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Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations

Geometric uncertainty relation, the symplectic area, and the J-holomorphic maps for mixed quantum states

arXiv

Authors: Hoshang Heydari

Year

2016

Paper ID

41577

Status

Preprint

Abstract Read

~2 min

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Abstract

In this paper we will establish a relation between geometric uncertainty relation and the determinant of the quantum covariance matrix for mixed quantum states. We will show that determinant of the covariance matrix represents the squared metric area of a parallelogram. In this setting the geometric uncertainty relation compares a metric area to a symplectic area. Moreover, we will in details investigate relation between J-holomorphic maps and geometric uncertainty relation for mixed quantum states. We will argue that determinant of the quantum covariance matrix is equal to the harmonic energy of a holomorphic map that minimize the areas.

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In this paper we will establish a relation between geometric uncertainty relation and the determinant of the quantum covariance matrix for mixed quantum states.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1612.08428 [2] arXiv https://arxiv.org/abs/1612.08428 [3] Publisher https://arxiv.org/abs/1612.08428

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