**Abstract**

There is a looming threat over current methods of data encryption through advances in quantum computation. Interestingly, this potential threat can be countered through the use of quantum resources such as coherent superposition, entanglement and inherent randomness. These, together with non-clonability of arbitrary quantum states, offer provably secure means of sharing encryption keys between two parties. This physically assured privacy is however provably secure only in theory but not in practice. Device independent approaches seek to provide physically assured privacy of devices of untrusted origin. The quest towards realization of such devices is predicated on conducting loop-hole-free Bell tests which require the use of certified quantum random number generators. The experimental apparatuses for conducting such tests themselves use non-ideal sources, detectors and optical components making such certification extremely difficult. This expository chapter presents a brief overview (not a review) of Device Independence and the conceptual and practical difficulties it entails.

**Keywords:** QRNG, QKD, device independence, loop-hole-free Bell tests, nonlocality

### **1. Introduction**

The advent of quantum technologies holds the promise of novel innovations in computing, communication and sensing. Quintessential quantum properties such as superposition and entanglement are perceived as essential resources for the realization of these technologies. Quantum states allow for non-local correlations under no-signaling conditions [1, 2]. Claims to "quantum supremacy" in quantum computing or provable security in quantum cryptography hinges on the assertion that quantum resources are not only needed, but can be gainfully employed for realizing functionalities, which classical resources cannot supply. Quantum cryptography or rather quantum key distribution (QKD) schemes are claimed to be provably secure based on the quantum nature of the carriers of information. The claim on information security relies on the fact, that perfect copies of arbitrary quantum states cannot be made (the "no-cloning" theorem) [3] and the fact that measurements disturb the state of the system in an irreversible fashion, resulting in perfectly random outcomes. In quantum key distribution protocols such as the Ekert's [4], non-local correlations between a pair of entangled photons are utilized to realize

secure key exchange between two parties in space-like separated regions. One of the key components of a QKD device is a quantum random number generator (QRNG) [5–7]. These devices are believed to generate perfect and inherently random sequences that cannot be produced by any device based on classical phenomena or by using mathematical algorithms however complex they might be. High-speed QRNGs are an important requirement not only for QKD but have potential uses in gambling, commerce, and classical cryptography. Given the importance of this device for cryptography, one should test this device before using it. When a consumer buys a piece of quantum-enabled equipment such as QKD boxes or QRNGs, there is a need to find out whether it is the "real McCoy" and the hardware performs as advertised. For instances, the QRNG, sourced through an untrusted party may generate a seemingly random sequences on demand, but it begs the question, whether these sequences arise from a genuine quantum process and have not been generated through some classical or algorithmic means? Alternately, the supplier of the device could have generated a very large sequence through a quantum process and stored it in the device while retaining copy for herself. Even without assuming any evil intent on part of the supplier, the device could also be unreliable because of imperfections in the source or detectors or even due the noise being well-above permissible thresholds. Standard statistical tests for randomness such as DIEHARD and DIEHARDER provided by NIST, USA [8, 9] are not the solution to this problem. Statistical tests for randomness merely certify the absence of certain patterns in the sequences within the bounds of finite computational power at the disposal of the of the user. It would be logical fallacy to think that absence of evidence is evidence of absence. Statistical tests are therefore not tests of genuine quantum randomness and most certainly do not provide any assurance regarding the privacy of the data that is generated. For the QRNG to satisfy its claimed performance not only should the output of the device be perfectly random to the user, but to any observer including the supplier of device. Then, and only then, could a "QRNG" be deemed to be a Perfect and Private Random Number generator or PPRNG as we shall call it henceforth. The advantages of quantum resources for secure communications or random number generation are a theoretical fact but, demonstrating that a piece of hardware actually exploits quantum properties of matter and fields in an effective manner is a non-trivial problem. The issue at hand is an important one because, it is related to very reliability of the quantum device itself. Extraordinary, though it seems, it is possible that a certain class of QRNGs and QKDs of illicit and unknown provenance, could be certified to be provably secure through the performance of certain class of tests called Bell tests performed on them [10–13]. Such Bell test certified devices are however extremely difficult to realize and currently the rates of random number generation with them are extremely small. Before we get into issues of device independence, we first examine some aspects of randomness, non-locality and non-local correlations.

