Restrictions on shareability of classical correlations for random multipartite quantum states

• URL: http://arxiv.org/abs/2008.09592v2
• Date: Tue, 1 Jun 2021 19:03:33 GMT
• Title: Restrictions on shareability of classical correlations for random multipartite quantum states
• Authors: Saptarshi Roy, Shiladitya Mal, Aditi Sen De
• Abstract summary: We explore the possibility of nontrivial upper bound by Haar uniformly generating random multipartite states. For a higher number of parties, the classical part of quantum discord and local work can follow monogamy-based upper bound on sharability. The trends of sharability for classical correlation measures in random states clearly demarcate between the axiomatic definition of classical correlations and the conventional ones.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Unlike quantum correlations, the shareability of classical correlations (CCs) between two-parties of a multipartite state is assumed to be free since there exist states for which CCs for each of the reduced states can simultaneously reach their algebraic maximum value. However, when one randomly picks out states from the state space, we find that the probability of obtaining those states possessing the algebraic maximum value is vanishingly small. We explore the possibility of nontrivial upper bound by Haar uniformly generating random multipartite states and computing the frequency distribution for various CC measures, conventional classical correlators, and two axiomatic measures of classical correlations, namely the classical part of quantum discord and local work of work-deficit. We find that the distributions are typically Gaussian-like and their standard deviations decrease with the increase in number of parties. It also reveals that among the multiqubit random states, most of the reduced density matrices possess a low amount of CCs which can also be confirmed by the mean of the distributions, thereby showing a kind of restrictions on the sharability of classical correlations for random states. Furthermore, we also notice that the maximal value for random states is much lower than the algebraic maxima obtained for a set of states, and the gap between the two increases further for states with a higher number of parties. We report that for a higher number of parties, the classical part of quantum discord and local work can follow monogamy-based upper bound on sharability while classical correlators have a different upper bound. The trends of sharability for classical correlation measures in random states clearly demarcate between the axiomatic definition of classical correlations and the conventional ones.

Related papers

• Multipartite entanglement theory with entanglement-nonincreasing operations [91.3755431537592]
  We extend the resource theory of entanglement for multipartite systems beyond the standard framework of local operations and classical communication. We demonstrate that in this adjusted framework, the transformation rates between multipartite states are fundamentally dictated by the bipartite entanglement entropies of the respective quantum states.
  arXiv  Detail & Related papers  (2023-05-30T12:53:56Z)
• Quantum Maximal Correlation for Gaussian States [2.9443230571766845]
  We compute the quantum maximal correlation for bipartite Gaussian states of continuous-variable systems. We show that the required optimization for computing the quantum maximal correlation of Gaussian states can be restricted to local operators that are linear in terms of phase-space quadrature operators.
  arXiv  Detail & Related papers  (2023-03-13T14:29:03Z)
• Upper Bounds on the Distillable Randomness of Bipartite Quantum States [15.208790082352351]
  distillable randomness of a bipartite quantum state is an information-theoretic quantity. We prove measures of classical correlations and prove a number of their properties. We then further bound these measures from above by some that are efficiently computable by means of semi-definite programming.
  arXiv  Detail & Related papers  (2022-12-18T12:06:25Z)
• Classical correlations for Generic States are Fragile under Decoherence [0.0]
  We show that when noise levels rise, the average value of the classical correlation measures for noisy output states decreases. We also demonstrate a connection between the CCors of the noise-affected multipartite states that are produced and the CCors of the initial states that exhibit exponential correlations.
  arXiv  Detail & Related papers  (2022-09-07T17:45:33Z)
• Chained Generalisation Bounds [26.043342234937747]
  We derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. We establish a duality between generalisation bounds based on the regularity of the loss function, and their chained counterparts.
  arXiv  Detail & Related papers  (2022-03-02T09:34:36Z)
• Exponential Tail Local Rademacher Complexity Risk Bounds Without the Bernstein Condition [30.401770841788718]
  The local Rademacher toolbox is one of the most successful general-purpose toolboxes. Applying the Bernstein theory to problems where optimal performance is only achievable via non-probable settings yields an exponential-tail excess risk. Our results apply to improper prediction regimes not covered by the toolbox.
  arXiv  Detail & Related papers  (2022-02-23T12:27:53Z)
• Nonclassical correlations in subsystems of globally entangled quantum states [0.0]
  We study the relation between genuine multipartite entanglement in the pure state of a collection of N qubits and the nonclassical correlations in its two-qubit subsystems.
  arXiv  Detail & Related papers  (2021-12-31T10:25:45Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Sets of Marginals and Pearson-Correlation-based CHSH Inequalities for a Two-Qubit System [22.1737984719789]
  We characterize a set of jointly classicable variables of a graphical model. A crucial feature of this inequality is its nonlinearity, which poses difficulties in the proof.
  arXiv  Detail & Related papers  (2021-07-05T06:52:49Z)
• Monogamy and trade-off relations for correlated quantum coherence [0.0]
  We study the monogamy properties of the correlated coherence for the l 1 -norm and relative entropy measures of coherence. We show that the correlated coherence is monogamous for tripartite pure quantum systems.
  arXiv  Detail & Related papers  (2020-06-24T20:45:36Z)

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.