Correlation Matrices of Two-Mode Bosonic Systems
Stefano Pirandola, Alessio Serafini, and Seth Lloyd
TL;DR
This paper thoroughly characterizes the algebraic conditions for 4x4 matrices to represent correlation matrices of two-mode bosonic systems, clarifying criteria for separability and entanglement using symplectic invariants.
Contribution
It introduces new conditions and criteria for identifying separable and entangled Gaussian states based on correlation matrices, enhancing understanding of quantum correlations.
Findings
Complete algebraic characterization of 4x4 correlation matrices
Criteria for separability and entanglement in Gaussian states
Introduction of symplectic invariant-based conditions
Abstract
We present a detailed analysis of all the algebraic conditions an arbitrary 4x4 symmetric matrix must satisfy in order to represent the correlation matrix of a two-mode bosonic system. Then, we completely clarify when this arbitrary matrix can represent the correlation matrix of a separable or entangled Gaussian state. In this analysis, we introduce new and alternative sets of conditions, which are expressed in terms of local symplectic invariants.
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Taxonomy
TopicsQuantum Information and Cryptography · Optical and Acousto-Optic Technologies · Quantum optics and atomic interactions