Ke Li's lemma for quantum hypothesis testing in general von Neumann algebras

• URL: http://arxiv.org/abs/2010.02177v3
• Date: Sun, 8 Jan 2023 15:01:49 GMT
• Title: Ke Li's lemma for quantum hypothesis testing in general von Neumann algebras
• Authors: Yan Pautrat, Simeng Wang
• Abstract summary: A lemma stated by Ke Li in [arXiv:120.1400] has been used in e.g. [arXiv:1510.04682,arXiv:1706.04590,arXiv:1612.01464,arXiv:1308.6503,arXiv:1602.08898] for various tasks in quantum hypothesis testing, data compression with quantum side information or quantum key distribution. Here we show that the use of modular theory allows to give more transparent meaning to the objects constructed by the lemma, and to prove it for general von Neumann algebras.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A lemma stated by Ke Li in [arXiv:1208.1400] has been used in e.g. [arXiv:1510.04682,arXiv:1706.04590,arXiv:1612.01464,arXiv:1308.6503,arXiv:1602.08898] for various tasks in quantum hypothesis testing, data compression with quantum side information or quantum key distribution. This lemma was originally proven in finite dimension, with a direct extension to type I von Neumann algebras. Here we show that the use of modular theory allows to give more transparent meaning to the objects constructed by the lemma, and to prove it for general von Neumann algebras. This yields a new proof of quantum Stein's lemma with slightly weaker assumption, as well as immediate generalizations of its second order asymptotics, for example the main results in [arXiv:1510.04682] and [arXiv:1208.1400].

Related papers

• Revisiting the operator extension of strong subadditivity [44.99833362998488]
  We give a new proof of the operator extension of the strong subadditivity of von Neumann entropy $rho_AB otimes sigma_C-1 leq rho_A otimes sigma_BC-1$ by identifying the mathematical structure behind it as Connes' theory of spatial derivatives.
  arXiv  Detail & Related papers  (2025-07-30T14:18:43Z)
• Strong converse rate for asymptotic hypothesis testing in type III [3.0846824529023382]
  We show the operational interpretation of sandwiched relative R'enyi entropy in general von Neumann algebras.<n> applicability in general von Neumann algebras opens potential new connections to random matrix theory and the quantum information theory of fundamental physics.
  arXiv  Detail & Related papers  (2025-07-10T17:58:54Z)
• Quantum Lifting for Invertible Permutations and Ideal Ciphers [47.33103206862089]
  We derive the first lifting theorems for establishing security in the quantum random permutation and ideal cipher models. These theorems relate the success probability of an arbitrary quantum adversary to that of a classical algorithm making only a small number of classical queries.
  arXiv  Detail & Related papers  (2025-04-25T09:07:55Z)
• Fine-Grained Complexity via Quantum Natural Proofs [5.306949367777188]
  We show how part of the QSETH conjecture that requires properties to be compression oblivious' can in many cases be replaced by assuming the existence of quantum-secure pseudorandom functions.
  arXiv  Detail & Related papers  (2025-04-14T16:09:55Z)
• On Strong Converse Theorems for Quantum Hypothesis Testing and Channel Coding [16.207627554776916]
  Strong converse theorems refer to the study of impossibility results in information theory. Mosonyi and Ogawa established a one-shot strong converse bound for quantum hypothesis testing. We show that the variational expression of measured R'enyi divergences is a direct consequence of H"older's inequality.
  arXiv  Detail & Related papers  (2024-03-20T13:34:23Z)
• Two Simple Proofs of Müller's Theorem [6.5268245109828005]
  M"uller's theorem is arguably the most important result in the intersection of algorithmic information theory and physics. The quantitative amount of information in classical sources is invariant to the physical model used.
  arXiv  Detail & Related papers  (2024-02-08T00:07:15Z)
• Two Results in the Quantum Theory of Measurements [44.99833362998488]
  The first one clarifies and amends von Neumann's Measurement Postulate used in the Copenhagen interpretation of quantum mechanics. The second one clarifies the relationship between events'' and measurements'' and the meaning of measurements in the $ETH$-Approach to quantum mechanics.
  arXiv  Detail & Related papers  (2023-12-01T14:05:04Z)
• Connecting classical finite exchangeability to quantum theory [45.76759085727843]
  Exchangeability is a fundamental concept in probability theory and statistics. It allows to model situations where the order of observations does not matter. It is well known that both theorems do not hold for finitely exchangeable sequences.
  arXiv  Detail & Related papers  (2023-06-06T17:15:19Z)
• Large $N$ von Neumann algebras and the renormalization of Newton's constant [0.0]
  I derive a family of Ryu--Takayanagi formulae valid in the large $N$ limit of holographic quantum error-correcting codes. I show that the renormalizations of the area term and the bulk entropy term exactly compensate each other.
  arXiv  Detail & Related papers  (2023-02-03T19:00:00Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• Integral formula for quantum relative entropy implies data processing inequality [0.0]
  We prove the monotonicity of quantum relative entropy under trace-preserving positive linear maps. For a simple application of such monotonicities, we consider any divergence' that is non-increasing under quantum measurements. An argument due to Hiai, Ohya, and Tsukada is used to show that the infimum of such a divergence' on pairs of quantum states with prescribed trace distance is the same as the corresponding infimum on pairs of binary classical states.
  arXiv  Detail & Related papers  (2022-08-25T16:32:02Z)
• On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources [51.243733928201024]
  We show that the proof of the generalised quantum Stein's lemma is not correct due to a gap in the argument leading to Lemma III.9. This puts into question a number of established results in the literature, in particular the reversibility of quantum entanglement.
  arXiv  Detail & Related papers  (2022-05-05T17:46:05Z)
• Genuine multipartite entanglement and quantum coherence in an electron-positron system: Relativistic covariance [117.44028458220427]
  We analyze the behavior of both genuine multipartite entanglement and quantum coherence under Lorentz boosts. A given combination of these quantum resources is shown to form a Lorentz invariant.
  arXiv  Detail & Related papers  (2021-11-26T17:22:59Z)
• Depth-efficient proofs of quantumness [77.34726150561087]
  A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover. In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
  arXiv  Detail & Related papers  (2021-07-05T17:45:41Z)
• Approximate recovery and relative entropy I. general von Neumann subalgebras [0.0]
  We prove the existence of a universal recovery channel that approximately recovers states on a v. Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki-Masuda $L_p$ norms.
  arXiv  Detail & Related papers  (2020-06-14T20:00:38Z)
• A refinement of Reznick's Positivstellensatz with applications to quantum information theory [72.8349503901712]
  In Hilbert's 17th problem Artin showed that any positive definite in several variables can be written as the quotient of two sums of squares. Reznick showed that the denominator in Artin's result can always be chosen as an $N$-th power of the squared norm of the variables.
  arXiv  Detail & Related papers  (2019-09-04T11:46:26Z)

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.