Values of cooperative quantum games

• URL: http://arxiv.org/abs/2310.17735v1
• Date: Thu, 26 Oct 2023 18:50:44 GMT
• Title: Values of cooperative quantum games
• Authors: Jason Crann, Rupert H. Levene, Ivan G.Todorov, Lyudmila Turowska
• Abstract summary: We analyse the quantum game values arising from the type hierarchy of quantum no-signalling correlations. We obtain an alternative description of the maximal tensor products of ternary rings of operators.
• Score: 0.5461938536945721
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a resource-theoretical approach that allows us to quantify values of two-player, one-round cooperative games with quantum inputs and outputs, as well as values of quantum probabilistic hypergraphs. We analyse the quantum game values arising from the type hierarchy of quantum no-signalling correlations, establishing tensor norm expressions for each of the correlation types. As a consequence, we provide metric characterisations of state convertibility via LOSR and LOCC.En route, we obtain an alternative description of the maximal tensor products of ternary rings of operators.

Related papers

• Transfer of quantum game strategies [0.0]
  We show a new class of QNS correlations needed for the transfer of strategies between games. We define jointly tracial correlations and show they correspond to traces acting on tensor products of canonical $rm C*$-algebras associated with individual game parties.
  arXiv  Detail & Related papers  (2024-10-12T17:25:58Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• A bound on the quantum value of all compiled nonlocal games [49.32403970784162]
  A cryptographic compiler converts any nonlocal game into an interactive protocol with a single computationally bounded prover. We establish a quantum soundness result for all compiled two-player nonlocal games.
  arXiv  Detail & Related papers  (2024-08-13T08:11:56Z)
• Geometrical Aspects Of Resources Distribution In Quantum Random Circuits [0.0]
  We focus on multipartite non-locality, but we also analyze quantum correlations by appealing to different entanglement and non-classicality measures. We compare universal vs non-universal sets of gates to gain insight into the problem of explaining quantum advantage.
  arXiv  Detail & Related papers  (2024-05-02T18:13:04Z)
• General quantum correlation from nonreal values of Kirkwood-Dirac quasiprobability over orthonormal product bases [0.0]
  A general quantum correlation, wherein entanglement is a subset, has been recognized as a resource in a variety of schemes of quantum information processing and quantum technology. We show that it satisfies certain requirements expected for a quantifier of general quantum correlations. Our results suggest a deep connection between the general quantum correlation and the nonclassical values of the KD quasiprobability and the associated strange weak values.
  arXiv  Detail & Related papers  (2022-08-06T04:29:15Z)
• Quantum speed limits on operator flows and correlation functions [0.0]
  Quantum speed limits (QSLs) identify fundamental time scales of physical processes by providing lower bounds on the rate of change of a quantum state or the expectation value of an observable. We derive two types of QSLs and assess the existence of a crossover between them, that we illustrate with a qubit and a random matrix Hamiltonian. We further apply our results to the time evolution of autocorrelation functions, obtaining computable constraints on the linear response of quantum systems out of equilibrium and the quantum Fisher information governing the precision in quantum parameter estimation.
  arXiv  Detail & Related papers  (2022-07-12T18:00:07Z)
• Dual Exponential Coupled Cluster Theory: Unitary Adaptation, Implementation in the Variational Quantum Eigensolver Framework and Pilot Applications [0.0]
  We have developed a unitary variant of a double exponential coupled cluster theory. The method relies upon the nontrivial action of a unitary, containing a set of rank-two scattering operators. We have shown that all our schemes can perform uniformly well throughout the molecular potential energy surface.
  arXiv  Detail & Related papers  (2022-07-12T05:10:58Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.