# Finding purifications with minimal entanglement

@article{Hauschild2018FindingPW, title={Finding purifications with minimal entanglement}, author={Johannes Hauschild and Eyal Leviatan and Jens H. Bardarson and Ehud Altman and Michael P. Zaletel and F. Pollmann}, journal={Physical Review B}, year={2018} }

Author(s): Hauschild, J; Leviatan, E; Bardarson, JH; Altman, E; Zaletel, MP; Pollmann, F | Abstract: © 2018 American Physical Society. Purification is a tool that allows to represent mixed quantum states as pure states on enlarged Hilbert spaces. A purification of a given state is not unique and its entanglement strongly depends on the particular choice made. Moreover, in one-dimensional systems, the amount of entanglement is linked to how efficiently the purified state can be represented using…

## 30 Citations

### Entanglement of purification: from spin chains to holography

- Physics
- 2017

A bstractPurification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of…

### Entanglement of purification in free scalar field theories

- Physics
- 2018

A bstractWe compute the entanglement of purification (EoP) in a 2d free scalar field theory with various masses. This quantity measures correlations between two subsystems and is reduced to the…

### Entanglement of purification and projection operator in conformal field theories

- PhysicsPhysics Letters B
- 2019

### Minimally entangled typical thermal state algorithms for finite temperature Matsubara Green functions

- Computer SciencePhysical Review B
- 2022

Finite-temperature tensor network methods are extended to compute Matsubara imaginary-time correlation functions, building on the minimally entangled typical thermal states (METTS) and purification algorithms, and the results are competitive with state-of-the-art continuous time Monte Carlo.

### Qubit-efficient simulation of thermal states with quantum tensor networks

- Physics
- 2022

We present a holographic quantum simulation algorithm to variationally prepare thermal states of d -dimensional interacting quantum many-body systems, using only enough hardware qubits to represent a…

### Holographic Entanglement of Purification from Conformal Field Theories.

- PhysicsPhysical review letters
- 2019

It is argued that, in AdS_{3}/CFT_{2}, the holographic entanglement of purification agrees with theEntanglement entropy for a purified state, obtained from a special Weyl transformation, called path-integral optimizations, by definition, this special purified state has minimal path-Integral complexity.

### Preentangling Quantum Algorithms -- the Density Matrix Renormalization Group-assisted Quantum Canonical Transformation

- Physics
- 2022

We propose the use of parameter-free preentanglers as initial states for quantum algorithms. We apply this idea to the electronic structure problem, combining a quantized version of the Canonical…

### Long Distance Entanglement of Purification and Reflected Entropy in Conformal Field Theory.

- Physics, Computer SciencePhysical review letters
- 2021

Using lattice techniques, an elementary proof is found that the decay of both the entanglement of purification and reflected entropy is enhanced with respect to the mutual information behavior by a logarithm of the distance between the subregions.

### Holographic entanglement of purification for thermofield double states and thermal quench

- PhysicsJournal of High Energy Physics
- 2019

A bstractWe explore the properties of holographic entanglement of purification (EoP) for two disjoint strips in the Schwarzschild-AdS black brane and the Vaidya-AdS black brane spacetimes. For two…

### Quantum information dynamics in multipartite integrable systems

- PhysicsEPL (Europhysics Letters)
- 2019

In a non-equilibrium many-body system, the quantum information dynamics between non-complementary regions is a crucial feature to understand the local relaxation towards statistical ensembles.…

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