Verifiable Quantum Secure Modulo Summation

Hayashi, Masahito; Koshiba, Takeshi

doi:10.48550/arxiv.1910.05976

Cited by 2 publications

(4 citation statements)

References 37 publications

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“…In [8], a causal broadcast channel with channel state information at the sender is analysed. In this work, we make use of the multi-party modulo summation protocols developed in [9] and [10], extending and optimising them for this this particular communication scenario when n modulo sums are needed.…”

Section: A Related Workmentioning

confidence: 99%

“…We propose a communication model with a sender and many receivers that can be used to ensure that either all receivers receive their message with certainty if they cooperate or otherwise none of them receive their message. We use protocols developed in [9,10] to develop a scheme that is fair and secure such that all receivers can decode messages from the sender fairly when the protocols run honestly, even when some receivers collude. We consider the trade-offs for allowing the receivers to share classical and quantum resources, and find when the receivers can share entanglement and can broadcast messages, they can verifiably securely perform the multi-party computation needed to determine the channel state which encrypts each transmission from the sender.…”

Section: B Summary Of Contributionsmentioning

confidence: 99%

“…We sketch the proof. To determine the channel state s, the receivers perform Protocol 4 for multi-party modulo summation extended from [10,Protocol 4], which offers verifiable randomness for zero-sum random variables and unconditional security. The protocol uses phase-GHZ states defined as follows.…”

Section: Classical Communication With Entanglementmentioning

confidence: 99%

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Undoing Causal Effects of a Causal Broadcast Channel with Cooperating Receivers using Entanglement Resources

DiAdamo,

Nötzel

2021

Preprint

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We analyse a communication scenario over a particular causal broadcast channel whose state depends on a modulo sum. The receivers of the broadcast receive channel state information and collaborate to determine the channel state as to decode their private messages. Further, the receivers of the broadcast can collude up to the minimum non-collusion condition to determine state information of the other noncolluding receivers. We analyse three resource scenarios for the receivers: receivers can share entanglement without classically communicating, can just use classical communication, or have both entanglement and classical communication. Using results from secure multi-party communication, we find that when the receivers can share entanglement and communicate classically, they can receive messages from the sender at a non-zero rate with verifiable secure collaboration. In the entanglement only case a positive capacity is not possible. In the classical communication case, a non-zero rate of communication is achievable but the communication complexity overhead grows quadratically in the number of receivers versus linear in the number of receivers with entanglement.

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Section: A Related Workmentioning

confidence: 99%

Section: B Summary Of Contributionsmentioning

confidence: 99%

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Undoing Causal Effects of a Causal Broadcast Channel with Cooperating Receivers using Entanglement Resources

DiAdamo,

Nötzel

2021

Preprint

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“…To improve the scaling, the authors in [HH18] proposed another self testing method for the same setting with O(n 4 log n) copies. Further, the paper [HK19] proposed a robust self testing protocol for GHZ states. Selftesting with Bell states of higher dimensions has been studied in [KŠT + 19, SSKA19].…”

Section: Introductionmentioning

confidence: 99%

Graph-Theoretic Framework for Self-Testing in Bell Scenarios

Bharti¹,

Ray²,

Xu³

et al. 2021

Preprint

Self Cite

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Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely, with minimal assumptions about the underlying quantum system. It is based on the observation that some extremal points in the set of quantum correlations can only be achieved, up to isometries, with specific states and measurements. Here, we present a new approach for quantum self-testing in Bell non-locality scenarios, motivated by the following observation: the quantum maximum of a given Bell inequality is, in general, difficult to characterize. However, it is strictly contained in an easy-to-characterize set: the theta body of a vertex-weighted induced subgraph (Gex, w) of the graph in which vertices represent the events and edges join mutually exclusive events. This implies that, for the cases where the quantum maximum and the maximum within the theta body (known as the Lovász theta number) of (Gex, w) coincide, self-testing can be demonstrated by just proving self-testability with the theta body of Gex. This graph-theoretic framework allows us to: (i) recover the self-testability of several quantum correlations that are known to permit selftesting (like those violating the Clauser-Horne-Shimony-Holt (CHSH) and three-party Mermin Bell inequalities for projective measurements of arbitrary rank, and chained Bell inequalities for rankone projective measurements), (ii) prove the self-testability of quantum correlations that were not known using existing self-testing techniques (e.g., those violating the Abner Shimony Bell inequality for rank-one projective measurements). Additionally, the analysis of the chained Bell inequalities, along with prior results in Bell non-locality literature, gives us a closed form expression of the Lovász theta number for a family of well studied graphs known as the Möbius ladders, which might be of independent interest in the community of discrete mathematics.

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Verifiable Quantum Secure Modulo Summation

Cited by 2 publications

References 37 publications

Undoing Causal Effects of a Causal Broadcast Channel with Cooperating Receivers using Entanglement Resources

Undoing Causal Effects of a Causal Broadcast Channel with Cooperating Receivers using Entanglement Resources

Graph-Theoretic Framework for Self-Testing in Bell Scenarios

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