Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps

• URL: http://arxiv.org/abs/2102.07773v3
• Date: Thu, 5 Aug 2021 16:17:10 GMT
• Title: Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps
• Authors: Bartosz Regula, Ryuji Takagi, Mile Gu
• Abstract summary: We study the non-physicality of linear maps based on different ways to approximate a given linear map with quantum channels. We show that for any trace-preserving map, the quantities both reduce to a fundamental distance measure: the diamond norm.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Although quantum channels underlie the dynamics of quantum states, maps which are not physical channels -- that is, not completely positive -- can often be encountered in settings such as entanglement detection, non-Markovian quantum dynamics, or error mitigation. We introduce an operational approach to the quantitative study of the non-physicality of linear maps based on different ways to approximate a given linear map with quantum channels. Our first measure directly quantifies the cost of simulating a given map using physically implementable quantum channels, shifting the difficulty in simulating unphysical dynamics onto the task of simulating linear combinations of quantum states. Our second measure benchmarks the quantitative advantages that a non-completely-positive map can provide in discrimination-based quantum games. Notably, we show that for any trace-preserving map, the quantities both reduce to a fundamental distance measure: the diamond norm, thus endowing this norm with new operational meanings in the characterisation of linear maps. We discuss applications of our results to structural physical approximations of positive maps, quantification of non-Markovianity, and bounding the cost of error mitigation.

Related papers

• Lindblad-like quantum tomography for non-Markovian quantum dynamical maps [46.350147604946095]
  We introduce Lindblad-like quantum tomography (L$ell$QT) as a quantum characterization technique of time-correlated noise in quantum information processors. We discuss L$ell$QT for the dephasing dynamics of single qubits in detail, which allows for a neat understanding of the importance of including multiple snapshots of the quantum evolution in the likelihood function.
  arXiv  Detail & Related papers  (2024-03-28T19:29:12Z)
• Locally purified density operators for noisy quantum circuits [17.38734393793605]
  We show that mixed states generated from noisy quantum circuits can be efficiently represented by locally purified density operators (LPDOs) We present a mapping from LPDOs of $N$ qubits to projected entangled-pair states of size $2times N$ and introduce a unified method for managing virtual and Kraus bonds.
  arXiv  Detail & Related papers  (2023-12-05T16:10:30Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system. This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Power of quantum measurement in simulating unphysical operations [10.8525801756287]
  We show that using quantum measurement in place of classical sampling leads to lower simulation costs for general Hermitian-preserving maps. We demonstrate our method in two applications closely related to error mitigation and quantum machine learning.
  arXiv  Detail & Related papers  (2023-09-18T17:39:38Z)
• Realizing Non-Physical Actions through Hermitian-Preserving Map Exponentiation [1.0255759863714506]
  We introduce the Hermitian-preserving mapiation algorithm, which can effectively realize the action of an arbitrary Hermitian-preserving map by encoding its output into a quantum process. Our findings present a pathway for systematically and efficiently implementing non-physical actions with quantum devices.
  arXiv  Detail & Related papers  (2023-08-15T18:00:04Z)
• Scalable Quantum State Tomography with Locally Purified Density Operators and Local Measurements [17.38734393793605]
  An efficient representation of quantum states enables realizing quantum state tomography with minimal measurements. We propose a new approach to state tomography that uses tensor network representations of mixed states through locally purified density operators. Our study opens new avenues in quantum state tomography for two-dimensional systems using tensor network formalism.
  arXiv  Detail & Related papers  (2023-07-31T03:14:31Z)
• Noise effects on purity and quantum entanglement in terms of physical implementability [27.426057220671336]
  Quantum decoherence due to imperfect manipulation of quantum devices is a key issue in the noisy intermediate-scale quantum (NISQ) era. Standard analyses in quantum information and quantum computation use error rates to parameterize quantum noise channels. We propose to characterize the decoherence effect of a noise channel by the physical implementability of its inverse.
  arXiv  Detail & Related papers  (2022-07-04T13:35:17Z)
• Entanglement and Quantum Correlation Measures from a Minimum Distance Principle [0.0]
  Entanglement, and quantum correlation, are precious resources for quantum technologies implementation based on quantum information science. We derive an explicit measure able to quantify the degree of quantum correlation for pure or mixed multipartite states. We prove that our entanglement measure is textitfaithful in the sense that it vanishes only on the set of separable states.
  arXiv  Detail & Related papers  (2022-05-14T22:18:48Z)
• Physical Implementability of Linear Maps and Its Application in Error Mitigation [12.539795808097063]
  We decompose a target linear map into a linear combination of physically implementable operations. We show this measure is efficiently computable by semidefinite programs. We endow this measure with an operational meaning within the quantum error mitigation scenario.
  arXiv  Detail & Related papers  (2020-12-20T16:03:09Z)
• Neural network quantum state tomography in a two-qubit experiment [52.77024349608834]
  Machine learning inspired variational methods provide a promising route towards scalable state characterization for quantum simulators. We benchmark and compare several such approaches by applying them to measured data from an experiment producing two-qubit entangled states. We find that in the presence of experimental imperfections and noise, confining the variational manifold to physical states greatly improves the quality of the reconstructed states.
  arXiv  Detail & Related papers  (2020-07-31T17:25:12Z)
• Quantifying quantum non-Markovianity based on quantum coherence via skew information [1.8969868190153274]
  We propose a non-Markovianity measure for open quantum processes. We find that it is equivalent to the three previous measures of non-Markovianity for phase damping and amplitude damping channels. We also use the modified Tsallis relative $alpha$ entropy of coherence to detect the non-Markovianity of dynamics of quantum open systems.
  arXiv  Detail & Related papers  (2020-01-05T15:37:15Z)

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.