Observable-projected ensembles

TL;DR

This paper introduces the observable-projected ensemble, a new measurement scheme in quantum many-body systems that allows efficient analysis of mixed states through local observable measurements, with theoretical and experimental advantages.

Contribution

The paper presents a novel measurement scheme called observable-projected ensemble, enabling analytical and efficient experimental study of mixed states in quantum systems.

Findings

Analytical computation of entanglement in conformal field theory

Detailed analysis of the free compact boson case

Reduced measurement complexity compared to standard methods

Abstract

Measurements in many-body quantum systems can generate non-trivial phenomena, such as preparation of long-range entangled states, dynamical phase transitions, or measurement-altered criticality. Here, we introduce a new measurement scheme that produces an ensemble of mixed states in a subsystem, obtained by measuring a local Hermitian observable on part of its complement. We refer to this as the observable-projected ensemble. Unlike standard projected ensembles-where pure states are generated by projective measurements on the complement-our approach involves projective partial measurements of specific observables. This setup has two main advantages: theoretically, it is amenable to analytical computations, especially within conformal field theories. Experimentally, it requires only a linear number of measurements, rather than an exponential one, to probe the properties of the ensemble. As a first step in exploring the observable-projected ensemble, we investigate its entanglement properties in conformal field theory and perform a detailed analysis of the free compact boson.