Abstract
In this paper, local distinguishability of the multipartite equi-coherent quantum states is studied in the bosonic subspace. A method is proposed to give an upper bound on the optimal success probability in terms of quantum coherence for equiprobable states. Then a necessary and sufficient condition to saturate this upper bound is presented. This condition enables us to give optimal measurements and success probabilities for several examples, including general pure states and n-qubit mixed states which may be linearly dependent. Perfect discrimination is possible for linearly independent states that have maximum quantum coherence. Finally, discrimination of these states when restricted to separable measurements is considered. To this aim an appropriate transformation is proposed to obtain separable measurements equivalent to the optimal measurement, in which the success probability for both is equal. So the upper bound is also valid for separable and LOCC protocol. The important advantage is that for the bosonic measurements it is always possible to obtain equivalent separable operators, not only for minimum error discrimination but also for all strategies of discrimination.
Graphical abstract
Similar content being viewed by others
References
J. Walgate, A.J. Short, L. Hardy, V. Vedral, Phys. Rev. Lett. 85, 4972 (2000)
N. Yu, R. Duan, M. Ying, Phys. Rev. A 84, 012304 (2011)
M. Horodecki, A. Sen(De), U. Sen, K. Horodecki, Phys. Rev. Lett. 90, 047902 (2003)
C.H. Bennett, D.P. DiVincenzo, C.A. Fuchs, T. Mor, E. Rains, P.W. Shor, J.A. Smolin, W.K. Wootters, Phys. Rev. A 59, 1070 (1999)
M. Nathanson, J. Math. Phys. 46, 062103 (2005)
M. Hillery, J. Mimih, Phys. Rev. A 67, 042304 (2003)
J. Watrous, Phys. Rev. Lett. 95, 080505 (2005)
R. Duan, Y. Feng, Y. Xin, M. Ying, IEEE Trans. Inform. Theory 55, 1320 (2009)
A. Chefles, Phys. Rev. A 69, 050307(R) (2004)
S. Virmani, M.F. Sacchi, M.B. Plenio, D. Markham, Phys. Lett. A 288, 62 (2001)
X. Wei, M. Chen, Int. J. Theor. Phys. 54, 812 (2015)
A. Chiuri, G. Vallone, N. Bruno, C. Macchiavello, D. Bruß, P. Mataloni, Phys. Rev. Lett. 105, 250501 (2010)
C. Thiel, J. von Zanthier, T. Bastin, E. Solano, G.S. Agarwal, Phys. Rev. Lett. 99, 193602 (2007)
S.S. Ivanov, P.A. Ivanov, I.E. Linington, N.V. Vitanov, Phys. Rev. A 81, 042328 (2010)
A. Chiuri, C. Greganti, M. Paternostro, G. Vallone, P. Mataloni, Phys. Rev. Lett. 109, 173604 (2012)
V. Giovannetti, S. Lloyd, L. Maccone, Nat. Photon. 5, 222 (2011)
M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, New York, 2000)
T. Baumgratz, M. Cramer, M.B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)
D. Mondal, Ch. Datta, Sk. Sazim, Phys. Lett. A 380, 689 (2016)
Yao Yao, Xing Xiao, Li Geand, C.P. Sun, Phys. Rev. A 92, 022112 (2015)
H.P. Yuen, R.S. Kennedy, M. Lax, IEEE T. Inform. Theory 21, 125 (1975)
A.S. Holevo, J. Multivariate Anal. 3, 337 (1973)
M.A. Jafarizadeh, R. Sufiani, Y.M. Khiavi, Phys. Rev. A 84, 012102 (2011)
Zh. Bai, Sh. Du, arXiv:1503.07103 (2015)
W.K. Wootters, Int. J. Quantum Inform. 04, 219 (2006)
A. Peres, W.K. Wootters, Phys. Rev. Lett. 66, 1119 (1991)
E. Chitambar, M.-H. Hsieh, Phys. Rev. A 88, 020302(R) (2013)
M.A. Jafarizadeh, Y. Mazhari, M. Aali, Quantum Inf. Process. 10, 155 (2010)
D.J. Rowe, M.J. Carvalho, J. Repka, Rev. Mod. Phys. 84, 711 (2012)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jafarizadeh, M., Akhgar, D., Mahmoudi, P. et al. Minimum error discrimination of equi-coherent bosonic states of n-qubit by separable measurement. Eur. Phys. J. D 70, 226 (2016). https://doi.org/10.1140/epjd/e2016-70204-8
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2016-70204-8