Unconditional security proofs of the Bennett-Brassard protocol of quantum key distribution have been obtained recently. These proofs cover also practical implementations that utilize weak coherent pulses in the four signal polarizations. Proven secure rates leave open the possibility that new proofs or new public discussion protocols obtain larger rates over increased distance. In this paper we investigate limits to error rate and signal losses that can be tolerated by future protocols and proofs.
We discuss long code problems in the Bennett-Brassard 1984 (BB84) quantum key distribution protocol and describe how they can be overcome by concatenation of the protocol. Observing that concatenated modified Lo-Chau protocol finally reduces to the concatenated BB84 protocol, we give the unconditional security of the concatenated BB84 protocol.
We propose a new kind of individual attack, based on randomly selected dissipation, on Bennett-Brassard 1984 protocol of practical quantum key distribution (QKD) system with lossy and noisy quantum channel. Since an adversary with super quantum channel can disguise loss and errors induced by his attack as that of the system, he can obtain innegligible amount of information for a practical QKD system, without being detected by legal participants.
This paper provides a formula for the sacrifice bit-length for privacy amplification with the Bennett-Brassard 1984 protocol for finite key lengths when we employ the decoy method. Using the formula, we can guarantee the security parameter for realizable quantum key distribution system. The key generation rates with finite key lengths are numerically evaluated. The proposed method improves the existing key generation rate even in the asymptotic setting.
The quantum key distribution protocol without public announcement of bases is equipped with a two-way classical communication symmetric entanglement purification protocol. This modified key distribution protocol is unconditionally secure and has a higher tolerable error rate of 20%, which is higher than previous scheme without public announcement of bases.
We calculate eavesdropper's optimal information on raw bits in Bennett-Brassard 1984 quantum key distribution (BB84 QKD) and six-state scheme in coherent attacks, using a formula by Lo and Chau [Science 283 (1999) 2050] with single photon assumption. We find that eavesdropper's optimal information in QKD without public announcement of bases [Phys. Lett. A 244 (1998) 489] is the same as that of a corresponding QKD WITH it in the coherent attack. We observe a sum-rule concerning each party's information.
We present a tight security analysis of the Bennett-Brassard 1984 protocol taking into account the finite size effect of key distillation, and achieving unconditional security. We begin by presenting a concise analysis utilizing the normal approximation of the hypergeometric function. Then next we show that a similarly tight bound can also be obtained by a rigorous argument without relying on any approximation. In particular, for the convenience of experimentalists who wish to evaluate the security of their QKD systems, we also give explicit procedures of our key distillation, and also show ho…
A central goal in information theory and cryptography is finding simple characterizations of optimal communication rates subject to various restrictions and security requirements. Ideally, the optimal key rate for a quantum key distribution (QKD) protocol would be given by {\em single-letter formula} involving a simple optimization over a single use of an effective channel. We explore the possibility of such a formula for one of the simplest and most widely used QKD protocols--Bennett-Brassard-84 (BB84) with one way classical post-processing. We show that a conjectured single-letter key-rate f…
Bennet-Brassard 1984 (BB84) protocol, we optimize the ratio of the choice of two bases, the bit basis and the phase basis by using the second order expansion for the length of the generation keys under the coherent attack. This optimization addresses the trade-off between the loss of transmitted bits due to the disagreement of their bases and the estimation error of the error rate in the phase basis. Then, we derive the optimum ratio and the optimum length of the generation keys with the second order asymptotics. Surprisingly, the second order has the order $n^{3/4}$, which is much larger than…
Most experimental realizations of quantum key distribution are based on the Bennett-Brassard 1984 (so-called BB84) protocol. In a typical optical implementation of this scheme, the sender uses an active source to produce the required BB84 signal states. While active state preparation of BB84 signals is a simple and elegant solution in principle, in practice passive state preparation might be desirable in some scenarios, for instance, in those experimental setups operating at high transmission rates. Passive schemes might also be more robust against side-channel attacks than active sources. Typ…
In practical quantum cryptography, the source sometimes produces multi-photon pulses, thus enabling the eavesdropper Eve to perform the powerful photon-number-splitting (PNS) attack. Recently, it was shown by Curty and Lutkenhaus [Phys. Rev. A 69, 042321 (2004)] that the PNS attack is not always the optimal attack when two photons are present: if errors are present in the correlations Alice-Bob and if Eve cannot modify Bob's detection efficiency, Eve gains a larger amount of information using another attack based on a 2->3 cloning machine. In this work, we extend this analysis to all distances…
