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… 

Figures from this paper

Entanglement of purification: from spin chains to holography

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

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

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

TLDR
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

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.

TLDR
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

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.

TLDR
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

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

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.

References

SHOWING 1-10 OF 89 REFERENCES

Entanglement of purification: from spin chains to holography

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

Purifications of multipartite states: limitations and constructive methods

TLDR
It is implied that a description of mixed states which is both efficient and locally positive semidefinite does not exist, but that good approximations do.

Universal slow growth of entanglement in interacting strongly disordered systems.

TLDR
This work shows that the logarithmic entanglement growth is a universal phenomenon characteristic of the many-body localized phase in any number of spatial dimensions, and reveals a broad hierarchy of dephasing time scales present in such a phase.

Entanglement of purification through holographic duality

The gauge/gravity correspondence discovered two decades ago has had a profound influence on how the basic laws in physics should be formulated. In spite of the predictive power of holographic

Symmetric minimally entangled typical thermal states for canonical and grand-canonical ensembles

TLDR
It is shown how grand-canonical ensembles can be simulated efficiently with symmetric METTS and how the choice of the collapse bases influences autocorrelations as well as the distribution of measurement values and, hence, convergence speeds.

Extracting Entanglement Geometry from Quantum States.

TLDR
This work develops an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state and analyzes the structure of the resulting unitary circuits.

Algorithms for Entanglement Renormalization: Boundaries, Impurities and Interfaces

We propose algorithms, based on the multi-scale entanglement renormalization ansatz, to obtain the ground state of quantum critical systems in the presence of boundaries, impurities, or interfaces.

The entanglement of purification

We introduce a measure of both quantum as well as classical correlations in a quantum state, the entanglement of purification. We show that the (regularized) entanglement of purification is equal to

Unbounded growth of entanglement in models of many-body localization.

TLDR
The significance for proposed atomic experiments is that local measurements will show a large but nonthermal entropy in the many-body localized state, which develops slowly over a diverging time scale as in glassy systems.

Finitely correlated states on quantum spin chains

We study a construction that yields a class of translation invariant states on quantum spin chains, characterized by the property that the correlations across any bond can be modeled on a
...