ZHAO Anting,FANG Ming,TAO Yuanhong.Quantum coherence of three - dimensional X states[J].Journal of Yanbian University,2023,(01):48-52.
三维X型态的相干值计算
- Title:
- Quantum coherence of three - dimensional X states
- 文章编号:
- 1004-4353(2023)01-0048-05
- Keywords:
- X state; quantum coherence; norm coherence measure; entropy coherence measure; skew information coherence
- 分类号:
- O177.3
- 文献标志码:
- A
- 摘要:
- 利用相干度量的定义式和三维X型态的密度矩阵对3类相干度量的解析表达式进行了研究,并给出了具体解析表达式.这3类相干度量分别为基于范数的相干度量(l1范数相干、 lp范数相干(p>1)、 α - 亲和度相干)、基于熵的相干度量(相对熵相干、Tsallis - α相对熵相干、 Rényi - α相对熵相干)和基于斜信息的相干度量.该研究结果可为在不同相干度量下讨论量子态的权衡关系、不确定性关系以及序关系提供参考.
- Abstract:
- Using the definition of coherence measure and the density matrix of three - dimensional X- type state, the analytical expressions of three kinds of coherence measures are studied and given.These three kinds of coherence measures are norm - based coherence measures, which are based on norms(l1 - norm coherence measure, lp - norm coherence measure(p > 1), Rényi - α relative entropy coherence), coherence based on entropy(relative entropy coherence measure, α - affinity coherence measure, Tsallis - α relative entropy coherence)and skew information coherence measure.The research results can provide a reference for discussing the trade - off, uncertainty and order relations of quantum states under different coherence measures.
参考文献/References:
[1] JHA P K, MREJEN M, KIM J, et al.Coherence - driven topological transition in quantum metamaterials [J].Phys Rev Lett, 2016,116(16):165502.
[2] LLOYD S.Quantum coherence in biological systems [J].J Phys Conf Ser, 2011,302(1):012037.
[3] BAUMGRATZ T, CRAMER M, PLENIO M B.Quantifying coherence [J].Phys Rev Lett, 2014,113(14):140401.
[4] YU X D, ZHANG D J, XU G F, et al.Alternative framework for quantifying coherence [J].Phys Rev A, 2016,94(6):060302.
[5] BAI Z F, DU S P.Maximally coherent states [J/OL].Quantum Information & Computation.(2015-03-24)[2022-01-12].https://arxiv.org/pdf/1503.07103.
[6] XIONG C H, KUMAR A, WU J D.Family of coherence measures and duality between quantum coherence and path distinguish ability [J].Phys Rev A, 2018,98(3):032324.
[7] ZHANG F G, SHAO L H, LUO Y, et al.Ordering states with Tsallis relative α - entropies of coherence [J].Quant Inf Proc, 2017,16:1 - 17.
[8] SHAO L H, LI Y M, LUO Y, et al.Quantum coherence quantifiers based on the Rényi - α relative entropy [J].Commun Theor Phys, 2017,67(6):631 - 636.
[9] STRELTSOV A, SINGH U, DHAR H S, et al.Measuring quantum coherence with entanglement [J].Phys Rev Lett, 2015,115(2):020403.
[10] SHAO L H, XI Z J, FAN H, et al.The fidelity and trace norm distances for quantifying coherence [J].Phys Rev A, 2015,91(4):042120.
[11] LIU C L, ZHANG D J, YU X D, et al.A new coherence measure based on fidelity [J].Quant Inf Proc, 2017,16:1 - 10.
[12] 孙柳,陶元红,李江鹏.二维量子态的相干值计算[J].延边大学学报(自然科学版),2022,48(2):107 - 111.
[13] ZHANG H J, CHEN B, LI M, et al.Estimation on geometric measure of quantum coherence [J].Commun Theor Phys, 2017,67(2):166 - 170.
[14] CHEN B, FEI S M.Notes on modified trace distance measure of coherence [J].Quant Inf Proc, 2018,17(5):107.
[15] 廉晓龙,李江鹏,孙柳,等.最大相干混合态的量子相干性[J].哈尔滨理工大学学报,2022,27(5):147 - 150.
[16] WANG Y K, GE L Z, TAO Y H.Quantum coherence in mutually unbiased bases [J].Quant Inf Proc, 2019,18(6):1 - 12.
[17] YU C S.Quantum coherence via skew information and its polygamy [J].Phys Rev A, 2017,95(4):042337.
备注/Memo
收稿日期: 2023-02-18
基金项目: 国家自然科学基金(11761073)
第一作者: 赵安婷(1999—),女,硕士研究生,研究方向为量子信息与量子计算.
通信作者: 陶元红(1973—),女,硕士,教授,研究方向为量子信息与量子计算.