, *R*dw *R*up is the horizontal diameter, the radius of the lower half and the radius of the upper half of the pattern of the beam trace profile. The time *τ* is the characteristic time of exponential relaxation of processes that control the pattern of the beam trace profile during the accumulation of QDs and the establishment of a steady state. The beginning of the movement of the cuvette with colloid took place after 3 seconds of illumination.

#### **Figure 1.**

*(a) The scheme of the experiment and the profile of the laser beam trace on the screen. (b) The trace profile of the input optical beam and the trace profiles of the output beam in the process of accumulation of long-lived QDs after the start of illumination, z = −29z0.*

It is obvious that the establishment of a stationary state takes place as a result of at least two processes. The first ~400 ms there is an increase in all sizes of the pattern of the beam trace profile. Then, we see a dramatic change in the size behavior of this pattern. An obvious reduction in all sizes of this pattern is observed. We should note that the increase and subsequent reduction in the size of the pattern is well extrapolated by exponential functions. Moreover, the pattern of the upper half of the beam trace profile is reduced to a much greater degree and significantly sooner. We will analyze these experimental results below. Here, we will consider the situation after the beginning of the movement of the cuvette with the colloid to another location along the *Z* axis. Individual frames of the pattern transformation are shown in **Figure 3**. The real transformation of the pattern in real time is in the video files "trans1-trans3."

The beginning of this movement took place after 3 seconds of continuous illumination. Obviously, the steady state was achieved during this time (see **Figure 2**). This movement caused a complete "whistleblower" or "orgy" of the dimensions of the beam trace profile pattern, which **Figures 2** and **3** demonstrate quite well. We must note that the pattern of the profile of a beam trace changes its structure in an abrupt manner. Details of the pattern of each frame in **Figure 3** do not coincide with the details of the pattern of the previous frame of the video. All patterns of each frame change their details "jump." Recall that the time between frames was 40 ms. Here we should especially note that all the processes that controlled the size of the pattern immediately before the beginning of the displacement had characteristic relaxation times of 200–300 ms, which significantly exceeded the actual time of a cardinal change of the pattern itself.

Another key result is that the axis of the output optical beam coincides with the axis of the input optical beam with all the "manipulations" with the cuvette with a colloid: its movement along the *Z* axis (±49*z*0); micro-shaking due to the unevenness of painting the surface of the table on which the table with the cuvette was moving. Here we note that the cuvette was oriented at a small angle to the axis of the

**55**

**Figure 3.**

*z = −15z0.*

**Figure 2.**

*waist of the focused beam.*

*Quantum Dots CdSe/ZnS as a Source Array of Entangled States*

input optical beam, and the axis of direct movement of the cuvette did not coincide

*Transformation of the pattern of the beam trace profile during the movement of the colloid from the position* 

*The establishment of a stationary beam trace profile pattern. The inserts show the direct transformation of the pattern after the beginning of the movement from the position along the axis* Z *= −15z0 to the side closer to the* 

**Figures 2**–**4** contain information that shows that the micro shake of a QDs colloid transforms the pattern of the beam trace profile over a time that is significantly

The pattern of the beam trace profile changes its structure and dimensions "abruptly" in each frame of the video. **Figure 4** shows how the digital profile of the beam trace profile pattern changes its structure and size after the beginning of the displacement (0 ms) of the cuvette along the z axis and after 120 ms. Here we have to remind that the beginning of movement took place after 3 seconds of continuous illumination, when the pattern of the beam trace profile was in a steady state with a

with the axis of the input optical beam.

characteristic exponential relaxation time *τ* ~200–300 ms.

*DOI: http://dx.doi.org/10.5772/intechopen.88558*

*Quantum Dots CdSe/ZnS as a Source Array of Entangled States DOI: http://dx.doi.org/10.5772/intechopen.88558*

#### **Figure 2.**

*Quantum Dots - Fundamental and Applications*

It is obvious that the establishment of a stationary state takes place as a result of at least two processes. The first ~400 ms there is an increase in all sizes of the pattern of the beam trace profile. Then, we see a dramatic change in the size behavior of this pattern. An obvious reduction in all sizes of this pattern is observed. We should note that the increase and subsequent reduction in the size of the pattern is well extrapolated by exponential functions. Moreover, the pattern of the upper half of the beam trace profile is reduced to a much greater degree and significantly sooner. We will analyze these experimental results below. Here, we will consider the situation after the beginning of the movement of the cuvette with the colloid to another location along the *Z* axis. Individual frames of the pattern transformation are shown in **Figure 3**. The real transformation of the pattern in real time is in the

