Commuting embeddings of game algebras, constructed via common Cartan decompositions, enable parallel non-local game strategies on fewer qubits than tensor products while preserving the ability to play multiple games simultaneously or select one at random.
Optimal robust quantum self-testing by binary nonlocal XOR games
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abstract
Self-testing a quantum device means verifying the existence of a certain quantum state as well as the effect of the associated measurements based only on the statistics of the measurement outcomes. Robust, i.e., error-tolerant, self-testing quantum devices are critical building blocks for quantum cryptographic protocols that rely on imperfect or untrusted quantum devices. We give a criterion which determines whether a given binary XOR game is robust self-testing with the asymptotically optimal error parameter. As an application, we prove that the celebrated CHSH game is an optimally robust self-test. We also prove the same for a family of tests recently proposed by Acin et al. (PRL 108:100402, 2012) for random number generation, thus extending the benefit of the latter tests to allow imperfect or untrusted quantum devices.
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UNVERDICTED 3representative citing papers
Analytical self-testing criterion proven for equal-coefficient symmetric three-qubit state; general family shown numerically self-testable via swap method and SDP.
New combinatorial proofs and circuit designs for quantum error correction reduce physical qubit overhead by up to 10x and time overhead by 2-6x for codes including Steane, Golay, and surface codes.
citing papers explorer
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Commuting Embeddings for Parallel Strategies in Non-local Games
Commuting embeddings of game algebras, constructed via common Cartan decompositions, enable parallel non-local game strategies on fewer qubits than tensor products while preserving the ability to play multiple games simultaneously or select one at random.
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Self-testing of symmetric three-qubit states
Analytical self-testing criterion proven for equal-coefficient symmetric three-qubit state; general family shown numerically self-testable via swap method and SDP.
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Lower overhead fault-tolerant building blocks for noisy quantum computers
New combinatorial proofs and circuit designs for quantum error correction reduce physical qubit overhead by up to 10x and time overhead by 2-6x for codes including Steane, Golay, and surface codes.