Minimax discrimination of two Pauli channels

We consider the problem of optimally discriminating two Pauli channels in the minimax strategy, maximizing the smallest of the probabilities of correct identification of the channel. We find the optimal input state at the channel and show the conditions under which using entanglement strictly enhances distinguishability. We finally compare the minimax strategy with the Bayesian one.

[1]  C. Helstrom.  Quantum detection and estimation theory , 1969 .

[2]  W. Wootters.  Statistical distance and Hilbert space , 1981 .

[3]  I. D. Ivanović.  How to differentiate between non-orthogonal states , 1987 .

[4]  D. Dieks.  Overlap and distinguishability of quantum states , 1988 .

[5]  A. Peres.  How to differentiate between non-orthogonal states , 1988 .

[6]  S. Braunstein,et al.  Statistical distance and the geometry of quantum states. , 1994, Physical review letters.

[7]  A. Shimony,et al.  Optimal distinction between two non-orthogonal quantum states , 1995 .

[8]  Anthony Chefles,et al.  Unambiguous discrimination between linearly independent quantum states , 1998, quant-ph/9807022.

[9]  John Preskill,et al.  Quantum information and precision measurement , 1999, quant-ph/9904021.

[10]  D. Gottesman.  An Introduction to Quantum Error Correction , 2000, quant-ph/0004072.

[11]  Vedral,et al.  Local distinguishability of multipartite orthogonal quantum states , 2000, Physical review letters.

[12]  G M D'Ariano,et al.  Using entanglement improves the precision of quantum measurements. , 2001, Physical review letters.

[13]  A. Acín.  Statistical distinguishability between unitary operations. , 2001, Physical review letters.

[14]  D. Markham,et al.  Optimal local discrimination of two multipartite pure states , 2001, quant-ph/0102073.

[15]  Dong Yang,et al.  Optimally conclusive discrimination of nonorthogonal entangled states by local operations and classical communications , 2002 .

[16]  Anthony Chefles,et al.  Quantum states: Discrimination and classical information transmission. A review of experimental progress , 2004 .

[17]  M. Raginsky,et al.  Operational distance and fidelity for quantum channels , 2004, quant-ph/0408159.

[18]  M. Keyl.  QUANTUM STATE ESTIMATION AND LARGE DEVIATIONS , 2004 .

[19]  N. Langford,et al.  Distance measures to compare real and ideal quantum processes (14 pages) , 2004, quant-ph/0408063.

[20]  Massimiliano F. Sacchi,et al.  Optimal discrimination of quantum operations , 2005 .

[21]  Massimiliano F. Sacchi,et al.  Entanglement can enhance the distinguishability of entanglement-breaking channels , 2005 .

[22]  E. Bagan,et al.  Multiple-copy two-state discrimination with individual measurements , 2004, quant-ph/0410097.

[23]  G. D’Ariano,et al.  Minimax quantum-state discrimination , 2005, quant-ph/0504048.

[24]  M. Ying,et al.  Optimal conclusive discrimination of two states can be achieved locally , 2004, quant-ph/0407120.