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

TL;DR

This paper develops quasi-local measurement operators in 2D conformal field theories and demonstrates their application in a quantum energy teleportation protocol, confirming its viability and analyzing quantum correlations.

Contribution

It introduces a new class of measurement operators based on shadow operators and OPE blocks, enabling the implementation of QET in 2D CFTs with UV-cutoff independence.

Findings

QET protocol is feasible in 2D CFTs using the new measurement operators.

Measurement operators are UV-cutoff independent in outcome probabilities.

CHSH inequality is analyzed using OPE blocks in the context of quantum correlations.

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.