Sample efficient identity testing and independence testing of quantum states
summary
Constructs an explicit independent measurement M on a D-dimensional state whose post-measurement classical distributions satisfy ||P-Q||_2 = ||rho-sigma||_2/(D+1) and ||P||_2,||Q||_2 ≤ sqrt(2/(D+1)), enabling reduction to classical L2-testing. This yields a deterministic identity tester requiring on the order of D^2 copies (up to epsilon factors) and an independence-testing framework using dimension-splitting into log D qubits; a stability lemma shows one-vs-many cuts amplify closeness by at most a factor 5M.
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chapters (10)
- 0:00Intro
- 0:47Distribution Testing
- 2:12Quantum sampling methods
- 2:56Property Testing: Classical vs Quantum
- 3:29Formal Statement-Independent Measurement
- 3:55Framework
- 5:01Identity Testing
- 5:46Independence testing
- 6:31Lower bound for joint measurement
- 8:00Dimension splitting
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