# Quantum state reduction: Generalized bipartitions from algebras of observables

@article{Kabernik2019QuantumSR, title={Quantum state reduction: Generalized bipartitions from algebras of observables}, author={Oleg Kabernik and Jason Pollack and Ashmeet Singh}, journal={arXiv: Quantum Physics}, year={2019} }

Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with the partial-trace map by ``tracing out'' part of the quantum state, but in many natural situations this reduction may not be achievable. We investigate the general problem of identifying how the quantum state reduces given a restriction on the observables. For…

## Figures and Tables from this paper

## 10 Citations

Quantum scrambling of observable algebras

- Physics
- 2021

In this paper we describe an algebraic/geometrical approach to quantum scrambling. Generalized quantum subsystems are described by a ∗-closed unital subalgebra A of operators evolving through a…

Understanding holographic error correction via unique algebras and atomic examples

- Physics
- 2021

We introduce a fully constructive characterisation of holographic quantum error-correcting codes. That is, given a code and an erasure error we give a recipe to explicitly compute the terms in RT…

Macro-to-micro quantum mapping and the emergence of nonlinearity

- Physics
- 2020

As a universal theory of physics, quantum mechanics must assign states to every level of description of a system, and also describe the interconnections among them. Assuming that we only have a…

Locality and entanglement of indistinguishable particles

- Medicine, PhysicsScientific reports
- 2021

It is proved that three of the aforementioned five entanglement definitions are incompatible with any locality notion defined as above.

Areas and entropies in BFSS/gravity duality

- Physics
- 2019

The BFSS matrix model provides an example of gauge-theory / gravity duality where the gauge theory is a model of ordinary quantum mechanics with no spatial subsystems. If there exists a general…

Reality as a Vector in Hilbert Space

- Physics
- 2021

I defend the extremist position that the fundamental ontology of the world consists of a vector in Hilbert space evolving according to the Schrödinger equation. The laws of physics are determined…

Microstate distinguishability, quantum complexity, and the eigenstate thermalization hypothesis

- PhysicsClassical and Quantum Gravity
- 2021

In this work, we use quantum complexity theory to quantify the difficulty of distinguishing eigenstates obeying the eigenstate thermalization hypothesis (ETH). After identifying simple operators with…

Quantum mereology: Factorizing Hilbert space into subsystems with quasiclassical dynamics

- PhysicsPhysical Review A
- 2021

We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a…

Eigenstate Thermalization and Disorder Averaging in Gravity.

- Physics, MedicinePhysical review letters
- 2020

It is shown how replica instantons and disorder averaging emerge naturally in an effective theory built from typical microscopic states, and a microcanonical description of wormholes and Euclidean black holes is found.

Entropic uncertainty relations and the quantum-to-classical transition

- Physics
- 2020

Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the…

## References

SHOWING 1-10 OF 95 REFERENCES

Quantum coarse graining, symmetries, and reducibility of dynamics

- Physics, MathematicsPhysical Review A
- 2018

The common idea behind complexity reduction in physical systems is separation of information into "physically meaningful" and "safely ignorable". Here we consider a generic notion of such separation…

Algebraic approach to quantum theory: a finite-dimensional guide

- Physics, Mathematics
- 2015

This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a…

Locality from the Spectrum

- Mathematics, PhysicsCommunications in Mathematical Physics
- 2019

It is argued that in fact, the energy spectrum alone almost always encodes a unique description of local degrees of freedom when such a description exists, allowing one to explicitly identify local subsystems and how they interact.

Emerging dynamics arising from coarse-grained quantum systems

- Physics
- 2017

The purpose of physics is to describe nature from elementary particles all the way up to cosmological objects like cluster of galaxies and black holes. Although a unified description for all this…

Quantum information measures for restricted sets of observables

- Physics
- 2018

We study measures of quantum information when the space spanned by the set of accessible observables is not closed under products, i.e., we consider systems where an observer may be able to measure…

Quantum Compression Relative to a Set of Measurements

- Mathematics, Physics
- 2017

In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this…

The Ryu–Takayanagi Formula from Quantum Error Correction

- Mathematics, Physics
- 2016

I argue that a version of the quantum-corrected Ryu–Takayanagi formula holds in any quantum error-correcting code. I present this result as a series of theorems of increasing generality, with the…

Space from Hilbert Space: Recovering Geometry from Bulk Entanglement

- Physics
- 2017

We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space H into a tensor…

Mad-Dog Everettianism: Quantum Mechanics at Its Most Minimal

- PhysicsThe Frontiers Collection
- 2019

To the best of our current understanding, quantum mechanics is part of the
most fundamental picture of the universe. It is natural to ask how pure and
minimal this fundamental quantum description…

Constraining quantum fields using modular theory

- Physics, MathematicsJournal of High Energy Physics
- 2019

A bstractTomita-Takesaki modular theory provides a set of algebraic tools in quantum field theory that is suitable for the study of the information-theoretic properties of states. For every open set…