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arXiv · 2210.03213

Subsystem Trace-Distances of Two Random States

Joaquim Telles de Miranda·Tobias Micklitz
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Abstract

We study two-state discrimination in chaotic quantum systems. Assuming that one of two $N$-qubit pure states has been randomly selected, the probability to correctly identify the selected state from an optimally chosen experiment involving a subset of $N-N_B$ qubits is given by the trace-distance of the states, with $N_B$ qubits partially traced out. In the thermodynamic limit $N\to\infty$, the average subsystem trace-distance for random pure states makes a sharp, first order transition from unity to zero at $f=1/2$, as the fraction $f=N_B/N$ of unmeasured qubits is increased. We analytically calculate the corresponding crossover for finite numbers $N$ of qubits, study how it is affected by the presence of local conservation laws, and test our predictions against exact diagonalization of models for many-body chaos.

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Joaquim Telles de Miranda, Tobias Micklitz. 2022-10-06. Subsystem Trace-Distances of Two Random States. https://doi.org/10.1088/1751-8121/acc770

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