2. What is the quantum measurement?

the business about human self-confidence, but the fear of our fate determination. If the glimpse of us can determine the cat's fate, who determines our fate? Trouble never singly comes; many researches find that "the moon is not there" in experiments [1] responding to what Albert Einstein said, "I like to think that the moon is there even if I don't look at it." According to the physicist's research, Albert Einstein seems worried because the world is quantum world and all things obey quantum mechanics. This means all the definite statuses we have observed are due to "a glimpse" of us or the god. Really? Is really the moon not here if we do not look at it, does really the cat not exist if we do not look at it, and do we not exist

It must be something to worry because the moon exists more than 4.5 billion years as the astronomer finding, which is much more than human history. We are not going to discuss the superpower of human and if the god exists or not in this book. We return to the fundamental of quantum mechanics and find that the hidden actor, quantum measurement, is the crime

There is a confliction in modern quantum physics after its birth. The confliction is concerning the full description between the superposition state for the behavior of matter on the microscopic level and the definite-status appearance as what we can observe on the macroscopic level in the real world. Schrödinger proposed Schrödinger cat in his essay to illustrate the "putative incompleteness" of quantum mechanics, but many researches show that quantum mechanics is still the best one of these "not satisfied theories." To alleviate the theory-to-world confliction, a new conception, quantum measurement, is brought out. It is the basic assumption in quantum mechanics, thought that the superposition state will be collapsed into one of the eigenstates with the square of amplification probability if we do a quantum measurement. Although the quantum measurement bridges the gap of the different behaviors of subatomic level and the macro-world, some problems still remain. For example, its physical mechanism is dim. We do not know what will lead to the quantum measurement and how the process that the quantum measurement undergoes. The words "stochastic", "instantaneous" and "irreversible" torment us more than 70 years, and we still have no way to integrate them into the "determinate", "time-costed" and "reversible" quantum evolution. In fact, the manual division for the world into two parts, quantum world and quantum measurement apparatus, is not satisfied, and we are finding

In this chapter, we will overview the mechanism of quantum measurement and the main kinds of interpretation of quantum measurement. Among these interpretations, a promised theory which can well interpret the quantum measurement quandaries—why the quantum state collapses into some eigenstates with "stochastic" and "instantaneity", and what causes the "basis-preferred"—is detailed. The advantage of this theory is it is just an extension of Feynman path integral (FPI) and is obviously compatible with the classical quantum theory. According the conclusions of this theory, we show that the "noise" world (or apparatus here when we do an experiment) causes the "random" and "nonlocal" mechanism of the quantum collapse. Actually, the world exists due to itself, and the god

if the god does not look at us?

136 Advanced Technologies of Quantum Key Distribution

a uniform description.

can go to have a rest.

culprit that causes these puzzling questions.

Quantum measurement is different from the classical measurement, in which the measurement accuracy is dependent on the measurement instruments. It means, we could infinitely approach the "absolute exact value" by upgrading instruments or improving methods in the classical measurement realm. However, the things change when we access to the quantum world. In quantum world, the "accuracy" does not exist. We cannot speak that the velocity of an electron is 1376:5 m=s or the distance of two electrons is 20 nm, etc., because these physical quantities exist in the form of quantum states in quantum world. Objects are always in the superposition states of these kinds of the basis state, such as momentum, position, energy, spin and so on. We can just get one of the basis states under every measurement, and the "absolute exact value" is never revealed under one measurement unless the state of the object is in the basis state.

In quantum mechanics, the projection operator is defined as Pb<sup>φ</sup><sup>i</sup> ¼ jφ<sup>i</sup> ⟩⟨φ<sup>i</sup> j, where jφ<sup>i</sup> ⟩ is an element of the basis-state set jφ<sup>k</sup> � �g. The measurement output for a mechanical quantity operator Qb under one quantum measurement is Qi ¼ φ<sup>i</sup> Qb � � � � � �φi D E <sup>¼</sup> Tr <sup>P</sup>b<sup>φ</sup><sup>i</sup> <sup>Q</sup><sup>b</sup> � �, and the initial state will instantaneously collapse into the basis state jφ<sup>i</sup> ⟨ with the probability pi ¼ Tr Pb<sup>φ</sup><sup>i</sup> brI � �, where <sup>b</sup>r<sup>I</sup> is the initial density matrix of an object, after the quantum measurement. For multi-measurements, the output we get is the average value <sup>Q</sup><sup>~</sup> <sup>¼</sup> <sup>P</sup> i pi Qi <sup>¼</sup> Tr <sup>Q</sup><sup>b</sup> <sup>b</sup>r<sup>I</sup> � �, and the final state of the many object systems becomes <sup>r</sup><sup>O</sup> <sup>¼</sup> <sup>P</sup> i pi Pbφi , which is very different from the initial state rI.

