Quantum Brascamp-Lieb Dualities

• URL: http://arxiv.org/abs/1909.02383v3
• Date: Mon, 20 Feb 2023 07:20:10 GMT
• Title: Quantum Brascamp-Lieb Dualities
• Authors: Mario Berta, David Sutter, Michael Walter
• Abstract summary: Brascamp-Lieb inequalities are entropy inequalities with a dual formulation as generalized Young inequalities. We introduce a fully quantum version of this duality, relating quantum relative entropy inequalities to matrix exponential inequalities of Young type. We find novel uncertainty relations for Gaussian quantum operations that can be interpreted as quantum duals of the well-known family of geometric' Brascamp-Lieb inequalities.
• Score: 10.43686705482655
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Brascamp-Lieb inequalities are entropy inequalities which have a dual formulation as generalized Young inequalities. In this work, we introduce a fully quantum version of this duality, relating quantum relative entropy inequalities to matrix exponential inequalities of Young type. We demonstrate this novel duality by means of examples from quantum information theory -- including entropic uncertainty relations, strong data-processing inequalities, super-additivity inequalities, and many more. As an application we find novel uncertainty relations for Gaussian quantum operations that can be interpreted as quantum duals of the well-known family of `geometric' Brascamp-Lieb inequalities.

Related papers

• Error exponents of quantum state discrimination with composite correlated hypotheses [40.82628972269358]
  We study the error exponents in quantum hypothesis testing between two sets of quantum states.<n>We introduce and compare two natural extensions of the quantum Hoeffding divergence and anti-divergence to sets of quantum states.
  arXiv  Detail & Related papers  (2025-08-18T13:04:06Z)
• Probe of Generic Quantum Contextuality and Nonlocality for qubits [6.975100375755745]
  We show that the entropic uncertainty relation (EUR) is able to connect intrinsically generic quantum contextuality and nonlocal entanglement. From a nonlocal viewpoint, we show that the single-party contextuality and two-party entanglement are related by the EUR with quantum memories.
  arXiv  Detail & Related papers  (2025-04-15T14:40:28Z)
• Uncertainty relations based on the $ρ$-absolute variance for quantum channels [7.363028199494752]
  Uncertainty principle reveals the intrinsic differences between the classical and quantum worlds, which plays a significant role in quantum information theory. We introduce the uncertainty of quantum channels and explore its properties. The summation form of the uncertainty inequalities based on the $rho$-absolute variance for arbitrary $N$ quantum channels are also investigated and the optimal lower bounds are presented.
  arXiv  Detail & Related papers  (2024-04-12T07:51:54Z)
• Embezzling entanglement from quantum fields [41.94295877935867]
  Embezzlement of entanglement refers to the counterintuitive possibility of extracting entangled quantum states from a reference state of an auxiliary system. We uncover a deep connection between the operational task of embezzling entanglement and the mathematical classification of von Neumann algebras.
  arXiv  Detail & Related papers  (2024-01-14T13:58:32Z)
• Entropy Uncertainty Relations and Strong Sub-additivity of Quantum Channels [17.153903773911036]
  We prove an entropic uncertainty relation for two quantum channels. Motivated by Petz's algebraic SSA inequality, we also obtain a generalized SSA for quantum relative entropy.
  arXiv  Detail & Related papers  (2023-01-20T02:34:31Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Quantum Fluctuation-Response Inequality and Its Application in Quantum Hypothesis Testing [6.245537312562826]
  We find a bound for the mean difference of an observable at two different quantum states. When the spectrum of the observable is bounded, the sub-Gaussian property is used to link the bound with the sub-Gaussian norm of the observable. We show the versatility of our results by their applications in problems like thermodynamic inference and speed limit.
  arXiv  Detail & Related papers  (2022-03-20T09:10:54Z)
• Leggett-Garg inequalities in the quantum field theory of neutrino oscillations [0.0]
  This finding relates temporal nonclassicality to quantum uncertainty. We show that Leggett-Garg inequalities are violated more strongly in quantum field theory than in quantum mechanics.
  arXiv  Detail & Related papers  (2021-11-18T23:47:07Z)
• Experimental violations of Leggett-Garg's inequalities on a quantum computer [77.34726150561087]
  We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
  arXiv  Detail & Related papers  (2021-09-06T14:35:15Z)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• Tightening the tripartite quantum memory assisted entropic uncertainty relation [0.0]
  In quantum information theory, Shannon entropy has been used as an appropriate measure to express the uncertainty relation. One can extend the bipartite quantum memory assisted entropic uncertainty relation to tripartite quantum memory assisted uncertainty relation.
  arXiv  Detail & Related papers  (2020-05-05T12:51:25Z)
• Entropic Uncertainty Relations and the Quantum-to-Classical transition [77.34726150561087]
  We aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations. We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities.
  arXiv  Detail & Related papers  (2020-03-04T14:01:17Z)
• Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction [0.0]
  We review the fundamental properties of the quantum relative entropy for finite-dimensional Hilbert spaces. We focus on several inequalities that are related to the second law of thermodynamics, where the positivity and the monotonicity of the quantum relative entropy play key roles.
  arXiv  Detail & Related papers  (2012-02-05T17:02:33Z)

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.