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arXiv:0903.4553 · Physical Review A

Extraction of pure entangled states from many-body systems by distant local projections

Jeanmaire Molina, Hannu Christian Wichterich, V. E. Korepin, Sougato Bose

Published Jun 11, 2009• 2 citations
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Abstract

We study the feasibility of extracting a pure entangled state of noncomplementary and potentially well-separated regions of a quantum many-body system. It is shown that this can indeed be accomplished in nonequilibrium scenarios as well as the ground state of the considered spin chain models when one locally measures observables such as the magnetization of separated blocks of spins. A general procedure which can search for the optimal way to extract a pure entangled state through local projections is presented. Our results indicate a connection of the projective extraction of entanglement to good quantum numbers of the underlying Hamiltonian.

DOI
10.1103/physreva.79.062310

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We study the feasibility of extracting a pure entangled state of noncomplementary and potentially well-separated regions of a quantum many-body system. It is shown that this can indeed be accomplished in nonequilibrium scenarios as well as the ground state of the considered spin chain models when one locally measures observables such as the magnetization of separated blocks of spins. A general procedure which can search for the optimal way to extract a pure entangled state through local projections is presented. Our results indicate a connection of the projective extraction of entanglement to good quantum numbers of the underlying Hamiltonian.
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We consider the problem of extracting work from isolated quantum systems composed of nnn subsystems. In this scenario the work can be naturally divided into two contributions: a local contribution from each subsystem, and a global contribution originating from correlations between subsystems. Here we focus on the latter and consider quantum systems which are locally thermal, thus from which work can only be extracted from correlations. We derive bounds on the extractable work for general quantum states, separable states, and states with fixed entropy. Our results show that while entanglement gives an advantage for small quantum systems, this gain vanishes for a large number of subsystems.
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Despite their fundamental importance in dictating the quantum-mechanical properties of a system, ground states of many-body local quantum Hamiltonians form a set of measure zero in the many-body Hilbert space. Hence determining whether a given many-body quantum state is ground-stateable is a challenging task. Here we propose an unsupervised machine learning approach, dubbed Entanglement Clustering ("EntanCl"), to separate out ground-stateable wave functions from those that must be excited-state wave functions using entanglement structure information. EntanCl uses snapshots of an ensemble of swap operators as input and projects these high-dimensional data to two dimensions, preserving important topological features of the data associated with distinct entanglement structure using the uniform manifold approximation and projection. The projected data are then clustered using K-means clustering with k = 2. By applying EntanCl to two examples, a one-dimensional free fermion model and the two-dimensional toric code, we demonstrate that EntanCl can successfully separate ground states from excited states with high computational efficiency. Being independent of a Hamiltonian and associated energy estimates, EntanCl offers a new paradigm for addressing quantum many-body wave functions in a computationally efficient manner.
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