Condition on the R\'enyi Entanglement Entropy under Stochastic Local Manipulation

• URL: http://arxiv.org/abs/2002.11779v2
• Date: Wed, 2 Sep 2020 13:27:16 GMT
• Title: Condition on the R\'enyi Entanglement Entropy under Stochastic Local Manipulation
• Authors: Hyukjoon Kwon, A. J. Paige, M. S. Kim
• Abstract summary: The R'enyi entanglement entropy (REE) is an entanglement quantifier considered as a natural generalisation of the entanglement entropy. Here, we establish a general condition that the probability distribution of the REE of any order obeys under SLOCC. The contribution from the higher-order moments imposes a strict limitation on entanglement distillation via SLOCC.
• Score: 4.812718493682455
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The R\'enyi entanglement entropy (REE) is an entanglement quantifier considered as a natural generalisation of the entanglement entropy. When it comes to stochastic local operations and classical communication (SLOCC), however, only a limited class of the REEs satisfy the monotonicity condition, while their statistical properties beyond mean values have not been fully investigated. Here, we establish a general condition that the probability distribution of the REE of any order obeys under SLOCC. The condition is obtained by introducing a family of entanglement monotones that contain the higher-order moments of the REEs. The contribution from the higher-order moments imposes a strict limitation on entanglement distillation via SLOCC. We find that the upper bound on success probabilities for entanglement distillation exponentially decreases as the amount of raised entanglement increases, which cannot be captured from the monotonicity of the REE. Based on the strong restriction on entanglement transformation under SLOCC, we design a new method to estimate entanglement in quantum many-body systems from experimentally observable quantities.

Related papers

• Freeness Reined in by a Single Qubit [36.94429692322632]
  We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order $O(1)$.<n>We trace their origin to non-uniformly distributed stationary quantum states, which we characterize analytically and confirm numerically.
  arXiv  Detail & Related papers  (2025-12-15T19:00:09Z)
• The Limits of Pure Exploration in POMDPs: When the Observation Entropy is Enough [40.82741665804367]
  We study a simple approach of maximizing the entropy over observations in place true latent states. We show how knowledge of the latter can be exploited to compute a regularization of the observation entropy to improve principled performance.
  arXiv  Detail & Related papers  (2024-06-18T17:00:13Z)
• Tamed Langevin sampling under weaker conditions [27.872857402255775]
  We investigate the problem of sampling from distributions that are not log-concave and are only weakly dissipative. We introduce a taming scheme which is tailored to the growth and decay properties of the target distribution. We provide explicit non-asymptotic guarantees for the proposed sampler in terms of the Kullback-Leibler divergence, total variation, and Wasserstein distance to the target distribution.
  arXiv  Detail & Related papers  (2024-05-27T23:00:40Z)
• Continuous spontaneous localization as the white-noise limit of spontaneous unitarity violation [0.0]
  Colored-noise driven collapse theories extend the equilibrium description of spontaneous symmetry breaking to spontaneous violations of unitarity. We show that this limit coincides with a subclass of continuous spontaneous localization (CSL) models collapsing in a basis of spatially localised energy eigenstates. We furthermore show that, as for the SUV models, the emergence of Born rule statistics in the Markovian limit is enforced by a fluctuation-dissipation relation.
  arXiv  Detail & Related papers  (2024-05-02T08:14:43Z)
• Apparent pathologies in stochastic entropy production in the thermalisation of an open two-level quantum system [0.0]
  We investigate the entropic consequences of the relaxation of an open two-level quantum system towards a thermalised statistical state. We demonstrate that thermalisation starting from a general state is accompanied by a persistent non-zero mean rate of change of the environmental component of entropy production.
  arXiv  Detail & Related papers  (2023-03-07T11:34:46Z)
• Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols [12.461503242570641]
  We show that it is no longer the case when one allows protocols that may only succeed with some probability. We show that this is no longer the case when one allows protocols that may only succeed with some probability.
  arXiv  Detail & Related papers  (2022-09-07T18:00:00Z)
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition [62.997667081978825]
  We analyze the role of boundary conditions in the statistics of topological defects. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate.
  arXiv  Detail & Related papers  (2022-07-08T09:55:05Z)
• Beyond the Edge of Stability via Two-step Gradient Updates [49.03389279816152]
  Gradient Descent (GD) is a powerful workhorse of modern machine learning. GD's ability to find local minimisers is only guaranteed for losses with Lipschitz gradients. This work focuses on simple, yet representative, learning problems via analysis of two-step gradient updates.
  arXiv  Detail & Related papers  (2022-06-08T21:32:50Z)
• Entropic CLT for Order Statistics [39.42561801744333]
  It is well known that central order statistics exhibit a central limit behavior and converge to a Gaussian distribution as the sample size grows. This paper strengthens this known result by establishing an entropic version of the CLT that ensures a stronger mode of convergence using the relative entropy.
  arXiv  Detail & Related papers  (2022-05-10T01:37:55Z)
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor [80.17270167652622]
  Quantum-body systems display rich phase structure in their low-temperature equilibrium states. We experimentally observe an eigenstate-ordered DTC on superconducting qubits. Results establish a scalable approach to study non-equilibrium phases of matter on current quantum processors.
  arXiv  Detail & Related papers  (2021-07-28T18:00:03Z)
• Quantum concentration inequalities [12.56413718364189]
  We establish transportation cost inequalities (TCI) with respect to the quantum Wasserstein distance. We prove Gibbs states of commuting Hamiltonians on arbitrary hypergraphs $H=(V,E)$ satisfy a TCI with constant scaling as $O(|V|)$. We argue that the temperature range for which the TCI holds can be enlarged by relating it to recently established modified logarithmic Sobolev inequalities.
  arXiv  Detail & Related papers  (2021-06-30T05:44:12Z)
• Exact Recovery in the General Hypergraph Stochastic Block Model [92.28929858529679]
  This paper investigates fundamental limits of exact recovery in the general d-uniform hypergraph block model (d-HSBM) We show that there exists a sharp threshold such that exact recovery is achievable above the threshold and impossible below it.
  arXiv  Detail & Related papers  (2021-05-11T03:39:08Z)
• Catalytic Transformations of Pure Entangled States [62.997667081978825]
  Entanglement entropy is the von Neumann entropy of quantum entanglement of pure states. The relation between entanglement entropy and entanglement distillation has been known only for the setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving results an operational meaning also in entangled single-copy setup.
  arXiv  Detail & Related papers  (2021-02-22T16:05:01Z)
• The variance of relative surprisal as single-shot quantifier [0.0]
  We show that (relative) surprisal gives sufficient conditions for approximate state-transitions between pairs of quantum states in single-shot setting. We further derive a simple and physically appealing axiomatic single-shot characterization of (relative) entropy.
  arXiv  Detail & Related papers  (2020-09-17T16:06:54Z)
• Extensive R\'enyi entropies in matrix product states [0.0]
  We prove that all R'enyi entanglement entropies of spin-chains described by generic (gapped) are extensive for disconnected sub-systems. For unital quantum channels this yields a very simple lower bound on the distribution of singular values and the expansion coefficient in terms of the Kraus-rank.
  arXiv  Detail & Related papers  (2020-08-26T18:53:46Z)

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.