It is the first scheme which allows the detection apparatus to achieve both the photon number of arriving signals and quantum bit error rate of the multiphoton pulses precisely. We show that the upper bound of the fraction of the tagged multiphoton pulses counts is $μ$, which is independent of the channel loss and the intensity of the decoy source. Such upper bound is $inherent$ and cannot be reduced any longer as long as the weak coherent scouces and high lossy channel are used. We show that our scheme can be implemented even if the channel loss is very high. A stronger intensity of the pulse…
Hong-Ou-Mandel test to verify indistinguishability of the states emitted from a quantum key distribution transmitter implementing decoy Bennett-Brassard 1984 protocol
We compare the performance of various quantum key distribution (QKD) systems using a novel single-photon detector, which combines frequency up-conversion in a periodically poled lithium niobate (PPLN) waveguide and a silicon avalanche photodiode (APD). The comparison is based on the secure communication rate as a function of distance for three QKD protocols: the Bennett-Brassard 1984 (BB84), the Bennett, Brassard, and Mermin 1992 (BBM92), and the coherent differential phase shift keying (DPSK). We show that the up-conversion detector allows for higher communication rates and longer communicati…
We investigate the security against the intercept/resend and translucent attacks on the quantum key distribution protocol based on the pre- and post-selection effect. In 2001, Bub proposed the quantum cryptography scheme, which was an application of the so-called mean king's problem. We evaluate a probability that legitimate users cannot detect eavesdropper's malicious acts for Bub's protocol. We also estimate a probability that the eavesdropper guesses right at the random secret key one of the legitimate users tries to share with the other one. From rigorous mathematical and numerical analyse…
We investigate a new strategy for incoherent eavesdropping in Ekert's entanglement based quantum key distribution protocol. We show that under certain assumptions of symmetry the effectiveness of this strategy reduces to that of the original single qubit protocol of Bennett and Brassard.
Cryptographic scheme proposed by Bennett, Brassard, and Mermin [Phys. Rev. Lett. {\bf 68}, 557 (1992)] is reformulated in a version involving two polarizing Mach-Zehnder interferometers. Such a form, although physically equivalent to the original one, makes its security explicit, suggestive and easy to explain to non-experts.
We constructed an optical interferometer for a Bennett-Brassard quantum key distribution system using integrated optics based on planar lightwave circuit technology, and tested its operation and stability. Experimental results show that this interferometer is useful in implementing a practical quantum key distribution system.
We discuss the potential of quantum key distribution (QKD) for long distance communication by proposing a new analysis of the errors caused by dark counts. We give sufficient conditions for a considerable improvement of the key generation rates and the security thresholds of well-known QKD protocols such as Bennett-Brassard 1984, Phoenix-Barnett-Chefles 2000, and the six-state protocol. This analysis is applicable to other QKD protocols like Bennett 1992. We examine two scenarios: a sender using a perfect single-photon source and a sender using a Poissonian source.
We study the role of discrete rotational symmetry in quantum key distribution by generalizing the well-known Bennett-Brassard 1984 (BB84) and Scarani-Acin-Ribordy-Gisin 2004 (SARG04) protocols. We observe that discrete rotational symmetry results in the protocol's invariance to continuous rotations, thus leading to a simplified relation between bit and phase error rates and consequently a straightforward security proof.
We consider the security of the Bennett-Brassard 1984 (BB84) protocol for Quantum Key Distribution (QKD), with arbitrary individual imperfections simultaneously in the source and detectors. We provide the secure key generation rate, and show that only two parameters must be bounded to ensure security; the basis dependence of the source and a detector blinding parameter. The system may otherwise be completely uncharacterized and contain large losses.
Quantum Key Distribution (QKD) with classical Bob has recently been suggested and proven robust. Following this work, QKD with classical Alice was also suggested and proven robust. The above protocols are ideal in the sense that they make use of qubits. However, in the past, well-known QKD protocols that were proven robust and even proven unconditionally secure, when qubits are used, were found to be totally insecure when photons are used. This is due to sensitivity to photon losses (e.g., Bennett's two-state protocol) or sensitivity to losses combined with multi-photon states (e.g., the photo…
This paper provides a security proof of the Bennett-Brassard (BB84) quantum key distribution protocol in practical implementation. To prove the security, it is not assumed that defects in the devices are absorbed into an adversary's attack. In fact, the only assumption in the proof is that the source is characterized. The proof is performed by lower-bounding adversary's Renyi entropy about the key before privacy amplification. The bound reveals the leading factors reducing the key generation rate.
