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Publication . Article . Preprint . 2018

Multistate and multihypothesis discrimination with open quantum systems

Alexander Holm Kiilerich; Klaus Mølmer;
Open Access
Published: 14 May 2018 Journal: Physical Review A (issn: 2469-9926, Copyright policy )
Abstract

We show how an upper bound for the ability to discriminate any number N of candidates for the Hamiltonian governing the evolution of an open quantum system may be calculated by numerically efficient means. Our method applies an effective master equation analysis to evaluate the pairwise overlaps between candidate full states of the system and its environment pertaining to the Hamiltonians. These overlaps are then used to construct an N -dimensional representation of the states. The optimal positive-operator valued measure (POVM) and the corresponding probability of assigning a false hypothesis may subsequently be evaluated by phrasing optimal discrimination of multiple non-orthogonal quantum states as a semi-definite programming problem. We investigate the structure of the optimal POVM and we provide three realistic examples of hypothesis testing with open quantum systems.

Comment: 9 pages, 5 figures

Subjects by Vocabulary

Microsoft Academic Graph classification: Upper and lower bounds Quantum technology Pairwise comparison Quantum state Semidefinite programming Physics Open quantum system Algorithm POVM Quantum

Subjects

nanoqtech, rare earth, quantum technologies, Quantum Physics (quant-ph), FOS: Physical sciences, Quantum Physics

34 references, page 1 of 4

[1] V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).

[2] K. Mølmer, “Hypothesis testing with open quantum systems,” Phys. Rev. Lett. 114, 040401 (2015). [OpenAIRE]

[3] C. W. Helstrom, “Quantum detection and estimation theory,” Journal of Statistical Physics 1, 231-252 (1969).

[4] D. Ha and Y. Kwon, “Complete analysis for three-qubit mixed-state discrimination,” Phys. Rev. A 87, 062302 (2013).

[5] M. Rosati, G. De Palma, A. Mari, and V. Giovannetti, “Optimal quantum state discrimination via nested binary measurements,” Phys. Rev. A 95, 042307 (2017).

[6] C. W. Helstrom, J. W. S. Liu, and J. P. Gordon, “Quantum-mechanical communication theory,” Proceedings of the IEEE 58, 1578-1598 (1970).

[7] E. Davies, “Information and quantum measurement,” IEEE Transactions on Information Theory 24, 596-599 (1978).

[8] A. Peres and D. R. Terno, “Optimal distinction between non-orthogonal quantum states,” Journal of Physics A: Mathematical and General 31, 7105 (1998). [OpenAIRE]

[9] K. M. R. Audenaert, J. Calsamiglia, R. Muñoz Tapia, E. Bagan, Ll. Masanes, A. Acin, and F. Verstraete, “Discriminating states: The quantum chernoff bound,” Phys. Rev. Lett. 98, 160501 (2007).

[10] K. Li, “Discriminating quantum states: the multiple chernoff distance,” The Annals of Statistics 44, 1661-1679 (2016).

Funded by
EC| NanOQTech
Project
NanOQTech
Nanoscale Systems for Optical Quantum Technologies
  • Funder: European Commission (EC)
  • Project Code: 712721
  • Funding stream: H2020 | RIA
Validated by funder
,
EC| NanOQTech
Project
NanOQTech
Nanoscale Systems for Optical Quantum Technologies
  • Funder: European Commission (EC)
  • Project Code: 712721
  • Funding stream: H2020 | RIA
Validated by funder
moresidebar