Subsystem Trace-Distances of Two Random States

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.

9 pages, 4 figures, published version

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Cited by in corpus (3)

• Order $p$ quantum Wasserstein distances from couplings
• Identifying quantum many-body integrability and chaos using eigenstates trace distances
• Efficient computation of average subsystem Bures distance between fermionic Gaussian states