Entropic uncertainty relations from equiangular tight frames and their applications

• URL: http://arxiv.org/abs/2112.12375v4
• Date: Fri, 18 Aug 2023 08:38:34 GMT
• Title: Entropic uncertainty relations from equiangular tight frames and their applications
• Authors: Alexey E. Rastegin
• Abstract summary: We derive uncertainty relations for a quantum measurement assigned to an equiangular tight frame. Also, we discuss applications of considered measurements to detect entanglement and other correlations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Finite tight frames are interesting in various topics including questions of quantum information. Each complex tight frame leads to a resolution of the identity in the Hilbert space. Symmetric informationally complete measurements are a special class of equiangular tight frames. Applications of such frames in quantum physics deserve more attention than they have obtained. We derive uncertainty relations for a quantum measurement assigned to an equiangular tight frame. Main results follow from estimation of the corresponding index of coincidence. State-dependent and state-independent formulations are both addressed. Also, we discuss applications of considered measurements to detect entanglement and other correlations.

Related papers

• Classification of joint quantum measurements based on entanglement cost of localization [42.72938925647165]
  We propose a systematic classification of joint measurements based on entanglement cost. We show how to numerically explore higher levels and construct generalizations to higher dimensions and multipartite settings.
  arXiv  Detail & Related papers  (2024-08-01T18:00:01Z)
• One-Shot Min-Entropy Calculation And Its Application To Quantum Cryptography [21.823963925581868]
  We develop a one-shot lower bound calculation technique for the min-entropy of a classical-quantum state. It gives an alternative tight finite-data analysis for the well-known BB84 quantum key distribution protocol. It provides a security proof for a novel source-independent continuous-variable quantum random number generation protocol.
  arXiv  Detail & Related papers  (2024-06-21T15:11:26Z)
• Uncertainty relations for quantum measurements from generalized equiangular tight frames [0.0]
  Informationally overcomplete measurements are a valuable tool in quantum information processing. The existence of $d+1$ mutually unbiased bases is proved for $d$ being a prime power. It is interesting that certain restrictions hold irrespectively to overcompleteness.
  arXiv  Detail & Related papers  (2024-05-30T09:57:21Z)
• 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)
• Quantification of Entanglement and Coherence with Purity Detection [16.01598003770752]
  Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence. Our research offers an efficient means of verifying large-scale quantum information processing.
  arXiv  Detail & Related papers  (2023-08-14T11:03:40Z)
• Analysing quantum systems with randomised measurements [0.4179230671838898]
  We present the advancements made in utilising randomised measurements in various scenarios of quantum information science. We describe how to detect and characterise different forms of entanglement, including genuine multipartite entanglement and bound entanglement. We also present an overview on the estimation of non-linear functions of quantum states and shadow tomography from randomised measurements.
  arXiv  Detail & Related papers  (2023-07-03T18:00:01Z)
• On Kirkwood--Dirac quasiprobabilities and unravelings of quantum channel assigned to a tight frame [0.0]
  Using vectors of the given tight frame to build principal Kraus operators generates quasiprobabilities with interesting properties. New inequalities for characterizing the location of eigenvalues are derived. A utility of the presented inequalities is exemplified with symmetric informationally complete measurement in dimension two.
  arXiv  Detail & Related papers  (2023-04-27T09:11:11Z)
• General framework of quantum complementarity from a measurement-based perspective [6.073419957391949]
  We develop a framework for demonstrating quantum complementarity in the form of information exclusion relations. We explore the applications of our theory in entanglement witnessing and elucidate that our IERs lead to an extended form of entropic uncertainty relations.
  arXiv  Detail & Related papers  (2022-10-03T14:20:52Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• 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)
• R\'{e}nyi formulation of uncertainty relations for POVMs assigned to a quantum design [0.0]
  Information entropies provide powerful and flexible way to express restrictions imposed by the uncertainty principle. In this paper, we obtain uncertainty relations in terms of min-entropies and R'enyi entropies for POVMs assigned to a quantum design.
  arXiv  Detail & Related papers  (2020-04-12T09:44:44Z)

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.