Quantum Hypothesis Testing and Discrimination of Quantum States

2006 ◽  
pp. 69-91
Keyword(s):  
Hypothesis Testing ◽  
Quantum States ◽  
Quantum Hypothesis ◽  
Quantum Hypothesis Testing

scholarly journals On Composite Quantum Hypothesis Testing

2021 ◽  
Author(s):  
Mario Berta ◽  
Fernando G. S. L. Brandão ◽  
Christoph Hirche
Keyword(s):  
Hypothesis Testing ◽  
Relative Entropy ◽  
Probability Distributions ◽  
Quantum States ◽  
Quantum Hypothesis ◽  
Error Exponent ◽  
Quantum Relative Entropy ◽  
Asymmetric Quantum ◽  
Alternative Hypotheses ◽  
Quantum Hypothesis Testing

AbstractWe extend quantum Stein’s lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponent for testing convex combinations of quantum states $$\rho ^{\otimes n}$$ ρ ⊗ n against convex combinations of quantum states $$\sigma ^{\otimes n}$$ σ ⊗ n can be written as a regularized quantum relative entropy formula. We prove that in general such a regularization is needed but also discuss various settings where our formula as well as extensions thereof become single-letter. This includes an operational interpretation of the relative entropy of coherence in terms of hypothesis testing. For our proof, we start from the composite Stein’s lemma for classical probability distributions and lift the result to the non-commutative setting by using elementary properties of quantum entropy. Finally, our findings also imply an improved recoverability lower bound on the conditional quantum mutual information in terms of the regularized quantum relative entropy—featuring an explicit and universal recovery map.

scholarly journals QUANTUM HYPOTHESIS TESTING AND NON-EQUILIBRIUM STATISTICAL MECHANICS

2012 ◽  
Vol 24 (06) ◽  
pp. 1230002 ◽  
Author(s):  
V. JAKŠIĆ ◽  
Y. OGATA ◽  
C.-A. PILLET ◽  
R. SEIRINGER
Keyword(s):  
Statistical Mechanics ◽  
Hypothesis Testing ◽  
Large Deviation ◽  
Quantum Statistical Mechanics ◽  
Entropy Flow ◽  
Quantum Hypothesis ◽  
Algebraic Setting ◽  
Recent Developments ◽  
Quantum Hypothesis Testing ◽  
Non Equilibrium

We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.

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