**6.1 Device independence QRNG (Di-QRNG)**

The very definition of randomness is fraught with problems of philosophical nature. We had earlier alluded to differences between pseudo-random number generators (PRNGs) realized through algorithmic techniques, true random number generators (TRNGs) of epistemic origins and quantum random generators (QRNGs) which is believed to ontological in nature. The task at hand is to certify that the device at hand is a genuine QRNG. The output of such a device should be certifiably random not only to the user but every possible user. The density matrix describing *N* perfectly random output of 0 or 1 with equal probability is described by completely mixed density matrix given in the computational basis by ^*<sup>ρ</sup>* <sup>¼</sup> <sup>1</sup> 2 . When this output is perfectly isolated from the environment is described by the product state:

$$
\hat{\rho} \bigotimes \hat{\rho}\_{\mathrm{E}} \tag{20}
$$

Where, *ρ*^*<sup>E</sup>* is the state of environment [2]. Since the nature of random sequences generated is of a physical origin, perfect and perfectly private randomness should be certifiable through quantum process. Therefore, nonlocal correlations witnessed by Bell's inequality violations could be employed to certify the QRNG. It stems from the fact that Bell tests on entangled sources generate perfectly random sequences under local measurements. The perfect randomness of local measurement outcomes attests to the fact that such measurements have been made on maximally entangled pure states. Maximally entangled states are subject to monogamy conditions [2] and hence cannot be entangled with environment. The correlations between measured outcomes are presented in terms of conditional probabilities as explained in the earlier sections. The catch however is that the demonstration of Bell's inequality violation should be loop-hole-free! The worst-case scenario for an unreliable QRNG is when the supplier of the device has packaged the device with pre-generated

random numbers. Such numbers would pass all tests of randomness but would hardly be private, since the supplier could have made copies of the same. The basic idea behind Quantum Mechanics certified randomness is that Bell's inequality violations can guarantee that the observed randomness is not pre-generated. Two conditions need to be fulfilled for demonstrating device independence and they are 1. The basis choice (a.k.a the measurement setting) in the two stations in Bell tests are independent of experimental devices and of any prior information of each of them as might be available and 2. The measurement outcomes of each station are independent of the measurement setting in the other station. The "Free-will" choice is an assumption that is ill-proven and anthropomorphic. In engineered system freewill is replaced by a source of intrinsic private randomness. This is rather curious because, the entire exercise that is undertaken for DI has to do with the certification of such sources. The second condition is however readily satisfied so long as the stations cannot communicate with each other (no signaling condition). This step could involve some public source of quantum random numbers. The initial seed could also be enlarged through the process of random number expansion see [random num exp] and references contained therein. The basic idea is that the numbers obtained through a Bell test are a source of certified randomness. It may be noted here that at least two devices are required to test for device independence.

In summary, DI-QRNGs [30, 31] use Bell inequality violations to certify the quantum state generated within the devices are pure entangled states. The purity of the quantum state ensures an absence of correlation not only between the devices at stations *A* and but also with the environment and observers. Under a local measurement of the sub-system of a pure entangled state generates a completely mixed states resulting in perfect randomness of the output as certified by some entropic measure. Bell certified randomness is of a quantum nature as classical devices always do not violate Bell inequalities. Many DI-QRNG proposals as well experimental realization by various types are available in the literature. We will not attempt any systematic review of the literature. Quantum random number generators which rely on non-locality testified by Bell tests are also called selftesting QRNGs [17], the main problem with such devices is that they are presently too slow.

#### **6.2 Device independence QKD (DI-QKD)**

The one-time pad is a provably secure method of encryption [32]. The principle behind one-time pad is extremely simple: To encrypt a message bitstring of *N* bits called the plain text, a random bitstring of the same size called the key is generated. Then a modular addition of the key and plain text is carried out to create a bitstring called the ciphertext. The ciphertext is then communicated through a public channel to the recipient with whom the key is shared through a secure means. A modular addition of the ciphertext with key by the recipient, yields the plain text or message. Finding the means of sharing the key between the sender and the recipient of the message is called the key distribution problem. Traditionally, a trusted courier was given this job. This of course is not a viable option for encrypting terabits of data per second in the modern context.

A QKD system is device that acts a trusted courier of key between two parties. The security of such systems by the rules of quantum mechanics. The carriers of information are photons derived from a weak coherent source (attenuated laser pulses) of entangled photon sources. The quantum state of a single photon cannot be copied perfectly (No-cloning theorem) and a quantum state will be disturbed by the act of observation due to the Heisenberg Uncertainty principle. These quantum features of photons are exploited to ensure provable security of the key that is

### *Device Independence and the Quest towards Physical Limits of Privacy DOI: http://dx.doi.org/10.5772/intechopen.100364*

exchanged between two parties. Typically, the sender prepares the photons by choosing randomly different bases for measurement and communicates each photon in one or the other eigenstates of the bases. The eigenstate is again chosen randomly. Usually, the sender uses a QRNG for this purpose. Likewise, the receiver chooses to measure the photon in one or the other basis. After exchanging a large number of photons, the basis choice made by both parties are compared and only those cases where the choice is the same, the corresponding measured outcomes are retained. Under ideal circumstances, this process would result in a privately shared keys that are identical. Practical Quantum Key distributions whether implemented on optical fibers or free-space are however inherently noisy because of photonic losses, and changes in the state during transmission. Such devices also use sources of single, heralded or entangled photons that are not perfect and detectors that usually have efficiencies below the requisite efficiency of 83%. These devices also use a variety of commercial components that are prone to side-channel attacks and are not the ideal ones used in a theory. Thus, the claim of provable security does not apply for practical systems. This makes QKD devices vulnerable to a variety of sidechannel attacks. Thus, the raw keys obtained through the quantum channel have to subjected a series of post-processing steps for the generation of the final keys. Since most of side-channel attacks were on the detector side, measurement device independent QKDs were proposed and implement. The final frontier of physical limits of privacy can be guaranteed only by device independent QKD systems. As in DI-QRNGs, DIQKD [33–35] also necessitate the performance of Bell tests between two distant parties. Bell test typically use the Clauser-Horne-Shimony-Holt (CHSH) variant of Bell tests, which employs maximally entangled states. The rate of key generation, distance of transmission and security assurance levels are all interrelated in practical systems. Usually when low efficiency detectors are employed and significant line losses occur, fair sampling is implicitly assumed. In DI-QKD or measurement device independent MDI-QKD [36–38], the measuring device is with the quantum hacker Eve and fair-sampling arguments are no longer valid. Security of DI-QKD depend on the monogamy of shared correlations between maximally entangled photonic states. As in the case of DI-QRNG, device independence accrues through the conduct of loop-hole-free Bell tests. Mayers and Yao [33] proposed an early version of DI-QKD dealing with specific case of imperfect sources. In this pioneering work, they proposed that the security of a QKD protocol may be tested using entanglement-based protocols. Jonathan Barrett, Lucien Hardy, and Adrian Kent showed that single shared bit with guaranteed security can be exchanged though the use Bell tests. Since these early results a variety of proposal and proof of concept implementations have been published in the literature. As in the case of QRNGs, DI-QKD systems are extremely difficult to implement because, the ultimate guarantee of physically assured privacy relies on the performance of loop-hole free Bell tests.