We analyse the finite-size security of the efficient Bennett-Brassard 1984 protocol implemented with decoy states and apply the results to a gigahertz-clocked quantum key distribution system. Despite the enhanced security level, the obtained secure key rates are the highest reported so far at all fibre distances.
In conventional quantum key distribution protocols, the secure key is normally extracted from the measurement outcomes of the system. Here, a different approach is proposed, where the secure key is extracted from the measurement bases, rather than outcomes. Compared to the original Bennett-Brassard-1984 protocol, the proposed protocol involves no hardware change but modifications in data postprocessing. We show that this protocol is more robust against detector efficiency attacks and photon-number-splitting attacks when practical detectors and photon sources are used.
We present an approach to the unconditional security of quantum key distribution protocols based on the uncertainty principle. The approach applies to every case that has been treated via the argument by Shor and Preskill, and relieve them from the constraints of finding quantum error correcting codes. It can also treat the cases with uncharacterized apparatuses. We derive a secure key rate for the Bennett-Brassard-1984 protocol with an arbitrary source characterized only by a single parameter representing the basis dependence.
In this work we present a security analysis for quantum key distribution, establishing a rigorous tradeoff between various protocol and security parameters for a class of entanglement-based and prepare-and-measure protocols. The goal of this paper is twofold: 1) to review and clarify the state-of-the-art security analysis based on entropic uncertainty relations, and 2) to provide an accessible resource for researchers interested in a security analysis of quantum cryptographic protocols that takes into account finite resource effects. For this purpose we collect and clarify several arguments sp…
We discuss the `no-clicking' event, which is harmful for legitimate users in Bennett-Brassard 1984 quantum key distribution: We describe an attack where no-clicking events are utilized in the same way as double-clicking events are utilized in the quantum Trojan-pony attack. We discuss how to deal with the no-clicking events. We discuss how to estimate the security of the protocol against the proposed attack by using a formula involved with the fraction of adversarial removals of events.
We consider the security of the Bennett-Brassard 1984 (BB84) protocol for Quantum Key Distribution (QKD), in the presence of bit and basis dependent detector flaws. We suggest a powerful attack that can be used in systems with detector efficiency mismatch, even if the detector assignments are chosen randomly by Bob. A security proof is provided, valid for any basis dependent, possibly lossy, linear optical imperfections in the channel/receiver/detectors. The proof does not assume the so-called squashing detector model.
We prove the unconditional security of quantum key distribution protocols using attenuated laser pulses with M different linear polarizations. When M=4, the proof covers the so-called SARG04 protocol [V.~Scarani et al., Phys. Rev.\ Lett. {\bf 92}, 057901 (2004)], which uses exactly the same quantum communication as the Bennett-Brassard 1984 protocol. For a channel with transmission $η$, we show that the key rate in SARG04 scales as $O(η^{3/2})$. When we increase the number of states to M=2k-1 or 2k, the key rate scaling improves as $O(η^{(k+1)/k})$.
A design is given for an optimized entangling probe attacking the BB84 (Bennett-Brassard 1984) protocol of quantum key distribution and yielding maximum information to the probe for a full range of induced error rates. Probe photon polarization states become optimally entangled with the signal states on their way between the legitimate transmitter and receiver. Although standard von-Neumann projective measurements of the probe yield maximum information on the pre-privacy amplified key, if instead the probe measurements are performed with a certain positive operator valued measure, then the mea…
In this article I present a protocol for quantum cryptography which is secure against attacks on individual signals. It is based on the Bennett-Brassard protocol of 1984 (BB84). The security proof is complete as far as the use of single photons as signal states is concerned. Emphasis is given to the practicability of the resulting protocol. For each run of the quantum key distribution the security statement gives the probability of a successful key generation and the probability for an eavesdropper's knowledge, measured as change in Shannon entropy, to be below a specified maximal value.
