arXiv:1711.01288 · Physical review. B./Physical review. B

Finding purifications with minimal entanglement

Johannes Hauschild, Eyal Leviatan, Jens Hjorleifur Bardarson, Ehud Altman, Michael P. Zaletel, Frank Pollmann

Published Dec 28, 2018• 62 citations

Abstract

Purification is a well-known tool to represent mixed quantum states as pure states on an enlarged Hilbert space. A purification of a given state is not unique and its spatial entanglement strongly depends on the particular choice. This entanglement is linked to how efficiently the purified state can be represented using matrix-product states (MPS). Here, the authors introduce an MPS-based method that allows the user to efficiently find the minimally entangled purification of a given mixed state and demonstrate that it can significantly reduce the entanglement in certain cases.

DOI: 10.1103/physrevb.98.235163

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arXiv:1711.01288 · Physical review. B./Physical review. B

Finding purifications with minimal entanglement

Johannes Hauschild, Eyal Leviatan, Jens Hjorleifur Bardarson, Ehud Altman, Michael P. Zaletel, Frank Pollmann

Published Dec 28, 2018• 62 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.98.235163

Related papers

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The classification of the multipartite entanglement is an important problem in quantum information theory. We propose a class of two qubit mixed states

σ_{AB}= p|χ_{1}\rangle\langleχ_{1}|\otimesρ_{1}+(1-p)|χ_{2}\rangle\langleχ_{2}|\otimesρ_{2}

, where

|χ_{1}\rangle=α|0\rangle+β|1\rangle

|χ_{2}\rangle=β|0\rangle+(-1)^{n}α|1\rangle

. We have shown that the state

σ_{AB}

represent a classical state when

n

is odd while it represent a non-classical state when

n

is even. The purification of the state

σ_{AB}

is studied and found that the purification is possible if the spectral decomposition of the density matrices

ρ_{1}

and

ρ_{2}

represent pure states. We have established a relationship between three tangle, which measures the amount of entanglement in three qubit system and the quantity

\langleχ_{1}|χ_{2}\rangle

, which identifies whether the two qubit mixed state is classical or non-classical. The three qubit purified state is then classified as a separable or biseparable or W-type or GHZ-type state using the quantum correlation, measured by geometric discord, of its reduced two qubit density matrix.

n

copies of a two-qubit state.