Toward a general theory of quantum games

Gutoski, Gus; Watrous, John

doi:10.1145/1250790.1250873

Cited by 194 publications

(343 citation statements)

References 40 publications

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“…From different points of view Refs. [33,61,62] studied the structure of multipartite causal channels, showing that they can always be realized as sequences of channels with memory. In this Section we show that all these results, originally obtained in quantum mechanics, actually hold in any causal theory with purification.…”

Section: Causally Ordered Channels and Channels With Memorymentioning

confidence: 99%

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Probabilistic theories with purification

2010

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We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible realization of every physical process, that is, to the fact that every physical process can be regarded as arising from a reversible interaction of the system with an environment, which is eventually discarded. From the purification principle we also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamio lkowski isomorphism in quantum theory. Such an isomorphism allows one to prove most of the basic features of quantum theory, like e.g. existence of pure bipartite states giving perfect correlations in independent experiments, no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, no programming, no bit commitment, complementarity between correctable channels and deletion channels, characterization of entanglement-breaking channels as measure-and-prepare channels, and others, without resorting to the mathematical framework of Hilbert spaces.

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Section: Causally Ordered Channels and Channels With Memorymentioning

confidence: 99%

“…[62] for the case of quantum games). In this scenario, the memory systems are the private systems available to a party, while the other input-output systems are the systems exchanged in the communication with other parties.…”

Section: B No Bit Commitmentmentioning

confidence: 99%

Probabilistic theories with purification

2010

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“…The CJ-isomorphism can also be used to represent 'superoperators' or 'processes' which map quantum maps to quantum maps, quantum states or probabilities [3,14,[17][18][19]. In this paper, we will focus on processes mapping two quantum operations x x a and h y b -corresponding to the CJ representation of Alice's and Bob's CP maps-to a probability (see figure 1).…”

Section: Causal Nonseparability and Causal Inequalitiesmentioning

confidence: 99%

Causally nonseparable processes admitting a causal model

2016

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A recent framework of quantum theory with no global causal order predicts the existence of 'causally nonseparable' processes. Some of these processes produce correlations incompatible with any causal order (they violate so-called 'causal inequalities' analogous to Bell inequalities) while others do not (they admit a 'causal model' analogous to a local model). Here we show for the first time that bipartite causally nonseparable processes with a causal model exist, and give evidence that they have no clear physical interpretation. We also provide an algorithm to generate processes of this kind and show that they have nonzero measure in the set of all processes. We demonstrate the existence of processes which stop violating causal inequalities but are still causally nonseparable when mixed with a certain amount of 'white noise'. This is reminiscent of the behavior of Werner states in the context of entanglement and nonlocality. Finally, we provide numerical evidence for the existence of causally nonseparable processes which have a causal model even when extended with an entangled state shared among the parties.

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“…Applications of GQIs in optimization problems can be found in [4][5][6][7][8][9][10][11] . The theory of GQIs was alternatively introduced 1 as a theory of higher order quantum functions, spawning interest in the investigation of more computational consequences of the properties of GQIs [12][13][14] . A similar approach to general affine functions on convex subsets of state spaces was recently published 15 , explicitly inspired to the concept of GQIs and quantum combs (namely singleton GQIs).…”

Section: Introductionmentioning

confidence: 99%

Extremal quantum protocols

D’Ariano

Perinotti

Sedlák

2011

Journal of Mathematical Physics

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Generalized quantum instruments correspond to measurements where the input and output are either states or more generally quantum circuits. These measurements describe any quantum protocol including games, communications, and algorithms.The set of generalized quantum instruments with a given input and output structure is a convex set. Here we investigate the extremal points of this set for the case of finite dimensional quantum systems and generalized instruments with finitely many outcomes. We derive algebraic necessary and sufficient conditions for extremality.

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Toward a general theory of quantum games

Cited by 194 publications

References 40 publications

Probabilistic theories with purification

Probabilistic theories with purification

Causally nonseparable processes admitting a causal model

Extremal quantum protocols

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