Introduces coherent swap regret against local CPTP maps and proves a three-level landscape where non-unital measurement-preparation channels force Theta(sqrt(d T log d)) minimax regret while unital channels have zero regret.
Toward a general theory of quantum games
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abstract
We study properties of quantum strategies, which are complete specifications of a given party's actions in any multiple-round interaction involving the exchange of quantum information with one or more other parties. In particular, we focus on a representation of quantum strategies that generalizes the Choi-Jamio{\l}kowski representation of quantum operations. This new representation associates with each strategy a positive semidefinite operator acting only on the tensor product of its input and output spaces. Various facts about such representations are established, and two applications are discussed: the first is a new and conceptually simple proof of Kitaev's lower bound for strong coin-flipping, and the second is a proof of the exact characterization QRG = EXP of the class of problems having quantum refereed games.
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Temporal state tomography reconstructs multi-time quantum processes from temporal quasiprobability distributions via a Bloch-type representation and derives the associated sample complexity.
citing papers explorer
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Coherent Swap Regret and Channel-Proof Learning
Introduces coherent swap regret against local CPTP maps and proves a three-level landscape where non-unital measurement-preparation channels force Theta(sqrt(d T log d)) minimax regret while unital channels have zero regret.
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Temporal State Tomography via Quantum Snapshotting the Temporal Quasiprobabilities
Temporal state tomography reconstructs multi-time quantum processes from temporal quasiprobability distributions via a Bloch-type representation and derives the associated sample complexity.