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arXiv:2301.11712 · Physical review. D/Physical review. D.

Criticality of quantum energy teleportation at phase transition points in quantum field theory

Kazuki Ikeda

Published Apr 17, 2023• 31 citations
arXivHTMLPDF

Abstract

Quantum field theory can be a new medium for communication through quantum energy teleportation. We perform a demonstration of quantum energy teleportation with a relativistic fermionic field theory of self-coupled fermions, called the massive Thirring model. Our results reveal that there is a close relationship between the amount of energy teleported and the phase diagram of the theory. In particular, we show that the teleported energy peaks near the phase transition points. Since these results are obtained by measuring the two local subsystems, the noise from the quantum computation can be considerably reduced, allowing for efficient quantum simulations. Moreover, it is a new entanglement-based method that reveals global structure through local measurements.

DOI
10.1103/physrevd.107.l071502

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arXiv:2402.00479•Physical review. D/Physical review. D.•Nov 12, 2024•9 citations
Quantum field theory can be a new medium for communication through quantum energy teleportation. We perform a demonstration of quantum energy teleportation with a relativistic fermionic field theory of self-coupled fermions, called the massive Thirring model. Our results reveal that there is a close relationship between the amount of energy teleported and the phase diagram of the theory. In particular, we show that the teleported energy peaks near the phase transition points. Since these results are obtained by measuring the two local subsystems, the noise from the quantum computation can be considerably reduced, allowing for efficient quantum simulations. Moreover, it is a new entanglement-based method that reveals global structure through local measurements.
Quantum Energy Teleportation provides a testbed for modern ideas involving the inter­play between quantum correlations and energy in the quantum thermodynamical regime. In this work, we provide a new class of Quantum Energy Teleportation protocols optimized for harnessing maximal amounts of correlations between subsystems. We also construct new measurement protocols for quantum fields which provide significant improvements for entanglement harvesting. Finally, we construct an efficient formalism for computing changes in energy due to localized interactions in quantum field theory.
We consider a quantum energy teleportation (QET) method to replicate the phase diagram of a one-dimensional XXZXXZXXZ spin chain featuring a Kondo effect coupling. In this setup, the energy supplier and receiver are spatially separated from the point impurity and do not interact directly with it. Nonetheless, they may successfully generate phase diagrams that closely mirror those produced via exact diagonalization. This can be achieved using only local operations on their respective subsystems, supplemented by classical communication. This feat is made possible due to a critical connection between the energy obtained through the QET approach and the system's quantum entanglement entropy. To substantiate these findings, we initially demonstrate that the quantum entanglement entropy serves as the relevant order parameter for the system. Intriguingly, changes in the gap spacing of the entanglement spectra align with the locations of peaks in both entanglement entropy and energy, as determined by QET. We hypothesize that this theoretical framework could, for example, be validated experimentally using a one-dimensional chain of Rydberg atoms.
Quantum energy teleportation (QET) has been studied in continuum field theory and in lattice many-body systems, but the relation between the two within a single interacting model is still not well understood. To address this question, we consider the massive Thirring model, equivalently the sine--Gordon theory. In the continuum, the trigonometric measurement is a weak binary Positive Operator-Valued Measure (POVM), and its leading signal is set by a conserved-current correlator in the bosonized theory, with both gapless behavior and gapped large-distance asymptotics. On the lattice, the conventional protocol does not access this neutral current sector. For Alice's local measurement, a lattice U(1)U(1)U(1) selection rule removes the neutral current contribution from Bob's subsystem, and the separated signal lies in charged sectors. On the same lattice Hamiltonian we construct a neutral current protocol whose weak signal is exactly a coarse-grained current correlator and whose extracted energy scales quadratically with the measurement strength. This identifies the neutral sector shared by the lattice and continuum descriptions, while separating it from the charged sector that governs the conventional qubit protocol.
Distinguishing non-local orders, including global and topological orders of states through solely local operations and classical communications (LOCC), is a highly non-trivial and challenging task since the topology of states is determined by the global characteristics of the many-body system, such as the system's symmetry and the topological space it is based on. Here, we report that we reproduced the phase diagram of Ising model and symmetry protected topological phases using the quantum energy teleportation protocol, which foresees non-trivial energy transfer between remote observers using the entanglement nature of the ground state and LOCC. The model we use includes the Haldane model, the AKLT model, and the Kitaev model. Therefore, our method paves a new general experimental framework to determine and quantify phase transitions in various condensed matter physics and statistical mechanics.
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.
In this article, we explore a feedback-control protocol in different quantum field theories (QFTs) to study the quantum correlation in nonunitary evolution of quantum systems. Traditional studies on QFTs focus on quantum entanglement of pure states under the unitary evolution, however, we examine quantum correlation in mixed states using quantum energy teleportation (QET), which is an energy transfer protocol by utilizing ground state entanglement, and introduce quantum discord as a measure. QET involves a midcircuit measurement, which disrupts pure state entanglement. Despite this, our analysis demonstrates that quantum discord maintains the correlation throughout the QET process. We conducted numerical analyses with benchmark models including the Nambu-Jona-Lasinio (NJL) model, revealing that quantum discord consistently acts as an order parameter for phase transitions. The model is extended in a way that it has both the chiral chemical potential and the chemical potential, which are useful to study the phase structures mimicking the chiral imbalance between left- and right- quarks coupled to the chirality density operator. In all cases we studied, the quantum discord behaved as an order parameter of the phase transition. Published by the American Physical Society 2024