On the Chernoff bound for efficiency of quantum hypothesis testing

The paper estimates the Chernoff rate for the efficiency of quantum hypothesis testing. For both joint and separate measurements, approximate bounds for the rate are given if both states are mixed, and exact expressions are derived if at least one of the states is pure. The efficiencies of tests with separate and joint measurements are compared. The results are illustrated by a test of quantum entanglement.

[1]  Masahito Hayashi,et al.  On error exponents in quantum hypothesis testing , 2004, IEEE Transactions on Information Theory.

[2]  R. Gill,et al.  State estimation for large ensembles , 1999, quant-ph/9902063.

[3]  C. H. Bennett,et al.  Quantum nonlocality without entanglement , 1998, quant-ph/9804053.

[4]  C. S. Wood,et al.  Deterministic Entanglement of Two Trapped Ions , 1998 .

[5]  O. Barndorff-Nielsen,et al.  On quantum statistical inference , 2003, quant-ph/0307189.

[6]  Richard D. Gill,et al.  Asymptotics in quantum statistics , 2001, math/0405571.

[7]  Jeroen van de Graaf,et al.  Cryptographic Distinguishability Measures for Quantum-Mechanical States , 1997, IEEE Trans. Inf. Theory.

[8]  K. R. Parthasarathy On Consistency of the Maximum Likelihood Method in Testing Multiple Quantum Hypotheses , 2001 .

[9]  I. N. Sanov On the probability of large deviations of random variables , 1958 .

[10]  J. Cirac,et al.  Quantum Computations with Cold Trapped Ions. , 1995, Physical review letters.

[11]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[12]  W. Hoeffding Asymptotically Optimal Tests for Multinomial Distributions , 1965 .

[13]  H. Chernoff A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[14]  A. Holevo Statistical structure of quantum theory , 2001 .

[15]  H. Yuen Quantum detection and estimation theory , 1978, Proceedings of the IEEE.

[16]  R. Werner,et al.  Estimating the spectrum of a density operator , 2001, quant-ph/0102027.

[17]  N. Mermin Quantum theory: Concepts and methods , 1997 .

[18]  Manuel A. Ballester Estimation of unitary quantum operations , 2004 .

[19]  Carlton M. Caves,et al.  Mathematical techniques for quantum communication theory , 1995 .

[20]  Tomohiro Ogawa,et al.  Strong converse and Stein's lemma in quantum hypothesis testing , 2000, IEEE Trans. Inf. Theory.

[21]  L. Santaló Integral geometry and geometric probability , 1976 .