Quantum key distribution can be performed with practical signal sources such as weak coherent pulses. One example of such a scheme is the Bennett-Brassard protocol that can be implemented via polarization of the signals, or equivalent signals. It turns out that the most powerful tool at the disposition of an eavesdropper is the photon-number splitting attack. We show that this attack can be extended in the relevant parameter regime such as to preserve the Poissonian photon number distribution of the combination of the signal source and the lossy channel.
The Fuchs-Peres-Brandt (FPB) probe realizes the most powerful individual attack on Bennett-Brassard 1984 quantum key distribution (BB84 QKD) by means of a single controlled-NOT (CNOT) gate. This paper describes a complete physical simulation of the FPB-probe attack on polarization-based BB84 QKD using a deterministic CNOT constructed from single-photon two-qubit quantum logic. Adding polarization-preserving quantum nondemolition measurements of photon number to this configuration converts the physical simulation into a true deterministic realization of the FPB attack.
We present and analyze a quantum key distribution protocol based on sending entangled N-qubit states instead of single-qubit ones as in the trail-blazing scheme by Bennett and Brassard (BB84). Since the qubits are sent individually, an eavesdropper is limited to accessing them one by one. In an intercept-resend attack, this fundamental restriction allows one to make the eavesdropper's information on the transmitted key vanish if even one of the qubits is not intercepted. The implied upper bound 1/(2N) for Eve's information is further shown not to be the lowest since in the case N = 2, the info…
This note presents a method of public key distribution using quantum communication of n photons that simultaneously provides a high probability that the bits have not been tampered. It is a three-state variant of the quantum method of Bennett and Brassard (BB84) where the transmission states have been decreased from 4 to 3 and the detector states have been increased from 2 to 3. Under certain assumptions regarding method of attack, it provides superior performance (in terms of the number of usable key bits) for n < 18 m, where m is the number of key bits used to verify the integrity of the pro…
We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution. We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof of security for a similar protocol. We then show that the security of this protocol implies the security of BB84. The entanglement-purification based protocol uses Calderbank-Shor-Steane (CSS) codes, and properties of these codes are used to remove the use of quantum computation from the Lo-Chau protocol.
In the postprocessing of quantum key distribution, the raw key bits from the mismatched-basis measurements, where two parties use different bases, are normally discarded. Here, we propose a postprocessing method that exploits measurement statistics from mismatched-basis cases, and prove that incorporating these statistics enables uncharacterized qubit sources to be used in the measurement-device-independent quantum key distribution protocol and the Bennett-Brassard 1984 protocol, a case which is otherwise impossible.
We provide a complete proof of the security of quantum cryptography against any eavesdropping attack including coherent measurements even in the presence of noise. Polarization-based cryptographic schemes are shown to be equivalent to EPR-based schemes. We also show that the performance of a noisy channel approaches that of a noiseless one as the error rate tends to zero. (i.e., the secrecy capacity $C_s (ε) \to C_s (0)$ as $ε\to 0$.) One implication of our results is that one can {\it double} the efficiency of a most well-known quantum cryptographic scheme proposed by Bennett and Brassard sim…
Quantum key distribution using three states in equiangular configuration combines a security threshold comparable with the one of the Bennett-Brassard 1984 protocol and a quantum bit error rate (QBER) estimation that does not need to reveal part of the key. We implement an entanglement-based version of the Renes 2004 protocol, using only passive optic elements in a linear scheme for the measurement POVM, generating an asymptotic secure key rate of more than 10 kbit/s, with a mean QBER of 1.6%. We then demonstrate its security in the case of finite key and evaluate the key rate for both collect…
We examine a situation that $n$ eavesdroppers attack the Bennett-Brassard cryptographic protocol via their own optimal and symmetric strategies. Information gain and mutual information with sender for each eavesdropper are explicitly derived. The receiver's error rate for the case of arbitrary $n$ eavesdroppers can be derived using a recursive relation. Although first eavesdropper can get mutual information without disturbance arising due to other eavesdroppers, subsequent eavesdropping generally increases the receiver's error rate. Other eavesdroppers cannot gain information on the input sign…
We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol for an arbitrary source whose averaged states are basis-independent, a condition that is automatically satisfied if the source is suitably designed. The proof is based on the observation that, to an adversary, the key extraction process is equivalent to a measurement in the sigma_x-basis performed on a pure sigma_z-basis eigenstate. The dependence of the achievable key length on the bit error rate is the same as that established by Shor and Preskill for a perfect source, indicating that the defects in the so…
