k-designs achieve maximal multi-copy discriminability for pure states when N suffices, mixed states outperform beyond that, and quantum offers quadratic advantage over classical in Bayes capacity terms.
Exact distinguishability between real-valued and complex-valued Haar random quantum states
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abstract
Haar random states are fundamental objects in quantum information theory and quantum computing. We study the density matrix resulting from sampling $t$ copies of a $d$-dimensional quantum state according to the Haar measure on the orthogonal group. In particular, we analytically compute its spectral decomposition. This allows us to compute exactly the trace distance between $t$-copies of a real Haar random state and $t$-copies of a complex Haar random state. Using this we show a lower-bound on the approximation parameter of real-valued state $t$-designs and improve the lower-bound on the number of copies required for imaginarity testing.
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The most discriminable quantum states in the multicopy regime
k-designs achieve maximal multi-copy discriminability for pure states when N suffices, mixed states outperform beyond that, and quantum offers quadratic advantage over classical in Bayes capacity terms.