Memory effects in quantum channel discrimination.

We consider quantum-memory assisted protocols for discriminating quantum channels. We show that for optimal discrimination of memory channels, memory assisted protocols are needed. This leads to a new notion of distance for channels with memory, based on the general theory of quantum testers. For discrimination and estimation of sets of independent unitary channels, we prove optimality of parallel protocols among all possible architectures.

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

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

[3]  G. D’Ariano,et al.  Optimal estimation of group transformations using entanglement , 2005, quant-ph/0506267.

[4]  S. Lloyd.  Enhanced Sensitivity of Photodetection via Quantum Illumination , 2008, Science.

[5]  N. Datta,et al.  The coding theorem for a class of quantum channels with long-term memory , 2006, quant-ph/0610049.

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

[7]  R. Werner,et al.  Quantum channels with memory , 2005, quant-ph/0502106.

[8]  C. Macchiavello,et al.  Entanglement-enhanced information transmission over a quantum channel with correlated noise , 2001, quant-ph/0107052.

[9]  M B Plenio,et al.  Spin chains and channels with memory. , 2007, Physical review letters.

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

[11]  G. D’Ariano,et al.  Minimax discrimination of two Pauli channels , 2005, quant-ph/0507081.

[12]  G Chiribella,et al.  Quantum circuit architecture. , 2007, Physical review letters.

[13]  Runyao Duan,et al.  Entanglement is not necessary for perfect discrimination between unitary operations. , 2007, Physical review letters.

[14]  R. Werner,et al.  Reexamination of quantum bit commitment: The possible and the impossible , 2006, quant-ph/0605224.

[15]  Masahide Sasaki,et al.  Unambiguous discrimination among oracle operators , 2007, quant-ph/0702245.

[16]  V. Paulsen.  Completely Bounded Maps and Operator Algebras: Contents , 2003 .

[17]  S. Mancini,et al.  Quantum channels with a finite memory , 2003, quant-ph/0305010.