This kind of measurement, to be exact, is the projective measurement. A more general formulation of measurement is the positive-operator valued measure (POVM), which can be seemed as the partial measurement in the subsystem of a projective measurement system. No matter what kind of quantum measurements there is, it is the kind of destructive manipulations and irreversible. It destroys the old state and rebuilds a new mixed state. The definition of the quantum measurement is simple and definite, but the problem is that we do not know why the quantum measurement acts as these strange behaviors. The irreversibility and unpredictability are incompatible with the smooth Schrodinger differential equation and are hated by physicists. What kind of objects has priority to do the quantum measurement? Taking the experiment of two-slit interference of electrons, for example, the detector behind the slits usually is regarded as a measurement tool, but the detector itself, which may be a microcavity or atom ensemble, is also a physical system and obeys the quantum mechanism. Therefore, it seems that the process of a quantum measurement is the interaction between the detector and electrons and should be a "quantum evolution process". However, the quantum evolution process is non-destructive and reversible. In fact, in the real world, it is hard for us to distinguish strictly which is the quantum evolution operation and which is the quantum measurement.

The second problem is the space–time nonlocality in the quantum measurement process. This nonlocality exists not only in the correlation between particles but also in the wave function of single particle. We still take the experiment of two-slit interference of electrons, for example. If the detector behind the slits has detected the signal and we can distinguish which slit the electrons pass, then the interference phenomenon will disappear. In language of quantum mechanics, the diffused wave function ψð Þ x; t of the electron will collapse into δð Þ x0; t immediately after this measurement. This process is very fast and does not seem to need to cost time. How this process happens and whether this process violates the law of causation of relativity theory are still unclear for us.

quantum mechanics. Moreover it also cannot answer how the nonlocality produces in quantum measurement process because, there is no seed for nonlocality growing no matter in

Stochastic Quantum Potential Noise and Quantum Measurement

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Many worlds interpretation was proposed by Hugh Everett in 1952. It supposes that there are a large, perhaps infinite, number of universes and every alternate state is in one of these universes [2, 3]. Many worlds interpretation denies the wave function collapse under quantum measurement. It asserts that the object that will be measured and the observer that will do the measurement are in a relative state. Each measurement will be a branch point and makes observer enter a universe. According to the thought of many worlds interpretation, the Schrödinger cat is alive in a universe and dead in the other universe. After the measurement,

The advantage of this interpretation is that the discussion of collapse mechanism is avoided. However, the basis-preferred problem is still the big issue in many worlds interpretation although the quantum decoherence had been introduced into in the period of "post-Everett". Some researchers still think the many worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved [4–6]. Using the decoherence to define the Everett branches will lead to an approximate specification of a preferred basis and contradicts

Many-minds interpretation is the extension of many worlds interpretation. It was proposed by Heinz-Dieter Zeh in 1970 to solve the "branch determining problem" and the puzzling concept of observers being in a superposition with themselves in many worlds interpretation [7–9]. The thought of this interpretation is when an observer measures a quantum system, then a state that is consistent with minds which produced by the observer brain, called mental states, will entangle with this quantum system. The mental state of the brain corresponding with this system is involving, and ultimately, only one mind is experienced, leading the others to branch off and become inaccessible. In this way, every sentient being is attributed with an infinity of minds, whose prevalence corresponds to the amplitude of the wave function. As an observer checks a measurement, the probability of realizing a specific measurement directly correlates to the number of minds they have where they see that

However, like the many worlds interpretation, the many-minds interpretation is still a local theory. Although the correlations of individual minds and objects could be the violation of Bell's inequality, the interactions between them that only take place are local, and only the separated events that are space-like separated could influence the minds of observers. Additionally, it tosses the basis-preferred problem to the mentality of observer and makes this

physical problem fall into an endless discussion of mental state of human.

classical physics or quantum mechanics.

the observer will enter one of these two universes.

with the "exact" definition of the Everett branches.

3.3. Many-minds interpretation

measurement.

3.2. Many worlds interpretation

The third problem is the basis-preferred problem. The basis-preferred problem refers to a quantum system that is measured which prefers to collapse to a set of eigenstates. For example, a spin system with an initial state j i ψ ⟩ ¼ aj i↑ ⟩ þ bj i↓ ⟩ can collapse into the state of the set f g j i ↑⟩ ; j i ↓⟩ , and it can also collapse into the state of the set 1= ffiffiffi 2 <sup>p</sup> ð Þ j i<sup>↑</sup> ⟩ <sup>þ</sup> j i<sup>↓</sup> ⟩ ; <sup>1</sup><sup>=</sup> ffiffiffi <sup>2</sup> � <sup>p</sup> ð Þg j i<sup>↑</sup> ⟩ � j i<sup>↓</sup> ⟩ , but under a certain measurement, this state prefers one of these sets. Why the state prefers some basis set under quantum measurement? Does it have awareness?

Without any exaggeration, quantum measurement is one the most interesting and fascinating topics in quantum theory. There are too many unsolved mysteries in quantum measurement, and these spur us to further understand the quantum measurement and find the answers.
