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arXiv:0907.3778 · Physical Review A

Security proof for cryptographic protocols based only on the monogamy of Bell’s inequality violations

Marcin Pawłowski

Published Sep 14, 2010• 145 citations
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Abstract

We show that monogamy of Bell's inequality violations, which is strictly weaker condition than the no-signaling principle is enough to prove security of quantum key distribution. We derive our results for a whole class of monogamy constraints and generalize our results to any theory that communicating parties may have access to. Some of these theories do not respect the no-signaling principle yet still allow for secure communication. This proves that no signaling is only a sufficient condition for the possibility of secure communication, but not the necessary one. We also present some new qualitative results concerning the security of existing quantum key distribution protocols.

DOI
10.1103/physreva.82.032313

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We show that monogamy of Bell's inequality violations, which is strictly weaker condition than the no-signaling principle is enough to prove security of quantum key distribution. We derive our results for a whole class of monogamy constraints and generalize our results to any theory that communicating parties may have access to. Some of these theories do not respect the no-signaling principle yet still allow for secure communication. This proves that no signaling is only a sufficient condition for the possibility of secure communication, but not the necessary one. We also present some new qualitative results concerning the security of existing quantum key distribution protocols.
We analyze a cryptographic protocol for generating a distributed secret key from correlations that violate a Bell inequality by a sufficient amount, and prove its security against eavesdroppers, constrained only by the assumption that any information accessible to them must be compatible with the non-signaling principle. The claim holds with respect to the state-of-the-art security definition used in cryptography, known as universally-composable security. The non-signaling assumption only refers to the statistics of measurement outcomes depending on the choices of measurements; hence security is independent of the internal workings of the devices - they do not even need to follow the laws of quantum theory. This is relevant for practice as a correct and complete modeling of realistic devices is generally impossible. The techniques developed are general and can be applied to other Bell inequality-based protocols. In particular, we provide a scheme for estimating Bell-inequality violations when the samples are not independent and identically distributed.
Standard quantum key distribution protocols are provably secure against eavesdropping attacks, if quantum theory is correct. It is theoretically interesting to know if we need to assume the validity of quantum theory to prove the security of quantum key distribution, or whether its security can be based on other physical principles. The question would also be of practical interest if quantum mechanics were ever to fail in some regime, because a scientifically and technologically advanced eavesdropper could perhaps use postquantum physics to extract information from quantum communications without necessarily causing the quantum state disturbances on which existing security proofs rely. Here we describe a key distribution scheme provably secure against general attacks by a postquantum eavesdropper limited only by the impossibility of superluminal signaling. Its security stems from violation of a Bell inequality.
The information causality principle (IC)(\mathcal{IC})(IC) was originally proposed as a promising means to understand the extent of quantum nonlocality without invoking the full mathematical formalism of quantum theory. Beyond the foundational significance, the problem of bounding nonlocal correlations by reasonable physical principles has meaningful practical consequences, particularly for device-independent (DI) cryptographic security. In this work, we advance in this direction, demonstrating that the IC\mathcal{IC}IC is enough to ensure DI security on quantum key distribution (QKD) protocols. Security is proven for a range of theoretically quantum-attainable parameters against individual attacks by a potentially postquantum eavesdropper. This result follows as a consequence of a strong form of monogamy of Bell's inequality violations, which we prove to be implied by the recently proposed multipartite formulation for IC\mathcal{IC}IC. Additionally, we demonstrate that the original bipartite formulation of IC\mathcal{IC}IC fails to imply monogamy relations, and hence, ensure security of DIQKD, thus stressing the necessity of the multipartite framework.
Most of the existing quantum key distribution protocols do not consider the fact that the source and measuring device cannot be trusted, which causes hidden danger, such as the side channel attack, resulting in unsafe quantum communication. Therefore, it is important to research quantum key distribution protocol under the conditions of non-trusted device. We show a quantum key distribution protocol from correlation that violates a Bell inequality under the condition that both the source and the measurement devices are untrusted. We analyze its security under minimal assumptions (the non-signaling principle). We take noises and detection efficiency of the user's (Alice and Bob) detectors into account when bounding the secret key rate. We achieve a lower detection efficiency threshold, to compare with Ref. [Phys. Rev. A 85, 010301, (2012)], which means in the case of low efficiency of the detector, the key distribution can also be successfully completed.
The phenomenon of monogamy of Bell inequality violations is interesting both from the fundamental perspective as well as in cryptographic applications such as the extraction of randomness and secret bits. In this article, we derive new and stronger monogamy relations for violations of Bell inequalities in general no-signaling theories. These relations are applicable to the class of binary output correlation inequalities known as XOR games, and to free unique games. In many instances of interest, we show that the derived relation provides a significant strengthening over previously known results. Our result connects, for the first time, the property of monogamy with that crucial part of the Bell expression that is necessary for revealing a contradiction with local realistic predictions, thus shifting the paradigm in the field of monogamy of correlations.