Additivity violation of quantum channels via strong convergence to semi-circular and circular elements

• URL: http://arxiv.org/abs/2101.00424v2
• Date: Fri, 30 Apr 2021 02:14:16 GMT
• Title: Additivity violation of quantum channels via strong convergence to semi-circular and circular elements
• Authors: Motohisa Fukuda, Takahiro Hasebe, Shinya Sato
• Abstract summary: We prove the additivity violation via Haagerup inequality for a new class of random quantum channels constructed by rectifying the above completely positive maps based on strong convergence.
• Score: 1.9336815376402714
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Additivity violation of minimum output entropy, which shows non-classical properties in quantum communication, had been proved in most cases for random quantum channels defined by Haar-distributed unitary matrices. In this paper, we investigate random completely positive maps made of Gaussian Unitary Ensembles and Ginibre Ensembles regarding this matter. Using semi-circular systems and circular systems of free probability, we not only show the multiplicativity violation of maximum output norms in the asymptotic regimes but also prove the additivity violation via Haagerup inequality for a new class of random quantum channels constructed by rectifying the above completely positive maps based on strong convergence.

Related papers

• Inner bounding the quantum entropy cone with subadditivity and subsystem coarse grainings [0.0]
  We show that all the extreme rays of both the three-party quantum entropy cone and the four-party stabilizer entropy cone can be obtained from subsystem coarse grainings of specific higher-party quantum states. This suggests that the study of the subadditivity cone'', and the set of its extreme rays realizable in quantum mechanics, provides a powerful tool for deriving inner bounds for the quantum and stabilizer entropy cones.
  arXiv  Detail & Related papers  (2023-12-07T06:42:13Z)
• Weyl channels for multipartite systems [42.37986459997699]
  Quantum channels describe unitary and non-unitary evolution of quantum systems. We show that these channels are completely characterized by elements drawn of finite cyclic groups.
  arXiv  Detail & Related papers  (2023-10-17T02:45:47Z)
• A Unified Theory of Barren Plateaus for Deep Parametrized Quantum Circuits [37.84307089310829]
  Variational quantum computing schemes have received considerable attention due to their high versatility and potential to make practical use of near-term quantum devices. At their core, these models train a loss function by sending an initial state through a parametrized quantum circuit, and evaluating the expectation value of some operator at the circuit's output. Despite their promise, the trainablity of these algorithms is hindered by barren plateaus induced by the expressiveness of the parametrized quantum circuit, entanglement of the input data, the locality of the observable, or the presence of hardware noise.
  arXiv  Detail & Related papers  (2023-09-17T18:14:10Z)
• 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)
• Quantum R\'{e}nyi Entropy Functionals for Bosonic Gaussian Systems [1.0619039878979954]
  We introduce a quantum analog of the classical R'enyi-$p$ entropy power inequality. The proposed inequality is expected to be useful for the nontrivial computing of quantum channel capacities.
  arXiv  Detail & Related papers  (2022-04-22T14:53:39Z)
• Spectral clustering under degree heterogeneity: a case for the random walk Laplacian [83.79286663107845]
  This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. In the special case of a degree-corrected block model, the embedding concentrates about K distinct points, representing communities.
  arXiv  Detail & Related papers  (2021-05-03T16:36:27Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Complete entropic inequalities for quantum Markov chains [17.21921346541951]
  We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality. We also establish the first general approximateization property of relative entropy.
  arXiv  Detail & Related papers  (2021-02-08T11:47:37Z)
• Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
  We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
  arXiv  Detail & Related papers  (2020-11-06T19:00:07Z)
• Generating random quantum channels [1.0499611180329802]
  Several techniques of generating random quantum channels, which act on the set of $d$-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show under which conditions they become mathematically equivalent. Additional results focus on the spectral gap and other spectral properties of random quantum channels and their invariant states.
  arXiv  Detail & Related papers  (2020-11-05T17:35:30Z)
• 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.