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arXiv:0911.3430 · Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

Ground-State Entanglement Gives Birth to Quantum Energy Teleportation

Masahiro Hotta

Published Jan 1, 2010• 2 citations
arXivHTMLPDF
DOI
10.1007/978-3-642-11731-2_9

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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.
A protocol of quantum energy teleportation is proposed for a one-dimensional harmonic chain. A coherent-state positive operator-valued measure (POVM) measurement is performed on coupled oscillators of the chain in the ground state accompanied by energy infusion to the system. This measurement consumes a part of the ground-state entanglement. Depending on the measurement result, a displacement operation is performed on a distant oscillator accompanied by energy extraction from the zero-point fluctuation of the oscillator. We find that the amount of consumed entanglement is bounded from below by a positive value that is proportional to the amount of teleported energy.
Many-body quantum systems in the ground states have zero-point energy due to the uncertainty relation. In many cases, the system in the ground state accompanies spatially entangled energy density fluctuation via the noncommutativity of the energy density operators, though the total energy takes a fixed value, i.e., the lowest eigenvalue of the Hamiltonian. Quantum energy teleportation (QET) is a protocol for the extraction of the zero-point energy out of one subsystem using information of a remote measurement of another subsystem. From an operational viewpoint of protocol users, QET can be regarded as an effective rapid energy transportation without breaking all physical laws, including causality and local energy conservation. In the protocol, the ground-state entanglement plays a crucial role. In this paper, we show analytically for a general class of spin-chain systems that the entanglement entropy is lower bounded by a positive quadratic function of the teleported energy between the regions of a QET protocol. This supports a general conjecture that ground-state entanglement is an evident physical resource for energy transportation in the context of QET. The result may also deepen our understanding of the energy density fluctuation in condensed-matter systems from a perspective of quantum information theory.