## **2. Randomness, nonlocality and non-local correlations**

The Famous paper by Einstein, Podolsky and Rosen in Physical Review (1935) [14] was a watershed event setting-off a vigorous debate on the so-called hidden variable theories. Their central conclusion was that quantum mechanical description of physical systems is incomplete and that, quantum mechanical rules must be supplemented with additional variables to exorcize the seemingly inherent randomness of nature. Bohr rebuts these arguments in Physical Review [15] claiming that quantum mechanics deals with the statistical outcomes of the

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

interactions of a microscopic system with a macroscopic classical apparatus and nothing further. In physical theories, classical or quantum, every system is associated with a mathematical description of it called the state. Given the state of a system at a certain instant of time, the time evolution of the system is described by Newton's laws of motion in classical mechanics and the Schrödinger equation in quantum mechanics respectively. Both these equations are perfectly deterministic and reversible in time. The time evolution of quantum states is described is unitary. In classical systems, randomness arises primarily due to inadequate information about the initial conditions especially when the degrees of freedom are extremely large. Quite often, we may also choose to ignore vast amounts of data simply because we do not have the computational resources to handle it. This sort of coarse graining of data becomes a practical expediency. The solution to handling fullblown turbulence by solving the Navier–Stokes equation would come to mind. In systems exhibiting classical chaos [16], even though the underlying equation of motion are deterministic, the apparent randomness and unpredictability arises because of sensitivity to initial conditions and the finite precision with which the initial conditions are supplied. In summary, classical randomness arises from ignorance or computational limitations and is therefore not an inherent property of nature. Such randomness is deemed to be epistemological in character. In quantum mechanics, while evolution itself is unitary, the outcomes of measurements performed on the quantum state are probabilistic. The expectation value of physical properties associated with observable *A*^ for an ensemble of measurements is given by the Born rule ⟨*A*^⟩ = Tr ^*ρA*^ *:* Given an ensemble of measurements *<sup>M</sup>* performed on identically prepared states, the probability of the *j*th outcome over a set of possible outcomes {Ei} is given by *p <sup>j</sup>* j*M* <sup>¼</sup> *Tr* ^*ρEj* ½ � <sup>2</sup> *:* The Born rule thus provides us the leeway that links the abstract quantum state with observed phenomena. The outcome of single observation measurement is believed to be completely and inherently unpredictable and is an essential aspect of nature herself. Quantum mechanics does not offer any clue as to the physical origins of the observed randomness of outcomes. The implicit assumption is that the God of all things does play dice and is indeed an inveterate and compulsive gambler. Quantum randomness is therefore said to be inherent or ontological (ontic) randomness. It would be wise to bear in mind that there is no finality to any of these assertions. They are provisional to way we understand nature as of now. It is in this context; we should make a distinction between ontic and epistemic randomness; Ontic randomness is intrinsically associated with observable quantities of the system and related to selfadjoint operators. One or the other of the possible eigenvalues of these operators are manifest upon an observation. No à priori value can be associated with properties of the system. It is in this sense that one asserts that "quantum phenomena" are not realistic. Robust average values can however be assigned to average or expectation values of observables, which is what the Born formula helps us compute. Quantum mechanics is then an ensemble theory which provides us with recipe to calculate averages of repeated measurements made on the system. There is rich literature regarding the nature quantum state, the wavefunction itself. There are interpretations of quantum mechanics that significantly differ in their viewpoint. Since our purpose here is not to get deeply mired into foundations of quantum mechanics, we shall desist from such digressions, given the limited ambitions of this chapter.

It is a something of a fundamental theorem that purely local operations performed on single device, cannot be used to establish that the random sequences emitted by a given device has not been simulated using only classical resources. However, Bell tests provide the unimpeachable means of certifying these devices.

Such a QRNG is dubbed Device Independent QRNG or DI-QRNG for short [17–22]. The interesting thing here is that such Quantum Random number generators can be certified, without any knowledge of the inner workings of the device. It is therefore solely through non-local correlations present in quantum states that such a certification becomes feasible. Device Independent QRNG that meets the requirements of the output being perfectly unpredictable to anyone and meets the stringent norm absolute privacy. For the case of QKDs, the successful performance of loop-holefree Bell tests, provides the information theoretical assurance that QKD supplies perfectly random keys to which only the authenticated parties are privy but no one else is.
