A Elena Piceno-Martínez and Laura E C Rosales-Zárate
{"title":"A generalised entropic measure of steering using Tsallis entropies and the relationship with existent steering criteria","authors":"A Elena Piceno-Martínez and Laura E C Rosales-Zárate","doi":"10.1088/2040-8986/ad7157","DOIUrl":null,"url":null,"abstract":"EPR steering is an asymmetric quantum correlation, as such, it is an important resource for quantum information protocols, like those used in quantum key distribution that are of tremendous relevance nowadays. The security of the aforementioned protocols can be shown by using entropic uncertainty measures, which are based on quantum information quantities, among which the entropies are found. In this work, we propose an entropic measure of steering, starting from the detection of steering given in a previous entropic uncertainty relation-based criterion, as well as using a generalised entropy, the Tsallis entropies. We define the entropic measure of steering in terms of an indicator, a quantity depending on the entropies of the measurements of the system, which assigns a value to the steering content of quantum states, while also comprising the asymmetry property of steering. We investigate the properties of the proposed quantity as a measure of steering and its asymmetry and show how it can be used for specific examples. For instance, a class of noisy two-qubit states that includes the Werner states is used to demonstrate the potential of such a proposal. Furthermore, a comparison is also made with the detection of steering in these states using existing steering criteria and the amount of steering a geometric measure for the Werner state gives.","PeriodicalId":16775,"journal":{"name":"Journal of Optics","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Optics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/2040-8986/ad7157","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0
Abstract
EPR steering is an asymmetric quantum correlation, as such, it is an important resource for quantum information protocols, like those used in quantum key distribution that are of tremendous relevance nowadays. The security of the aforementioned protocols can be shown by using entropic uncertainty measures, which are based on quantum information quantities, among which the entropies are found. In this work, we propose an entropic measure of steering, starting from the detection of steering given in a previous entropic uncertainty relation-based criterion, as well as using a generalised entropy, the Tsallis entropies. We define the entropic measure of steering in terms of an indicator, a quantity depending on the entropies of the measurements of the system, which assigns a value to the steering content of quantum states, while also comprising the asymmetry property of steering. We investigate the properties of the proposed quantity as a measure of steering and its asymmetry and show how it can be used for specific examples. For instance, a class of noisy two-qubit states that includes the Werner states is used to demonstrate the potential of such a proposal. Furthermore, a comparison is also made with the detection of steering in these states using existing steering criteria and the amount of steering a geometric measure for the Werner state gives.
期刊介绍:
Journal of Optics publishes new experimental and theoretical research across all areas of pure and applied optics, both modern and classical. Research areas are categorised as:
Nanophotonics and plasmonics
Metamaterials and structured photonic materials
Quantum photonics
Biophotonics
Light-matter interactions
Nonlinear and ultrafast optics
Propagation, diffraction and scattering
Optical communication
Integrated optics
Photovoltaics and energy harvesting
We discourage incremental advances, purely numerical simulations without any validation, or research without a strong optics advance, e.g. computer algorithms applied to optical and imaging processes, equipment designs or material fabrication.