9 research outputs found
Quantum Query Complexity of Boolean Functions under Indefinite Causal Order
The standard model of quantum circuits assumes operations are applied in a
fixed sequential "causal" order. In recent years, the possibility of relaxing
this constraint to obtain causally indefinite computations has received
significant attention. The quantum switch, for example, uses a quantum system
to coherently control the order of operations. Several ad hoc computational and
information-theoretical advantages have been demonstrated, raising questions as
to whether advantages can be obtained in a more unified complexity theoretic
framework. In this paper, we approach this problem by studying the query
complexity of Boolean functions under general higher order quantum
computations. To this end, we generalise the framework of query complexity from
quantum circuits to quantum supermaps to compare different models on an equal
footing. We show that the recently introduced class of quantum circuits with
quantum control of causal order cannot lead to any reduction in query
complexity, and that any potential advantage arising from causally indefinite
supermaps can be bounded by the polynomial method, as is the case with quantum
circuits. Nevertheless, we find some functions for which the minimum error with
which they can be computed using two queries is strictly lower when exploiting
causally indefinite supermaps.Comment: 6+11 page
Improving social welfare in non-cooperative games with different types of quantum resources
We investigate what quantum advantages can be obtained in multipartite non-cooperative games by studying how different types of quantum resources can improve social welfare, a measure of the quality of a Nash equilibrium. We study how these advantages in quantum social welfare depend on the bias of the game, and improve upon the separation that was previously obtained using pseudo-telepathic strategies. Two different quantum settings are analysed: a first, in which players are given direct access to an entangled quantum state, and a second, which we introduce here, in which they are only given classical advice obtained from quantum devices. For a given game G, these two settings give rise to different equilibria characterised by the sets of equilibrium correlations Qcorr(G) and Q(G), respectively. We show that Q(G) ⊆ Qcorr(G) and, by considering explicit example games and exploiting SDP optimisation methods, provide indications of a strict separation between the social welfare attainable in the two settings. This provides a new angle towards understanding the limits and advantages of delegating quantum measurements
Improving social welfare in non-cooperative games with different types of quantum resources
International audienceWe investigate what quantum advantages can be obtained in multipartite non-cooperative games by studying how different types of quantum resources can lead to new Nash equilibria and improve social welfare -- a measure of the quality of an equilibrium. Two different quantum settings are analysed: a first, in which players are given direct access to an entangled quantum state, and a second, which we introduce here, in which they are only given classical advice obtained from quantum devices. For a given game G, these two settings give rise to different equilibria characterised by the sets of equilibrium correlations Qcorr(G) and Q(G), respectively. We show that Q(G)⊆Qcorr(G), and by exploiting the self-testing property of some correlations, that the inclusion is strict for some games G. We make use of SDP optimisation techniques to study how these quantum resources can improve social welfare, obtaining upper and lower bounds on the social welfare reachable in each setting. We investigate, for several games, how the social welfare depends on the bias of the game and improve upon a separation that was previously obtained using pseudo-telepathic solutions
Improving social welfare in non-cooperative games with different types of quantum resources
We investigate what quantum advantages can be obtained in multipartite non-cooperative games by studying how different types of quantum resources can improve social welfare, a measure of the quality of a Nash equilibrium. We study how these advantages in quantum social welfare depend on the bias of the game, and improve upon the separation that was previously obtained using pseudo-telepathic strategies. Two different quantum settings are analysed: a first, in which players are given direct access to an entangled quantum state, and a second, which we introduce here, in which they are only given classical advice obtained from quantum devices. For a given game G, these two settings give rise to different equilibria characterised by the sets of equilibrium correlations Qcorr(G) and Q(G), respectively. We show that Q(G) ⊆ Qcorr(G) and, by considering explicit example games and exploiting SDP optimisation methods, provide indications of a strict separation between the social welfare attainable in the two settings. This provides a new angle towards understanding the limits and advantages of delegating quantum measurements
Improving social welfare in non-cooperative games with different types of quantum resources
We investigate what quantum advantages can be obtained in multipartite non-cooperative games by studying how different types of quantum resources can improve social welfare, a measure of the quality of a Nash equilibrium. We study how these advantages in quantum social welfare depend on the bias of the game, and improve upon the separation that was previously obtained using pseudo-telepathic strategies. Two different quantum settings are analysed: a first, in which players are given direct access to an entangled quantum state, and a second, which we introduce here, in which they are only given classical advice obtained from quantum devices. For a given game G, these two settings give rise to different equilibria characterised by the sets of equilibrium correlations Qcorr(G) and Q(G), respectively. We show that Q(G) ⊆ Qcorr(G) and, by considering explicit example games and exploiting SDP optimisation methods, provide indications of a strict separation between the social welfare attainable in the two settings. This provides a new angle towards understanding the limits and advantages of delegating quantum measurements
Quantum Query Complexity of Boolean Functions under Indefinite Causal Order
International audienceThe standard model of quantum circuits assumes operations are applied in a fixed sequential "causal" order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention. The quantum switch, for example, uses a quantum system to coherently control the order of operations. Several ad hoc computational and information-theoretical advantages have been demonstrated, raising questions as to whether advantages can be obtained in a more unified complexity theoretic framework. In this paper, we approach this problem by studying the query complexity of Boolean functions under general higher order quantum computations. To this end, we generalise the framework of query complexity from quantum circuits to quantum supermaps to compare different models on an equal footing. We show that the recently introduced class of quantum circuits with quantum control of causal order cannot lead to any reduction in query complexity, and that any potential advantage arising from causally indefinite supermaps can be bounded by the polynomial method, as is the case with quantum circuits. Nevertheless, we find some functions for which the minimum error with which they can be computed using two queries is strictly lower when exploiting causally indefinite supermaps