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arXiv:1708.09544 · Physics Letters B

Quantum measurement in two-dimensional conformal field theories: Application to quantum energy teleportation

Wu-zhong Guo, Feng-Li Lin

Published May 17, 2018• 3 citations
arXivHTMLPDF

Abstract

We construct a set of quasi-local measurement operators in 2D CFT, and then use them to proceed the quantum energy teleportation (QET) protocol and show it is viable. These measurement operators are constructed out of the projectors constructed from shadow operators, but further acting on the product of two spatially separated primary fields. They are equivalently the OPE blocks in the large central charge limit up to some UV-cutoff dependent normalization but the associated probabilities of outcomes are UV-cutoff independent. We then adopt these quantum measurement operators to show that the QET protocol is viable in general. We also check the CHSH inequality a la OPE blocks.

DOI
10.1016/j.physletb.2018.05.007

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We construct a set of quasi-local measurement operators in 2D CFT, and then use them to proceed the quantum energy teleportation (QET) protocol and show it is viable. These measurement operators are constructed out of the projectors constructed from shadow operators, but further acting on the product of two spatially separated primary fields. They are equivalently the OPE blocks in the large central charge limit up to some UV-cutoff dependent normalization but the associated probabilities of outcomes are UV-cutoff independent. We then adopt these quantum measurement operators to show that the QET protocol is viable in general. We also check the CHSH inequality a la OPE blocks.
We propose a simplified protocol of quantum energy teleportation (QET) for the holographic conformal field theory in three-dimensional anti--de Sitter space with or without a black hole. As a tentative proposal, we simplify the standard QET by replacing Alice's local measurement with the local projection, which excites the system from the ground state into a particular state dual to a Banados geometry. We then mimic Bob's local operation of the usual QET for extracting energy by deforming the UV surface with a local bump. Adopting the surface-state duality, this deformation corresponds to local unitary. We evaluate the extraction of energy from the holographic stress tensor and find that Bob always gains energy extraction in our protocol. This could be related to the positive energy theorem of the dual gravity. Moreover, the ratio of extraction energy to the injection one is a universal function of the UV surface deformation profile.
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.
The mutual information of measurement of a local operator between two spatial regions characterizes the reduction in the uncertainty of measurement outcomes in one region given the outcome in the other. We study the Rényi-Shannon mutual information of measurement in conformal field theories (CFTs). Explicit calculations for scalar primaries and descendants in large NNN CFTs are performed in the two extreme limits of the intervals being adjacent or largely separated. The results depend on only the cross ratio and the scaling dimension ΔΔΔ of the operator being measured, with striking similarities to the mutual information of entanglement. We find a surprising quadratic dependence as (Δ−1/2)2(Δ-1/2)^2(Δ−1/2)2 for adjacent intervals. This dependence superficially seems to violate the information processing inequality, which we discuss and resolve. We also offer a holographic interpretation of the mutual information of measurement.
A bstract We study two novel approaches to efficiently encoding universal constraints imposed by conformal symmetry, and describe applications to quantum chaos in higher dimensional CFTs. The first approach consists of a reformulation of the shadow operator formalism and kinematic space techniques. We observe that the shadow operator associated with the stress tensor (or other conserved currents) can be written as the descendant of a field ε with negative dimension. Computations of stress tensor contributions to conformal blocks can be systematically organized in terms of the “soft mode” ε , turning them into a simple diagrammatic perturbation theory at large central charge. Our second (equivalent) approach concerns a theory of reparametrization modes, generalizing previous studies in the context of the Schwarzian theory and two-dimensional CFTs. Due to the conformal anomaly in even dimensions, gauge modes of the conformal group acquire an action and are shown to exhibit the same dynamics as the soft mode ε that encodes the physics of the stress tensor shadow. We discuss the calculation of the conformal partial waves or the conformal blocks using our effective field theory. The separation of conformal blocks from shadow blocks is related to gauging of certain symmetries in our effective field theory of the soft mode. These connections explain and generalize various relations between conformal blocks, shadow operators, kinematic space, and reparametrization modes. As an application we study thermal physics in higher dimensions and argue that the theory of reparametrization modes captures the physics of quantum chaos in Rindler space. This is also supported by the observation of the pole skipping phenomenon in the conformal energy-energy two-point function on Rindler space.
Quantum energy teleportation (QET) is a process that leverages quantum entanglement and local operations to transfer energy between two spatially separated locations without physically transporting particles or energy carriers. We construct a QET-based quantum key distribution (QKD) protocol and analyze its security and robustness to noise in both the classical and the quantum channels. We generalize the construction to an NNN-party information sharing protocol, possessing a feature that dishonest participants can be detected.
Quantum energy teleportation (QET) is a protocol that unlocks the extraction of local energy and has been thought to fundamentally require classical communication (CC), since Bob must normally learn Alice's measurement outcome to perform the proper conditional operation (CO).In this work, we demonstrate that CC itself can be removed for the purpose of QET: When Bob's local operation is implemented through a weak coupling to an auxiliary qubit, the interaction naturally adapts to Alice's post-measurement state, thereby realizing the necessary CO without any classical message.This establishes a CC-free form of QET, which broadens its conceptual scope and suggests practical applications such as indirect external control for charging of quantum batteries.