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Quantum Energy Teleportation Between Spin Particles in a Gibbs State

Michael R. Frey, K. Gerlach, Masahiro Hotta

Published Jan 1, 2013• 13 citations
OpenAlex

Abstract

Energy in a multipartite quantum system appears from an operational perspective to be distributed to some extent non-locally because of correlations extant among the system's components. This non-locality allows users to transfer, in effect, locally accessible energy between sites of different system components by local operations and classical communication (LOCC). Quantum energy teleportation is a three-step LOCC protocol, accomplished without an external energy carrier, for effectively transferring energy between two physically separated, but correlated, sites. We apply this LOCC teleportation protocol to a model Heisenberg spin particle pair initially in a quantum thermal Gibbs state, making temperature an explicit parameter. We find in this setting that energy teleportation is possible at any temperature, even at temperatures above the threshold where the particles' entanglement vanishes. This shows for Gibbs spin states that entanglement is not fundamentally necessary for energy teleportation; correlation other than entanglement can suffice. Dissonance-quantum correlation in separable states-is in this regard shown to be a quantum resource for energy teleportation, more dissonance being consistently associated with greater energy yield. We compare energy teleportation from particle A to B in Gibbs states with direct local energy extraction by a general quantum operation on B and find a temperature threshold below which energy extraction by a local operation is impossible. This threshold delineates essentially two regimes: a high temperature regime where entanglement vanishes and the teleportation generated by other quantum correlations yields only vanishingly little energy relative to local extraction and a second low-temperature teleportation regime where energy is available at B only by teleportation.

Related papers

Quantum energy teleportation between spin particles in a Gibbs state

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Energy teleportation with no energy carrier between two physically separated sites was demonstrated in principle by M. Hotta in 2008. His demonstration used a three-step protocol applied to a Heisenberg spin particle pair initially in its fully entangled ground state. We apply the Hotta protocol to the same Heisenberg pair but now suppose the pair is, more generally, in a thermal state, introducing temperature as an explicit parameter. These thermal states show a degree of quantum correlation (thermal discord) at all temperatures. We find that at any temperature energy teleportation is possible with the Hotta protocol, even at temperatures beyond the threshold where the particles’ entanglement vanishes. This shows that entanglement is not fundamentally necessary for energy teleportation; quantum discord generally can suffice. It is also a new instance in which quantum dissonance (discord without entanglement) is seen to act as a quantum resource.

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We propose a protocol for quantum energy teleportation which transports energy in spin chains to distant sites only by local operations and classical communication. By utilizing ground-state entanglement and notion of negative energy density region, energy is teleported without breaking any physical laws including causality and local energy conservation. Because not excited physical entity but classical information is transported in the protocol, the dissipation Quantum entanglement opens the door to several interesting quantum phenomena, including quantum teleportation (QT) [1], by which an unknown quantum state can be teleported to a distant place by local operations and classical communication (LOCC). However, QT cannot transport excitation