*(a) The scheme of the experiment and the profile of the laser beam trace on the screen. (b) The trace profile of the input optical beam and the trace profiles of the output beam in the process of accumulation of long-lived* 

The beginning of this movement took place after 3 seconds of continuous illumination. Obviously, the steady state was achieved during this time (see **Figure 2**). This movement caused a complete "whistleblower" or "orgy" of the dimensions of the beam trace profile pattern, which **Figures 2** and **3** demonstrate quite well. We must note that the pattern of the profile of a beam trace changes its structure in an abrupt manner. Details of the pattern of each frame in **Figure 3** do not coincide with the details of the pattern of the previous frame of the video. All patterns of each frame change their details "jump." Recall that the time between frames was 40 ms. Here we should especially note that all the processes that controlled the size of the pattern immediately before the beginning of the displacement had characteristic relaxation times of 200–300 ms, which significantly exceeded the actual time of a

Another key result is that the axis of the output optical beam coincides with the axis of the input optical beam with all the "manipulations" with the cuvette with a colloid: its movement along the *Z* axis (±49*z*0); micro-shaking due to the unevenness of painting the surface of the table on which the table with the cuvette was moving. Here we note that the cuvette was oriented at a small angle to the axis of the

**54**

video files "trans1-trans3."

*QDs after the start of illumination, z = −29z0.*

**Figure 1.**

cardinal change of the pattern itself.

*The establishment of a stationary beam trace profile pattern. The inserts show the direct transformation of the pattern after the beginning of the movement from the position along the axis* Z *= −15z0 to the side closer to the waist of the focused beam.*

#### **Figure 3.**

*Transformation of the pattern of the beam trace profile during the movement of the colloid from the position z = −15z0.*

input optical beam, and the axis of direct movement of the cuvette did not coincide with the axis of the input optical beam.

The pattern of the beam trace profile changes its structure and dimensions "abruptly" in each frame of the video. **Figure 4** shows how the digital profile of the beam trace profile pattern changes its structure and size after the beginning of the displacement (0 ms) of the cuvette along the z axis and after 120 ms. Here we have to remind that the beginning of movement took place after 3 seconds of continuous illumination, when the pattern of the beam trace profile was in a steady state with a characteristic exponential relaxation time *τ* ~200–300 ms.

**Figures 2**–**4** contain information that shows that the micro shake of a QDs colloid transforms the pattern of the beam trace profile over a time that is significantly

**Figure 4.**

*Digital profile of horizontal slice "a" and vertical slice "b" of the beam trace pattern 120 ms after the beginning of the movement (0 ms).*

shorter than the characteristic exponential relaxation time of the steady state of the QDs colloid. Here we recall that the pattern of the beam trace profile is a pattern of wave aberrations of the wave surface of the light-induced refractive index volume [17, 18]. The photoinduced refractive index of a colloid of QDs results from the accumulation of the concentration of QDs with a light-induced metastable exciton [16]. Consequently, the transformation of the pattern of the beam trace profile is the result of the transformation of the distribution of the concentration of QDs with a metastable exciton in the illuminated volume of the QDs suspension. **Figure 4** convincingly shows that a substantial concentration of QDs with a metastable exciton, providing phase addition to the wave front of the input beam, for example, at 14*π* disappears without a trace for a time shorter than the characteristic relaxation time of the steady-state stationary concentration of QDs.

In principle, this behavior of the QDs concentration is expected. Micro-shaking is a source of forces that can cause flows in a liquid, which mix the concentration of QDs. But, the fact is that micro-shock causes forces with an arbitrary direction. It is obvious that such forces should cause arbitrary concentration flows in a liquid, which should cause an arbitrary geometric displacement of the optical beam, its axis, in the first place. The experiment shows that arbitrary QDs concentration fluxes with a

**57**

*Quantum Dots CdSe/ZnS as a Source Array of Entangled States*

of the forces not "burdened" by the opposition of any other forces.

this it is necessary to confuse the quantum states of charged qubits.

but in the size of an ordinary laboratory table opens.

