Quantum magic rectangles: Characterization and application to certified randomness expansion

Adamson, Sean A.; Wallden, Petros

doi:10.1103/physrevresearch.2.043317

Cited by 7 publications

(15 citation statements)

References 30 publications

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“…The graph incidence groups of most of the graphs in this characterization do not have interesting structure, but an exception is the family of graphs K 3,n , which we analyze in Subsection 5.3. The games G(K m,n , b) have also recently been studied in [AW20,AW22] under the title of magic rectangle games, although our results do not seem to overlap. The proofs of Theorems 1.4 and 1.5 are given in Section 5.…”

Section: Introductionmentioning

confidence: 52%

Arkhipov's theorem, graph minors, and linear system nonlocal games

Paddock¹,

Russo²,

Silverthorne³

et al. 2022

Preprint

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The perfect quantum strategies of a linear system game correspond to certain representations of its solution group. We study the solution groups of graph incidence games, which are linear system games in which the underlying linear system is the incidence system of a (non-properly) twocoloured graph. While it is undecidable to determine whether a general linear system game has a perfect quantum strategy, for graph incidence games this problem is solved by Arkhipov's theorem, which states that the graph incidence game of a connected graph has a perfect quantum strategy if and only if it either has a perfect classical strategy, or the graph is nonplanar. Arkhipov's criterion can be rephrased as a forbidden minor condition on connected twocoloured graphs. We extend Arkhipov's theorem by showing that, for graph incidence games of connected two-coloured graphs, every quotient closed property of the solution group has a forbidden minor characterization. We rederive Arkhipov's theorem from the group theoretic point of view, and then find the forbidden minors for two new properties: finiteness and abelianness. Our methods are entirely combinatorial, and finding the forbidden minors for other quotient closed properties seems to be an interesting combinatorial problem. the most restrictive model of finite-dimensional strategies. Commuting-operator strategies refers to the most permissive model of infinite-dimensional strategies.

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Section: Introductionmentioning

confidence: 52%

Arkhipov's theorem, graph minors, and linear system nonlocal games

Paddock¹,

Russo²,

Silverthorne³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Figure 1: A quantum strategy for the magic square game, in which the players share the entangled state given in Eq. (10). Observables X, Ŷ , and Ẑ are the Pauli spin operators, and I is the identity operator.…”

Section: S3mentioning

confidence: 99%

“…The magic square game can be generalised to be played on an m × n table [10]. Such a magic rectangle game corresponds to m possible questions for Alice and n for Bob.…”

Section: Magic Rectangle Gamesmentioning

confidence: 99%

“…Conversely, exploring how different nonlocal games that appear elsewhere in the literature can be used for self-testing and what (if any) advantages these offer over other self-tests is, in its own right, an interesting endeavour. Here we examine the recently introduced generalisation of the magic square game to rectangular dimensions [10] and obtain a family of self-tests that compare favourably to other self-tests.…”

Section: Introductionmentioning

confidence: 99%

“…Aravind [12] gives a nontechnical demonstration of the Mermin-Peres magic square game. In [10] an extension of the magic square game to arbitrary rectangular dimensions was examined, and this is used as a basis for the self-test presented here.…”

Section: Introductionmentioning

confidence: 99%

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Practical parallel self-testing of Bell states via magic rectangles

Adamson,

Wallden

2021

Preprint

Self Cite

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Self-testing is a method to verify that one has a particular quantum state from purely classical statistics. For practical applications, such as device-independent delegated verifiable quantum computation, it is crucial that one self-tests multiple Bell states in parallel while keeping the quantum capabilities required of one side to a minimum. In this work we use the 3 × n magic rectangle games (generalisations of the magic square game) to obtain a self-test for n Bell states where the one side needs only to measure single-qubit Pauli observables. The protocol requires small input size (constant for Alice and O(log n) bits for Bob) and is robust with robustness O(n 5/2 √ ε), where ε is the closeness of the observed correlations to the ideal. To achieve the desired self-test we introduce a one-side-local quantum strategy for the magic square game that wins with certainty, generalise this strategy to the family of 3 × n magic rectangle games, and supplement these nonlocal games with extra check rounds (of single and pairs of observables).

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A block cipher algorithm developed using Magic Square in the seventh Order

Alattar

Monem

2021

J. Phys.: Conf. Ser.

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This paper use the magic square of order 7 to develop Block encryption algorithms that work for encoding color images and text in GF(P) and GF(28). The algorithm use key with length = 35 and a message with length =14 are used, First, the keys are placed in the previously agreed positions and the remaining positions remain for the message, then the magic sum for each of them is calculated. Complexity, velocity, NIST calculations, and histogram calculations were calculated and the results were compared with the 5th degree magic square, where the complexity was with using GF(P) = (256)14 × (P)35 and using GF(28) = (256)14 × (256)35, The magic square of the seventh degree is better than the magic square of the fifth degree in cryptography in terms of complexity and a slight difference in speed.

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Quantum magic rectangles: Characterization and application to certified randomness expansion

Cited by 7 publications

References 30 publications

Arkhipov's theorem, graph minors, and linear system nonlocal games

Arkhipov's theorem, graph minors, and linear system nonlocal games

Practical parallel self-testing of Bell states via magic rectangles

A block cipher algorithm developed using Magic Square in the seventh Order

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