Entanglement spectrum and entropy of two-mode squeezed vacuum states

Abstract

Mode entanglement in a two-mode squeezed state is studied. The entanglement spectrum is derived and interpreted as Boltzmann coefficients of harmonic oscillator eigenstates at thermal equilibrium. The effective temperature is expressed in terms of squeezing parameters and is equal to zero when the state is unsqueezed and increases without bound as the state is infinitely squeezed. It is demonstrated that the reduced density operator can be identified as a canonical ensemble of single harmonic oscillator at some effective temperature T_e. The Rényi entanglement entropy is calculated and found to increase without bound as the squeezing parameter increases. The single-copy entanglement, which is a limiting value of the Rényi entropy, is interpreted as a partition function.