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arXiv:0908.2674 · Journal of Physics A Mathematical and Theoretical

Quantum energy teleportation with an electromagnetic field: discrete versus continuous variables

Masahiro Hotta

Published Feb 18, 2010• 28 citations
arXivHTMLPDF

Abstract

It is well known that usual quantum teleportation protocols cannot transport energy. Recently, new protocols called quantum energy teleportation (QET) have been proposed, which transport energy by local operations and classical communication with the ground states of many-body quantum systems. In this paper, we compare two different QET protocols for transporting energy with the electromagnetic field. In the first protocol, a 1/2 spin (a qubit) is coupled with the quantum fluctuation in the vacuum state and measured in order to obtain one-bit information about the fluctuation for the teleportation. In the second protocol, a harmonic oscillator is coupled with the fluctuation and measured in order to obtain continuous-variable information about the fluctuation. In the spin protocol, the amount of teleported energy is suppressed by an exponential damping factor when the amount of input energy increases. This suppression factor becomes power damping in the case of the harmonic oscillator protocol. Therefore, it is concluded that obtaining more information about the quantum fluctuation leads to teleporting more energy. This result suggests a profound relationship between energy and quantum information.

DOI
10.1088/1751-8113/43/10/105305

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It is well known that usual quantum teleportation protocols cannot transport energy. Recently, new protocols called quantum energy teleportation (QET) have been proposed, which transport energy by local operations and classical communication with the ground states of many-body quantum systems. In this paper, we compare two different QET protocols for transporting energy with the electromagnetic field. In the first protocol, a 1/2 spin (a qubit) is coupled with the quantum fluctuation in the vacuum state and measured in order to obtain one-bit information about the fluctuation for the teleportation. In the second protocol, a harmonic oscillator is coupled with the fluctuation and measured in order to obtain continuous-variable information about the fluctuation. In the spin protocol, the amount of teleported energy is suppressed by an exponential damping factor when the amount of input energy increases. This suppression factor becomes power damping in the case of the harmonic oscillator protocol. Therefore, it is concluded that obtaining more information about the quantum fluctuation leads to teleporting more energy. This result suggests a profound relationship between energy and quantum information.
Quantum energy teleportation (QET) is the phenomenon in which locally inaccessible energy is activated as extractable work through collaborative local operations and classical communication (LOCC) with an entangled partner. It closely resembles the more well-known quantum information teleportation (QIT) where quantum information can be sent through an entangled pair with LOCC. It is tempting to ask how QET is related to QIT. Here we report a first study of this connection. Despite the apparent similarity, we show that these two phenomena are not only distinct but moreover are mutually competitive. We show a perturbative trade-off relation between their performance in a thermal entangled chaotic many-body system, in which both QET and QIT are simultaneously implemented through a traversable wormhole in an emergent spacetime. Motivated by this example, we study a generic setup of two entangled qudits and prove a universal non-perturbative trade-off bound. It shows that for any teleportation protocol, the overall performance of QET and QIT together is constrained by the entanglement resource. We discuss some explanations of our results.
Quantum energy teleportation (QET) is, from the operational viewpoint of distant protocol users, energy transportation via local operations and classical communication. QET has various links to fundamental research fields including black-hole physics, the quantum theory of Maxwell's demon, and quantum entanglement in condensed-matter physics. However, the energy that has been extracted using a previous QET protocol is limited by the distance between two protocol users; the upper bound of the energy being inversely proportional to the distance. In this paper, we prove that introducing squeezed vacuum states with local vacuum regions between the two protocol users overcomes this limitation, allowing energy teleportation over practical distances.
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.
FINDING: Quantum teleportation transmits quantum *states* (information), not matter; recent work extends this to teleporting *energy* via superconducting hardware, with earth-to-space distance records (1,400 km). | MATH: Core protocol: Bell-state measurement + classical communication (2 classical bits) + unitary correction (Pauli operators X,Z,iYX, Z, iYX,Z,iY). State transfer fidelity F=⟨ψ∣ρout∣ψ⟩F = \langle \psi | \rho_{\text{out}} | \psi \rangleF=⟨ψ∣ρout​∣ψ⟩ — experiments report F>0.9F > 0.9F>0.9 (often ~0.9–0.99). Energy teleportation (arXiv:2301.02666) uses a quantum energy teleportation (QET) protocol: local measurement on one qubit, conditional feedback on a distant entangled qubit, extracting energy from the vacuum fluctuation of the entangled pair. Key quantity: extractable energy ΔE=⟨HB⟩after−⟨HB⟩before>0\Delta E = \langle H_B \rangle_{\text{after}} - \langle H_B \rangle_{\text{before}} > 0ΔE=⟨HB​⟩after​−⟨HB​⟩before​>0, bounded by entanglement entropy S(ρAB)S(\rho_{AB})S(ρAB​) and local operation classical communication (LOCC) constraints. No new fundamental constants Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
We establish a novel quantum protocol called Timelike Quantum Energy Teleportation (TQET) between two separated parties AAA and BBB, designed for transporting quantum energy across spacetime. The amount of energy gained through TQET is always greater than or equal to that obtained via natural time evolution for any spin chain where AAA and BBB are distinguishable. This protocol uses temporal and spatial quantum correlations between agents separated by space and time. The energy supplier injects energy into the system by measuring the ground state of a many-body system that evolves over time, while the distant recipient performs a conditional operation using feedback from the supplier. When Bob acts immediately after receiving Alice's outcome, the protocol reduces to conventional QET. We present a proof-of-concept demonstration in the Ising model using quantum simulations. TQET increases energy efficiency from approximately 3\% to around 40\%, representing over a 13-fold improvement compared to QET. Furthermore, we analyzed the relationship between entanglement in time and TQET, validating the role of temporal correlations in energy activation between agents across spacetime.
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.