Quantum hypothesis testing with group symmetry
arXiv:0904.0704 · doi:10.1063/1.3234186
Abstract
The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with the problems of the Chernoff bound, the Hoeffding bound and Stein's lemma, and derive bounds on these quantities in terms of their corresponding statistical distance measures. A special emphasis is put on the comparison of the performances of group-invariant and unrestricted measurements.
33 pages
References in corpus (10)
- The Quantum Chernoff Bound
- The Chernoff lower bound for symmetric quantum hypothesis testing
- Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
- The Converse Part of The Theorem for Quantum Hoeffding Bound
- Error exponents in hypothesis testing for correlated states on a spin chain
- Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing
- Large deviations and Chernoff bound for certain correlated states on a spin chain
- Hypothesis testing for Gaussian states on bosonic lattices
- Typical support and Sanov large deviations of correlated states
- Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems
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- Second-order asymptotics for quantum hypothesis testing in settings beyond i.i.d. - quantum lattice systems and more
- Probing light polarization with the quantum Chernoff bound
- On the error exponents of binary state discrimination with composite hypotheses
- Local hypothesis testing between a pure bipartite state and the white noise state
- Quantum hypothesis testing for quantum Gaussian states: Quantum analogues of chi-square, t and F tests
- How not to Rényi generalize the Quantum Conditional Mutual Information
- Binary Discrimination in Quantum Systems via Hypothesis Testing
- Quantum hypothesis testing between qubit states with parity