A monogamy-of-entanglement game with applications to device-independent quantum cryptography

The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes of incompatible measurements on one physical system, and a second reference system. We provide a more stringent formulation of both the uncertainty principle and the information exclusion principle, with direct applications for, e.g., the security analysis of quantum key distribution, entanglement estimation, and quantum communication. We also highlight a fundamental distinction between the complementarity of observables in terms of uncertainty and in terms of information.

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“…Apply (31) In Sec. II we noted that this bound can be rewritten in an alternative form that may be easier to calculate.…”

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confidence: 99%

Improved entropic uncertainty relations and information exclusion relations

2014

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“…It plays an important role in recent results on device-independent quantum key distribution [HR09,MPA11] and related cryptographic primitives [TFKW13]. The latter work considers parallel repetition of a game with quantum messages, a setting which is also the focus of [CJPP11].…”

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confidence: 99%

A parallel repetition theorem for entangled projection games

2015

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We study the behavior of the entangled value of two-player one-round projection games under parallel repetition. We show that for any projection game G of entangled value 1 − ε < 1, the value of the k-fold repetition of G goes to zero as O((1 − ε c ) k ), for some universal constant c ≥ 1. If furthermore the constraint graph of G is expanding we obtain the optimal c = 1. Previously exponential decay of the entangled value under parallel repetition was only known for the case of XOR and unique games. To prove the theorem we extend an analytical framework introduced by Dinur and Steurer for the study of the classical value of projection games under parallel repetition. Our proof, as theirs, relies on the introduction of a simple relaxation of the entangled value that is perfectly multiplicative. The main technical component of the proof consists in showing that the relaxed value remains tightly connected to the entangled value, thereby establishing the parallel repetition theorem. More generally, we obtain results on the behavior of the entangled value under products of arbitrary (not necessarily identical) projection games.Relating our relaxed value to the entangled value is done by giving an algorithm for converting a relaxed variant of quantum strategies that we call "vector quantum strategy" to a quantum strategy. The algorithm is considerably simpler in case the bipartite distribution of questions in the game has good expansion properties. When this is not the case, the algorithm relies on a quantum analogue of Holenstein's correlated sampling lemma which may be of independent interest. Our "quantum correlated sampling lemma" generalizes results of van Dam and Hayden on universal embezzlement to the following approximate scenario: two non-communicating parties, given classical descriptions of bipartite states |ψ , |ϕ respectively such that |ψ ≈ |ϕ , are able to locally generate a joint entangled state |Ψ ≈ |ψ ≈ |ϕ using an initial entangled state that is independent of their inputs.

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“…Assuming that the devices carry at least some memory of past interactions is an extremely realistic assumption due to technical limitations, even if Alice and Bob prepare their own trusted, but imperfect, devices, highlighting the extreme importance of such analyses for the implementation of device independent QKD. In contrast, relatively little is known about device independence outside the realm of QKD [12][13][14][15].Conference key agreement [16,17] (CKA or N-CKA) is the task of distributing a secret key among N parties. In order to achieve this goal, one could make use of N −1 individual QKD protocols to distribute N − 1 different keys between one of the parties (Alice) and the others (Bob 1 , .…”

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Fully device-independent conference key agreement

2018

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We present the first security analysis of conference key agreement (CKA) in the most adversarial model of device independence (DI). Our protocol can be implemented by any experimental setup that is capable of performing Bell tests (specifically, the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality), and security can in principle be obtained for any violation of the MABK inequality that detects genuine multipartite entanglement among the N parties involved in the protocol. As our main tool, we derive a direct physical connection between the N -partite MABK inequality and the CHSH inequality, showing that certain violations of the MABK inequality correspond to a violation of the CHSH inequality between one of the parties and the other N − 1. We compare the asymptotic key rate for DICKA to the case where the parties use N − 1 DIQKD protocols in order to generate a common key. We show that for some regime of noise the DICKA protocol leads to better rates.Quantum communication allows cryptographic security that is provably impossible to obtain using any classical means. Probably the most famous example of a quantum advantage is quantum key distribution (QKD) [1,2], which allows two parties, Alice and Bob, to exchange an encryption key whose security is guaranteed even if the adversary has an arbitrarily powerful quantum computer. What's more, properties of entanglement lead to the remarkable feature that security is sometimes possible even if the quantum devices used to execute the protocol are largely untrusted. Specifically, the notion of device independent (DI) security [3-5] models quantum devices as black boxes in which we may only choose measurement settings and observe measurement outcomes. Yet, the quantum state and measurements employed by such boxes are unknown, and may even be prepared arbitrarily by the adversary.Significant efforts have been undertaken to establish the security of device independent QKD [5][6][7][8][9][10][11], leading to ever more sophisticated security proofs. Initial proofs assumed a simple model in which the devices act independently and identically (i.i.d.) in each round of the protocol. This significantly simplifies the security analysis since the underlying properties of the devices may first be estimated by gaining statistical confidence from the observation of the measurement outcomes in the tested rounds. The main challenge overcome by the more recent security proofs [8][9][10][11] was to establish security even if the devices behave arbitrarily from one round to the next, including having an arbitrary memory of the past that they might use to thwart the efforts of Alice and Bob. Assuming that the devices carry at least some memory of past interactions is an extremely realistic assumption due to technical limitations, even if Alice and Bob prepare their own trusted, but imperfect, devices, highlighting the extreme importance of such analyses for the implementation of device independent QKD. In contrast, relatively little is known about device independence outside the realm ...

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A monogamy-of-entanglement game with applications to device-independent quantum cryptography

Cited by 113 publications

References 69 publications

Improved entropic uncertainty relations and information exclusion relations

Improved entropic uncertainty relations and information exclusion relations

A parallel repetition theorem for entangled projection games

Fully device-independent conference key agreement

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