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Quantum Simulation Entanglement Theory Quantum Correlations

Describing orbit space of global unitary actions for mixed qudit states

arXiv

Authors: Vladimir Gerdt, Arsen Khvedelidze, Yuri Palii

Year

2013

Paper ID

31853

Status

Preprint

Abstract Read

~2 min

Abstract Words

112

Citations

N/A

Abstract

The unitary U(d)-equivalence relation between elements of the space mathfrak{P}_+ of mixed states of d-dimensional quantum system defines the orbit space mathfrak{P}_+/ U(d) and provides its description in terms the ring mathbb{R}\[mathfrak{P}_+\]^U(d) of U(d)-invariant polynomials. We prove that the semi-algebraic structure of mathfrak{P}_+/ U(d) is determined completely by two basic properties of density matrices, their semi-positivity and Hermicity. Particularly, it is shown that the Processi-Schwarz inequalities in elements of integrity basis for mathbb{R}\[mathfrak{P}_+\]^U(d) defining the orbit space, are identically satisfied for all elements of mathfrak{P}_+.

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The unitary U(d)-equivalence relation between elements of the space mathfrakP_+ of mixed states of d-dimensional quantum system defines the orbit space mathfrakP_+/ U(d) and...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1311.4649 [2] arXiv https://arxiv.org/abs/1311.4649 [3] Publisher https://arxiv.org/abs/1311.4649

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