Quantum entanglements, ε-entropy, and value of quantum information

Justin R. David, Surbhi Khetrapal, S. Prem Kumar

We study the time evolution of single interval Rényi and entanglement entropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width ϵ. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Rényi and entanglement entropies at order ϵ2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the ϵ2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential μ. We calculate the time dependence of the order ϵ2 correction to the entanglement entropy for small μ, and show that the contribution at order μ 2 is universal. We verify our arguments against exact results for minimal models and the free fermion theory.

Zeilinger

D. A. M. Abo-Kahla, Ahmed Farouk

Throughout this paper, we describe an analytical solution for a three-qubit system characterized by a finite temperature within a thermodynamic limit influenced by a quantum spin environment. As applications to the presented solution, we investigate the effect of the temperature, the coupling constant ϵ 0 within the spin- qubit system and an external magnetic field on the three-particles residual entanglement N a b c , the concurrence C ( ρ ) , the information entropy H ( σ Z ) and the linear entropy P P ( t ) . The results show an inverse relationship between the entanglement and entropy, where the degree of both is controlled by controlling the temperature T and the coupling constant ϵ 0 .

Steven T. Flammia, Ryan O’Donnell

For quantum state tomography on rank- r dimension- d states, we show that O~(r.5d1.5/ϵ)≤O~(d2/ϵ) copies suffice for accuracy ϵ with respect to (Bures) χ2 -divergence, and O~(rd/ϵ) copies suffice for accuracy ϵ with respect to quantum relative entropy. The best previous bound was O~(rd/ϵ)≤O~(d2/ϵ) with respect to infidelity; our results are an improvement since infidelity is bounded above by both the relative entropy and the χ2 -divergence. For algorithms that are required to use single-copy measurements, we show that O~(r1.5d1.5/ϵ)≤O~(d3/ϵ) copies suffice for χ2 -divergence, and O~(r2d/ϵ) suffice for relative entropy.Using this tomography algorithm, we show that O~(d2.5/ϵ) copies of a d×d -dimensional bipartite state suffice to test if it has quantum mutual information 0 or at least ϵ . As a corollary, we also improve the best known sample complexity for the classical version of mutual information testing to O~(d/ϵ) .

Andrew G. White, Daniel F. V. James, William J. Munro +1 more