Observable-projected ensembles

Alexey Milekhin; Sara Murciano

doi:10.22331/q-2025-10-20-1888

Observable-projected ensembles

Alexey Milekhin¹ and Sara Murciano^1,2,3

¹Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, USA
²Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, USA
³Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA

Published:	2025-10-20, volume 9, page 1888
Editor:	Leon Loveridge
Eprint:	arXiv:2410.21397v3
Doi:	https://doi.org/10.22331/q-2025-10-20-1888
Citation:	Quantum 9, 1888 (2025).

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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 $\textit{observable-projected ensemble}$. 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.

Featured image: Schematic representation of an “observable-projected ensemble”.

Popular summary

When we measure part of a quantum system, the rest of it changes in strange and fascinating ways due to entanglement – the famous "spooky action in distance". Usually, physicists imagine performing a complete measurement on one part and then studying what happens to the remainder. But such full measurements are extremely hard to do in practice and difficult to describe analytically.

In this paper, we suggest a simpler and more realistic approach. Instead of measuring everything, we propose measuring just one physical quantity — a single observable — in the surrounding region. This procedure still alters the rest of the system, but in a more subtle way. We call the resulting collection of possible outcomes an “observable-projected ensemble”.

We show that this setup can be analyzed more easily and is more amenable for experimental implementations. In particular, we demonstrate how to use field-theory techniques to derive analytical results and use them to distinguish quantum states.

► BibTeX data

@article{Milekhin2025observableprojected,
  doi = {10.22331/q-2025-10-20-1888},
  url = {https://doi.org/10.22331/q-2025-10-20-1888},
  title = {Observable-projected ensembles},
  author = {Milekhin, Alexey and Murciano, Sara},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1888},
  month = oct,
  year = {2025}
}

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