Practical significance and novelty lies in the fact that quantum teleportation allows you to register super-weak forces. Obviously, a super-weak force can impart to a super-small mass a sufficiently large acceleration, which is easy to register, especially in the absence of internal friction. On this basis, the possibility of developing super sensitive sensors, for example, for registration of gravitational waves,

To conclude this section, we formulate the physics of the quantum teleportation process of entangled quantum states. The obvious condition of quantum teleportation is that entangled quantum states must occupy a macroscopic volume. It is the volume in which the geometric displacement of quantum states takes place. In this work, this volume determines the geometry of the input optical beam, as well as, for example, in [20]. This optical beam light induces a second stable quantum state (QD with a metastable exciton) from the first state (QD in the ground quantum state), in other words, the optical beam generates classical two-level qubits, which at a sufficiently high concentration self-organize into a quantum state of quantum superposition with 2*<sup>N</sup>* entangled quantum states. Decoherence takes place under the influence of both internal and external forces. It is under the action of these forces that the "disentangling" of 2*<sup>N</sup>* quantum states into one of the stable states |0〉 or |1〉 of each individual qubit from *N* classical qubits takes place. The concentration distribution of these particular qubits is easily measured, since they are already in the classical space. The specific geometrical place where the quantum states |0〉 or |1〉 fall into is determined by internal forces (concentration compression as QDs accumulate with a metastable exciton) or external forces (whistle of the beam trace

metastable exciton really arise, but all these fluxes "spin" around the axis of the input optical beam. The axis of the input beam has "unshakable" directions and retains its direction for all mechanical perturbations of the cell with QDs colloid. This means only one thing: there are no real flows of QDs concentration in the liquid, and what we see is the result of teleportation of the quantum states of a metastable exciton. Quantum teleportation "transfers" only quantum states from one quantum object to another quantum object. The trajectory of the transfer, of course, is absent. We have implemented a unique situation where mechanical classical forces are small enough to cause a real disturbance of the fluid, but these forces easily cause quantum teleportation, which does not have a trajectory of movement in classical space. The lack of a trajectory of movement clearly means that there is no actual movement of objects in space. Obviously, there is no movement; therefore, there are no forces that prevent this movement. This means that what we see is the result of the direct action

The fundamental and practical significance, as well as novelty, of these results cannot be overestimated. The fundamental significance and novelty lies in the fact that the resource of entangled quantum states creates a macroscopic wave function regardless of temperature. Quantum teleportation transports quantum states of neutral particles, for example, quantum dots with a metastable exciton, without a specific trajectory of motion in classical space. Since there is no movement trajectory, then there is no movement itself. Movement is not, means that there are no forces that impede movement. There are no such force, which means that there is no internal friction. There is no internal friction in a fluid, for example, in a colloid of quantum dots, and there is a real displacement of a quantum dot, since a quantum state with a metastable exciton is another stable quantum state of quantum dots in classical space, and therefore it is another quantum object. Moving quantum objects in a liquid without internal friction is the basis for the implementation of a superfluid quantum liquid, regardless of temperature. Superconductivity can be realized regardless of the temperature on the same quantum entanglement resource, but for

*DOI: http://dx.doi.org/10.5772/intechopen.88558*

#### *Quantum Dots CdSe/ZnS as a Source Array of Entangled States DOI: http://dx.doi.org/10.5772/intechopen.88558*

*Quantum Dots - Fundamental and Applications*

shorter than the characteristic exponential relaxation time of the steady state of the QDs colloid. Here we recall that the pattern of the beam trace profile is a pattern of wave aberrations of the wave surface of the light-induced refractive index volume [17, 18]. The photoinduced refractive index of a colloid of QDs results from the accumulation of the concentration of QDs with a light-induced metastable exciton [16]. Consequently, the transformation of the pattern of the beam trace profile is the result of the transformation of the distribution of the concentration of QDs with a metastable exciton in the illuminated volume of the QDs suspension. **Figure 4** convincingly shows that a substantial concentration of QDs with a metastable exciton, providing phase addition to the wave front of the input beam, for example, at 14*π* disappears without a trace for a time shorter than the characteristic

*Digital profile of horizontal slice "a" and vertical slice "b" of the beam trace pattern 120 ms after the beginning* 

In principle, this behavior of the QDs concentration is expected. Micro-shaking is a source of forces that can cause flows in a liquid, which mix the concentration of QDs. But, the fact is that micro-shock causes forces with an arbitrary direction. It is obvious that such forces should cause arbitrary concentration flows in a liquid, which should cause an arbitrary geometric displacement of the optical beam, its axis, in the first place. The experiment shows that arbitrary QDs concentration fluxes with a

relaxation time of the steady-state stationary concentration of QDs.