We propose a decoy-state method to overcome the photon-number-splitting attack for Bennett-Brassard 1984 quantum key distribution protocol in the presence of high loss: A legitimate user intentionally and randomly replaces signal pulses by multi-photon pulses (decoy-states). Then they check the loss of the decoy-states. If the loss of the decoy-states is abnormally less than that of signal pulses, the whole protocol is aborted. Otherwise, to continue the protocol, they estimate loss of signal multi-photon pulses based on that of decoy-states. This estimation can be done with an assumption that…
In the cryptographic context, an earlier unexplored application of the temporal version of the Bell-type inequality is shown here in the device-independent (DI) scenario. This is done by using the Leggett-Garg inequality (LGI) to demonstrate the security against eavesdropping in a quantum key distribution (QKD) scheme. This typically involves a higher dimensional attack against which the standard BB84 protocol is insecure. For this purpose, we invoke an appropriate form of LGI. While the key generation is done by the usual Bennett-Brassard 1984 (BB84) method, the security check against device …
This paper is withdrawn. We study the quantum key distribution (QKD) protocol based on a quantum retrodiction protocol, namely the so-called mean king problem. The security is analyzed by considering the eavesdropping on both the preparation of the entangled pair and the transmission of the quantum state. This QKD protocol can generate efficiently a bit of raw key in every single run. We find that, for qubit system, it is more secure than the QKD Bennett-Brassard 1984 protocol and the six-state protocol. This QKD protocol works also for higher dimensional system.
We derive a bound for the security of QKD with finite resources under one-way post-processing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective attacks, unconditional security follows immediately for standard protocols like Bennett-Brassard 1984 and six-states. For single-qubit implementations of such protocols, we find that the secret key rate becomes positive when at least N\sim 10^5 signals are exchanged and processed. For any other discrete-variable protocol, unconditional security can be obtained us…
Now that fundamental quantum principles of indeterminacy and measurement have become the basis of new technologies that provide secrecy between two communicating parties, there is a need to provide teaching laboratories that illustrate how these technologies work. In this article we describe a laboratory exercise in which students perform quantum key distribution with single photons, and see how the secrecy of the communication is ensured by the principles of quantum superposition and state projection. We used a table-top apparatus, similar to those used in correlated-photon undergraduate labo…
We propose an information-theoretically secure encryption scheme for classical messages with quantum ciphertexts that offers detection of eavesdropping attacks, and re-usability of the key in case no eavesdropping took place: the entire key can be securely re-used for encrypting new messages as long as no attack is detected. This is known to be impossible for fully classical schemes, where there is no way to detect plain eavesdropping attacks. This particular application of quantum techniques to cryptography was originally proposed by Bennett, Brassard and Breidbart in 1982, even before propos…
The lists of bits processed in quantum key distribution are necessarily of finite length. The need for finite-key unconditional security bounds has been recognized long ago, but the theoretical tools have become available only very recently. We provide finite-key unconditional security bounds for two practical implementations of the Bennett-Brassard 1984 coding: prepare-and-measure implementations without decoy states, and entanglement-based implementations. A finite-key bound for prepare-and-measure implementations with decoy states is also derived under a simplified treatment of the statisti…
We present security proofs for a protocol for Quantum Key Distribution (QKD) based on encoding in finite high-dimensional Hilbert spaces. This protocol is an extension of Bennett's and Brassard's basic protocol from two bases, two state encoding to a multi bases, multi state encoding. We analyze the mutual information between the legitimate parties and the eavesdropper, and the error rate, as function of the dimension of the Hilbert space, while considering optimal incoherent and coherent eavesdropping attacks. We obtain the upper limit for the legitimate party error rate to ensure uncondition…
We discuss the Bennett-Brassard 1984 (BB84) quantum key distribution protocol in the light of quantum algorithmic information. While Shannon's information theory needs a probability to define a notion of information, algorithmic information theory does not need it and can assign a notion of information to an individual object. The program length necessary to describe an object, Kolmogorov complexity, plays the most fundamental role in the theory. In the context of algorithmic information theory, we formulate a security criterion for the quantum key distribution by using the quantum Kolmogorov …
