Abstract

The entropy of an ensemble of systems is defined in classical statistical mechanics by the relation where k is the Boltzmann constant and p_n is the probability of finding the system in state n. It is possible to generalize this definition of entropy to a quantum state ψ(x) with Fourier transform ϕ(p) by defining p_n as¹ The corresponding entropies for the two quadratures $\widehat{x}$ and $\widehat{p}$ are defined as For the coherent state ${\mathcal{S}}^{(x)}={\mathcal{S}}^{(p)}$ and has the minimum value. For the x quadrature squeezed state, ${\mathcal{S}}^{(x)}$ decreases at the expense of ${\mathcal{S}}^{(p)}$ and vice versa. This definition of entropy has applications in information theory and optical communication using squeezed states.

© 1987 Optical Society of America