**56**

**Figure 4.**

*of the movement (0 ms).*

metastable exciton really arise, but all these fluxes "spin" around the axis of the input optical beam. The axis of the input beam has "unshakable" directions and retains its direction for all mechanical perturbations of the cell with QDs colloid. This means only one thing: there are no real flows of QDs concentration in the liquid, and what we see is the result of teleportation of the quantum states of a metastable exciton. Quantum teleportation "transfers" only quantum states from one quantum object to another quantum object. The trajectory of the transfer, of course, is absent. We have implemented a unique situation where mechanical classical forces are small enough to cause a real disturbance of the fluid, but these forces easily cause quantum teleportation, which does not have a trajectory of movement in classical space. The lack of a trajectory of movement clearly means that there is no actual movement of objects in space. Obviously, there is no movement; therefore, there are no forces that prevent this movement. This means that what we see is the result of the direct action of the forces not "burdened" by the opposition of any other forces.

The fundamental and practical significance, as well as novelty, of these results cannot be overestimated. The fundamental significance and novelty lies in the fact that the resource of entangled quantum states creates a macroscopic wave function regardless of temperature. Quantum teleportation transports quantum states of neutral particles, for example, quantum dots with a metastable exciton, without a specific trajectory of motion in classical space. Since there is no movement trajectory, then there is no movement itself. Movement is not, means that there are no forces that impede movement. There are no such force, which means that there is no internal friction. There is no internal friction in a fluid, for example, in a colloid of quantum dots, and there is a real displacement of a quantum dot, since a quantum state with a metastable exciton is another stable quantum state of quantum dots in classical space, and therefore it is another quantum object. Moving quantum objects in a liquid without internal friction is the basis for the implementation of a superfluid quantum liquid, regardless of temperature. Superconductivity can be realized regardless of the temperature on the same quantum entanglement resource, but for this it is necessary to confuse the quantum states of charged qubits.

Practical significance and novelty lies in the fact that quantum teleportation allows you to register super-weak forces. Obviously, a super-weak force can impart to a super-small mass a sufficiently large acceleration, which is easy to register, especially in the absence of internal friction. On this basis, the possibility of developing super sensitive sensors, for example, for registration of gravitational waves, but in the size of an ordinary laboratory table opens.

To conclude this section, we formulate the physics of the quantum teleportation process of entangled quantum states. The obvious condition of quantum teleportation is that entangled quantum states must occupy a macroscopic volume. It is the volume in which the geometric displacement of quantum states takes place. In this work, this volume determines the geometry of the input optical beam, as well as, for example, in [20]. This optical beam light induces a second stable quantum state (QD with a metastable exciton) from the first state (QD in the ground quantum state), in other words, the optical beam generates classical two-level qubits, which at a sufficiently high concentration self-organize into a quantum state of quantum superposition with 2*<sup>N</sup>* entangled quantum states. Decoherence takes place under the influence of both internal and external forces. It is under the action of these forces that the "disentangling" of 2*<sup>N</sup>* quantum states into one of the stable states |0〉 or |1〉 of each individual qubit from *N* classical qubits takes place. The concentration distribution of these particular qubits is easily measured, since they are already in the classical space. The specific geometrical place where the quantum states |0〉 or |1〉 fall into is determined by internal forces (concentration compression as QDs accumulate with a metastable exciton) or external forces (whistle of the beam trace

profile pattern). An analogue of the physics of such teleportation is the precipitation of raindrops (quantum states) from a macroscopic rain cloud (quantum superposition) under the action of internal forces (for example, the turbulent distribution of condensation centers) or external forces (for example, turbulent flows or wind gusts).
