Quantum Renyi relative entropies on a spin chain with interface defects

Arias, Raúl

doi:10.1088/1742-5468/ab5d0d

Cited by 4 publications

(5 citation statements)

References 36 publications

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“…In general, the behaviour of the half-chain entanglement depends crucially on whether a density bias is applied between the fermionic leads separated by the defect. For the unbiased case, one finds a logarithmic growth of entanglement, with the same prefactor that governs the equilibrium entropy scaling in the presence of a defect, which was studied both numerically and analytically for hopping chains [15][16][17][18][19] as well as in the continuum [20,21]. The exact same relation can actually be found in conformal field theory (CFT) calculations [22], connecting entropy dynamics after the quench to the problem of ground-state entanglement across a conformal interface [23,24].…”

Section: Introductionmentioning

confidence: 72%

Time evolution of entanglement negativity across a defect

Gruber¹,

Eisler²

2020

J. Phys. A: Math. Theor.

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We consider a quench in a free-fermion chain by joining two homogeneous half-chains via a defect. The time evolution of the entanglement negativity is studied between adjacent segments surrounding the defect. In case of equal initial fillings, the negativity grows logarithmically in time and essentially equals one-half of the Rényi mutual information with index α = 1/2 in the limit of large segments. In sharp contrast, in the biased case one finds a linear increase followed by the saturation at an extensive value for both quantities, which is due to the backscattering from the defect and can be reproduced in a quasiparticle picture. Furthermore, a closer inspection of the subleading corrections reveals that the negativity and the mutual information have a small but finite difference in the steady state. Finally, we also study a similar quench in the XXZ spin chain via density-matrix renormalization group methods and compare the results for the negativity to the fermionic case.

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Section: Introductionmentioning

confidence: 72%

Time evolution of entanglement negativity across a defect

Gruber¹,

Eisler²

2020

J. Phys. A: Math. Theor.

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“…As far as the authors are aware, the expressions (6.26) and (6.33) for relative entropy and its variance have not appeared in the literature before. However, sandwiched Rényi relative entropy between RDMs of a free fermion chain was computed in [35] (see also [36]) and one can check that the relative entropy (6.26) matches with the first derivative of their expression. Unfortunately, we did not manage to compute the second derivative to see whether the result matches with the variance.…”

Section: Relative Entropy and Its Variance For Free Fermionsmentioning

confidence: 99%

“…In quantum field theory and many-body theory, there has been much progress in studying well-known distinguishing measures both analytically and numerically. For example, in the context of conformal field theory and critical lattice models, there are studies of fidelity F (ρ, σ) [1,2], relative entropy S(ρ σ) [2][3][4][5][6][7], generalized divergences [8][9][10][11][12][13] and trace distance D(ρ, σ) = 1 2 ρ − σ [14,15]. In this work, our focus is instead to distinguish two states by measurements.…”

Section: Introductionmentioning

confidence: 99%

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Quantum hypothesis testing in many-body systems

2021

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One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as ``is the system in state A or state B?''. In quantum mechanics, the latter type of measurements can be studied and optimized using the framework of quantum hypothesis testing. In many cases one can explicitly find the optimal measurement in the limit where one has simultaneous access to a large number n of identical copies of the system, and estimate the expected error as n becomes large. Interestingly, error estimates turn out to involve various quantum information theoretic quantities such as relative entropy, thereby giving these quantities operational meaning. In this paper we consider the application of quantum hypothesis testing to quantum many-body systems and quantum field theory. We review some of the necessary background material, and study in some detail the situation where the two states one wants to distinguish are parametrically close. The relevant error estimates involve quantities such as the variance of relative entropy, for which we prove a new inequality. We explore the optimal measurement strategy for spin chains and two-dimensional conformal field theory, focusing on the task of distinguishing reduced density matrices of subsystems. The optimal strategy turns out to be somewhat cumbersome to implement in practice, and we discuss a possible alternative strategy and the corresponding errors.

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“…The relative entropy attracted a lot of interests from the field theory community, see e.g. [33][34][35][36][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57], also, but not only, for its relation with the modular Hamiltonian [58,59] and quantum null energy condition [60]. However, the relative entropy has a major drawback as a measure of distinguishability.…”

Section: Introductionmentioning

confidence: 99%

Symmetry resolved relative entropies and distances in conformal field theory

Capizzi,

Calabrese

2021

Preprint

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We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory having an internal U(1) symmetry. We provide analytic expressions for the charged moments corresponding to the resolution of both relative entropies and distances for general integer n. For the relative entropies, these formulas are manageable and the analytic continuation to n = 1 can be worked out in most of the cases. Conversely, for the distances the corresponding charged moments become soon untreatable as n increases. A remarkable result is that relative entropies and distances are the same for all symmetry sectors, i.e. they satisfy entanglement equipartition, like the entropies. Moreover, we exploit the OPE expansion of composite twist fields, to provide very general results when the subsystem is much smaller than the total system. We focus on the massless compact boson and our results are tested against exact numerical calculations in the XX spin chain.

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Quantum Renyi relative entropies on a spin chain with interface defects

Cited by 4 publications

References 36 publications

Time evolution of entanglement negativity across a defect

Time evolution of entanglement negativity across a defect

Quantum hypothesis testing in many-body systems

Symmetry resolved relative entropies and distances in conformal field theory

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