Non-Abelian symmetry can increase entanglement entropy

Majidy, Shayan; Lasek, Aleksander; Huse, David A.; Halpern, Nicole Yunger

doi:10.48550/arxiv.2209.14303

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2023

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“…If multiple charges are conserved, entanglement is (on average) promoted if the charges fail to commute with each other. That is, Page curves for non-commuting charges lie above that of commuting charges, as recently pointed out in [12]. Moreover, in the presence of locally conserved charges, the entire charge distributions of initial states are conserved.…”

Section: Introductionmentioning

confidence: 53%

Subsystem trace-distances of two random states

Telles¹,

Micklitz²

2023

J. Phys. A: Math. Theor.

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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 →∞, 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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Section: Introductionmentioning

confidence: 53%