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.

arXiv comment9 pages, 4 figures, published version

References in corpus (25)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Average Entropy of a Subsystem
• Quantum thermalization through entanglement in an isolated many-body system
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Quantum state discrimination and its applications
• Canonical Thermal Pure Quantum State
• Thermal Pure Quantum States at Finite Temperature
• Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians
• Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
• Subsystem ETH
• Universality in volume law entanglement of pure quantum states
• Typical entanglement entropy in the presence of a center: Page curve and its variance
• Symmetry-resolved Page curves
• Subsystem Trace Distance in Quantum Field Theory
• Thermalization of entanglement
• Distinguishability of generic quantum states
• Symmetry-resolved entanglement in a long-range free-fermion chain
• Non-Abelian symmetry can increase entanglement entropy
• Distinguishing Random and Black Hole Microstates
• Quantum ergodicity in the many-body localization problem
• Page curve and symmetries
• Maximum entropy quantum state distributions

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