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arXiv:1710.00005 · Physical Review A

Quantum information or entanglement transfer between subsystems

Steven B. Giddings, Massimiliano Rota

Published Dec 26, 2018• 12 citations
arXivHTMLPDF

Abstract

The size of quantum information---or entanglement---transfer rates between subsystems is a generic question in problems ranging from decoherence in quantum computation and sensing, to quantum underpinnings of thermodynamics, to the behavior of quantum black holes. We investigate such rates for given couplings between subsystems, for sufficiently random subsystem evolution, and find evidence of a conjectured relation of these rates to the size of the couplings. This provides a direct connection between entanglement transfer and the microphysical couplings in the Hamiltonian that are responsible for it.

DOI
10.1103/physreva.98.062329

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The size of quantum information---or entanglement---transfer rates between subsystems is a generic question in problems ranging from decoherence in quantum computation and sensing, to quantum underpinnings of thermodynamics, to the behavior of quantum black holes. We investigate such rates for given couplings between subsystems, for sufficiently random subsystem evolution, and find evidence of a conjectured relation of these rates to the size of the couplings. This provides a direct connection between entanglement transfer and the microphysical couplings in the Hamiltonian that are responsible for it.
General features of information transfer between quantum subsystems, via unitary evolution, are investigated, with applications to the problem of information transfer from a black hole to its surroundings. A particularly direct form of quantum information transfer is ``subsystem transfer,'' which can be characterized by the saturation of a subadditivity inequality. We also describe more general unitary quantum information transfer, and categorize different models for black hole evolution. Evolution that only creates paired excitations inside/outside the black hole is shown not to extract information, but information-transferring models exist both in the ``saturating'' and ``nonsaturating'' category. The former more closely capture thermodynamic behavior; the latter generically have an enhanced energy flux, beyond that of Hawking.
We study entanglement transfer in a minimal model of two qubits that are coupled with one another through an antiferromagnetic Heisenberg exchange (J~\tilde{J}J~), and where one of them is additionally coupled to a fermionic environment through another antiferromagnetic Heisenberg exchange (JKJ_{K}JK​). By tuning the coupling ratio JK/J~J_{K}/\tilde{J}JK​/J~, the system undergoes a quantum phase transition at T=0T=0T=0, accompanied by a redistribution of entanglement from the d′−dd'-dd′−d qubit-subsystem to the environment. Remarkably, the resulting physics exhibits properties that bear analogy with a quantum-information theoretic perspective of the physics of black hole thermodynamics. Carefully selected bipartite and tripartite mutual information measures displays behaviour analogous to the dynamical evolution of black hole entropy, Hawking entropy, and the Page curve expected during the process of evaporation. An effective temperature scale is obtained from the variation of the ground state energy with respect to changes in the bipartite mutual information between the subsystem and the bath. A steady growth of this temperature with the coupling ratio resembles that of the Hawking temperature with the inverse mass of the black hole. Concomitantly, the emergence of non-Fermi liquid behaviour observed near the quantum critical point and in the strong-coupling phase resembles strange-metal-like physics expected near the event horizon from a holographic duality perspective. Our results establish the minimal model as a platform for studying entanglement transfer and information scrambling within a fully unitary quantum framework, and offer new insights into a resolution of the black hole information paradox.
The thermodynamic entropy of an isolated system is given by its von Neumann entropy. Over the last few years, there has been an intense activity to understand the thermodynamic entropy from the principles of quantum mechanics. More specifically, is there a relation between the (von Neumann) entropy of entanglement between a system and some (separate) environment and the thermodynamic entropy? It is difficult to obtain the relation for many body systems, hence, most of the work in the literature has focused on small number systems. In this work, we consider black holes—which are simple yet macroscopic systems—and show that a direct connection could not be made between the entropy of entanglement and the Hawking temperature. In this work, within the adiabatic approximation, we explicitly show that the Hawking temperature is indeed given by the rate of change of the entropy of entanglement across a black hole’s horizon with regard to the system energy. This is yet other numerical evidence leading to understanding the key features of black-hole thermodynamics from the viewpoint of quantum information theory.
My aim in this paper is a modest one. I do not have any particular thesis to advance about the nature of entanglement, nor can I claim novelty for any of the material I shall discuss. My aim is simply to raise some questions about entanglement that spring naturally from certain developments in quantum information theory and are, I believe, worthy of serious consideration by philosophers of science. The main topics I discuss are different manifestations of quantum nonlocality, entanglement-assisted communication, and entanglement thermodynamics.
The central question in this article is how information does leak out from black holes. Relying on algebraic arguments and the concept of superselection sectors, we propose the existence of certain operators whose correlations extend across the black hole atmosphere and range into the interior. Contained in the full algebra, these black hole intertwiners will not belong to the subalgebra describing semiclassical bulk physics. We study this proposal in the context of operator reconstructions for code spaces containing a large number of microstates. As long as the atmosphere is excluded from a particular subsystem, the global state seen under the action of the associated algebra is maximally mixed and therefore described by a single classical background. Once the relevant correlations are encoded, i.e. if the algebra is sufficiently enlarged, perfect state distinguishability becomes possible. We arrive at this by computing the von Neumann entropy which may explain the result obtained by applying the quantum extremal surface prescription to the mixed state. We then examine these insights in the context of black hole evaporation and argue that information is transferred to the radiation via black hole intertwiners. We derive the Page curve. The mechanism above suggests that black hole information is topologically protected. An infalling observer would experience no drama. This may resolve the unitarity problem without running into any firewall or state puzzle, the latter being evident in generalized entropy computations. We also examine the question of how certain wormhole topologies may be understood given these findings. We argue that their occurrence in gravity replica computations may be related to the maximal correlation between radiation and atmosphere surrounding the old black hole. This may suggest a connection between topology change and near horizon quantum gravitational effects.