Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits

• URL: http://arxiv.org/abs/2301.09193v1
• Date: Sun, 22 Jan 2023 20:15:49 GMT
• Title: Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits
• Authors: Julio Guerrero, Antonio Sojo, Alberto Mayorgas and Manuel Calixto
• Abstract summary: We study the entanglement in symmetric $N$-quDit systems using generalizations to $U(D)$ of spin $U(2)$ coherent states. Diverse properties of the Schmidt eigenvalues are studied and, in particular, for the (rescaled) double thermodynamic limit ($N,Mrightarrowinfty,,M/N$ fixed), we reproduce and generalize quDits known results for photon loss of parity adapted coherent states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In this paper we study the entanglement in symmetric $N$-quDit systems. In particular we use generalizations to $U(D)$ of spin $U(2)$ coherent states and their projections on definite parity $\mathbb{C}\in\mathbb{Z}_2^{D-1}$ (multicomponent Schr\"odinger cat) states and we analyse their reduced density matrices when tracing out $M<N$ quDits. The eigenvalues (or Schmidt coefficients) of these reduced density matrices are completely characterized, allowing to proof a theorem for the decomposition of a $N$-quDit Schr\"odinger cat state with a given parity $\mathbb{C}$ into a sum over all possible parities of tensor products of Schr\"odinger cat states of $N-M$ and $M$ particles. Diverse asymptotic properties of the Schmidt eigenvalues are studied and, in particular, for the (rescaled) double thermodynamic limit ($N,M\rightarrow\infty,\,M/N$ fixed), we reproduce and generalize to quDits known results for photon loss of parity adapted coherent states of the harmonic oscillator, thus providing an unified Schmidt decomposition for both multi-quDits and (multi-mode) photons. These results allow to determine the entanglement properties of these states and also their decoherence properties under quDit loss, where we demonstrate the robustness of these states.

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