•Aug 4, 2013•63 citations
Energy in a multipartite quantum system appears from an operational perspective to be distributed to some extent non-locally because of correlations extant among the system's components. This non-locality allows users to transfer, in effect, locally accessible energy between sites of different system components by local operations and classical communication (LOCC). Quantum energy teleportation is a three-step LOCC protocol, accomplished without an external energy carrier, for effectively transferring energy between two physically separated, but correlated, sites. We apply this LOCC teleportation protocol to a model Heisenberg spin particle pair initially in a quantum thermal Gibbs state, making temperature an explicit parameter. We find in this setting that energy teleportation is possible at any temperature, even at temperatures above the threshold where the particles' entanglement vanishes. This shows for Gibbs spin states that entanglement is not fundamentally necessary for energy teleportation; correlation other than entanglement can suffice. Dissonance-quantum correlation in separable states-is in this regard shown to be a quantum resource for energy teleportation, more dissonance being consistently associated with greater energy yield. We compare energy teleportation from particle A to B in Gibbs states with direct local energy extraction by a general quantum operation on B and find a temperature threshold below which energy extraction by a local operation is impossible. This threshold delineates essentially two regimes: a high temperature regime where entanglement vanishes and the teleportation generated by other quantum correlations yields only vanishingly little energy relative to local extraction and a second low-temperature teleportation regime where energy is available at B only by teleportation.
Energy in a multipartite quantum system appears from an operational perspective to be distributed to some extent non-locally because of correlations extant among the system's components. This non-locality allows users to transfer, in effect, locally accessible energy between sites of different system components by local operations and classical communication (LOCC). Quantum energy teleportation is a three-step LOCC protocol, accomplished without an external energy carrier, for effectively transferring energy between two physically separated, but correlated, sites. We apply this LOCC teleportation protocol to a model Heisenberg spin particle pair initially in a quantum thermal Gibbs state, making temperature an explicit parameter. We find in this setting that energy teleportation is possible at any temperature, even at temperatures above the threshold where the particles' entanglement vanishes. This shows for Gibbs spin states that entanglement is not fundamentally necessary for energy teleportation; correlation other than entanglement can suffice. Dissonance—quantum correlation in separable states—is in this regard shown to be a quantum resource for energy teleportation, more dissonance being consistently associated with greater energy yield. We compare energy teleportation from particle A to B in Gibbs states with direct local energy extraction by a general quantum operation on B and find a temperature threshold below which energy extraction by a local operation is impossible. This threshold delineates essentially two regimes: a high temperature regime where entanglement vanishes and the teleportation generated by other quantum correlations yields only vanishingly little energy relative to local extraction and a second low-temperature teleportation regime where energy is available at B only by teleportation.
Energy teleportation with no energy carrier between two physically separated sites was demonstrated in principle by M. Hotta in 2008. His demonstration used a three-step protocol applied to a Heisenberg spin particle pair initially in its fully entangled ground state. We apply the Hotta protocol to the same Heisenberg pair but now suppose the pair is, more generally, in a thermal state, introducing temperature as an explicit parameter. These thermal states show a degree of quantum correlation (thermal discord) at all temperatures. We find that at any temperature energy teleportation is possible with the Hotta protocol, even at temperatures beyond the threshold where the particles’ entanglement vanishes. This shows that entanglement is not fundamentally necessary for energy teleportation; quantum discord generally can suffice. It is also a new instance in which quantum dissonance (discord without entanglement) is seen to act as a quantum resource.
In this work, we explore quantum energy teleportation (QET) protocols, focusing on their behavior at finite temperatures , in ground and excited states. We analyze the role of entanglement as a resource for QET, particularly in thermal states, and compare the performance of QET across these initial states. We then introduce a method to extract ground-state energy through a protocol that employs only quantum measurements, local operations, and classical communication (LOCC), without requiring the ground state to be quantum correlated either through entanglement or quantum discord. To illustrate this, we propose a minimal model comprising two interacting qubits. These findings indicate that, in addition to the established QET framework where quantum correlation serves as a resource, it is possible to extract energy from an product ground state. This broadens the scope of QET's applicability across diverse quantum systems.
Although extraction of energy from the ground state is forbidden, one can utilize Quantum Energy Teleportation (QET) protocol for energy extraction -- a two-step protocol involving quantum measurements followed by LOCC. This is an unique method to ``extract energy from ground states'' of quantum systems. QET requires some correlation in the ground state, and entanglement correlation plays a crucial roles as a resource. The general belief is that if the ground state is quantum-correlated via entanglement for two different sites in a quantum system, and if we perform measurements on one of the sites, we can find an LOCC for the other site to successfully accomplish QET. In this paper, we show that this belief may not be true in the case of the Toric Code. We demonstrate this by performing a PVM measurements on spins in the Toric Code. Based on the measurement outcomes, we found that there is no LOCC for successful QET.
In general, it is important to identify what is the informational resource for quantum tasks. Quantum energy teleportation (QET) is a quantum task, which attains energy transfer in an operational sense by local operations and classical communication, and is expected to play a role in future development of nano-scale smart grids. We consider QET protocols in a three-element Ising spin system with non-periodic boundary conditions coupled to a thermal bath. The open chain is the minimal model of QET between two edge spins that allows the measurement and operation steps of the QET protocol to be optimized without restriction. It is possible to analyze how two-body correlations of the system, such as mutual information, entanglement and quantum discord, can be resources of this QET at each temperature. In particular, we stress that quantum discord is not the QET resource in some cases, even if arbitrary measurements and operations are available.
We propose a protocol for quantum energy teleportation which transports energy in spin chains to distant sites only by local operations and classical communication. By utilizing ground-state entanglement and notion of negative energy density region, energy is teleported without breaking any physical laws including causality and local energy conservation. Because not excited physical entity but classical information is transported in the protocol, the dissipation Quantum entanglement opens the door to several interesting quantum phenomena, including quantum teleportation (QT) [1], by which an unknown quantum state can be teleported to a distant place by local operations and classical communication (LOCC). However, QT cannot transport excitation