In the original BB84 protocol by Bennett and Brassard, an eavesdropper is detected because his attempts to intercept information result in a quantum bit error rate (QBER) of at least 25%. Here we design an alternative quantum key distribution protocol, where Alice and Bob use two mutually unbiased bases with one of them encoding a "0" and the other one encoding a "1." The security of the scheme is due to a minimum index transmission error rate (ITER) introduced by an eavesdropper which increases significantly for higher-dimensional photon states. This allows for more noise in the transmission …
We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the source and detector are under the limited control of an adversary. Our proof applies when both the source and the detector have small basis-dependent flaws, as is typical in practical implementations of the protocol. We derive a general lower bound on the asymptotic key generation rate for weakly basis-dependent eavesdropping attacks, and also estimate the rate in some special cases: sources that emit weak coherent states with random phases, detectors with basis-dependent efficiency, an…
We propose the use of intra-particle entanglement to enhance the security of a practical implementation of the Bennett-Brassard-1984 (BB84) quantum key distribution scheme. Intra-particle entanglement is an attractive resource since it can be easily generated using only linear optics. Security is studied under a simple model of incoherent attack for protocols involving two or all five mutually unbiased bases. In terms of efficiency of secret key generation and tolerable error rate, the latter is found to be superior to the former. We find that states that allow secrecy distillation are necessa…
Phase randomization is a very important assumption in the Bennett-Brassard 1984 quantum key distribution (QKD) system with a weak coherent source. Thus an active phase modulator is needed to randomize the phase of source. However, it is hard to check whether the phase of source is randomized totally or not in practical QKD systems. In this paper a partially random phase attack is proposed to exploit this imperfection. Our analysis shows that Eve can break the security of a two-way QKD system by using our attack, even if an active phase randomization is adopted by Alice. Furthermore, the numeri…
We show how single system steering can be exhibited by classical light, a feature originating from superposition in classical optics that also enables entanglement and Bell-violation by classical light beams. Single system steering is the temporal analogue of Einstein-Podolsky-Rosen (EPR) steering in the quantum domain, enabling control of the state of a remote system, and can hence be connected to the security of secret key generation between two remote parties. We derive the steering criterion for a single mode coherent state when displaced parity measurements are performed at two different …
Single photon sources (SPS) are a fundamental building block for optical implementations of quantum information protocols. Among SPSs, multiple crystal heralded single photon sources seem to give the best compromise between high pair production rate and low multiple photon events. In this work, we study their performance in a practical quantum key distribution experiment, by evaluating the achievable key rates. The analysis focuses on the two different schemes, symmetric and asymmetric, proposed for the practical implementation of heralded single photon sources, with attention on the performan…
Temporal steering, which is a temporal analogue of Einstein-Podolsky-Rosen steering, refers to temporal quantum correlations between the initial and final state of a quantum system. Our analysis of temporal steering inequalities in relation to the average quantum bit error rates reveals the interplay between temporal steering and quantum cloning, which guarantees the security of quantum key-distribution based on mutually-unbiased bases against individual attacks. The key distributions analyzed here include the Bennett-Brassard 1984 protocol (BB84) and the six-state 1998 protocol by Bruss (B98)…
An attack on the ``Bennett-Brassard 84''(BB84) quantum key-exchange protocol in which Eve exploits the action of gravitation to infer information about the quantum-mechanical state of the qubit exchanged between Alice and Bob, is described. It is demonstrated that the known laws of physics do not allow to describe the attack. Without making assumptions that are not based on broad consensus, the laws of quantum gravity, unknown up to now, would be needed even for an approximate treatment. Therefore, it is currently not possible to predict with any confidence if information gained in this attack…
Despite enormous progress both in theoretical and experimental quantum cryptography, the security of most current implementations of quantum key distribution is still not established rigorously. One of the main problems is that the security of the final key is highly dependent on the number, M, of signals exchanged between the legitimate parties. While, in any practical implementation, M is limited by the available resources, existing security proofs are often only valid asymptotically for unrealistically large values of M. Here, we demonstrate that this gap between theory and practice can be …
We show that (1) the violation of the Ekert 91 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 92 (BBM) inequality is, also, a sufficient condition for certification of the KS theorem. Therefore the success in each QKD protocol reveals the nonclassical feature of quantum theory, in the sense that the KS realism is violated. Further, it turned out that the Ekert inequality and the BBM inequality are depictured by distillable entanglement witness inequalities. Here, we connect the success in these two…
