Phase-difference operator

Abstract

We introduce a unitary operator representing the exponential of the phase difference between two modes of the electromagnetic field. The eigenvalue spectrum has a discrete character that is fully analyzed. We relate this operator with a suitable polar decomposition of the Stokes parameters of the field, obtaining a natural classical limit. The cases of weakly and highly excited states are considered, discussing to what extent it is possible to talk about the phase for a single-mode field. This operator is applied to some interesting two-mode fields.

Measurable entanglement criterion for two qubits

“…However, there exists a complementary property to phase, which is excitation. (More precisely, relative phase, and relative excitation are complementary operators [31,32]). The joint properties with respect to this complementary quantity are not probed by Γ.…”

Single-particle nonlocality and entanglement with the vacuum

“…In the n = 0 energy manifold, there is only one associated state, so in this manifold there exist no relative-phasedependent projector. In all other manifolds the eigenstate |ξ (n) (φ) is similar in form to the eigenstates of the relative-phase operator [33]. The projection probabilities in the two arms on the states |ξ (nc) (φ c ) and |ξ (n d ) (φ d ) , respectively, and the joint probability of detecting the relative phases φ c and φ d and the photon numbers n c > 0 and n d > 0 become:…”

Operational approach to complementarity and duality relations

“…In our case the phase difference is represented in the quantum domain by the states ͉ ͘ [14]. It can be appreciated that in Eq.…”

“…The path variable is represented by the operator z , while the phase observable is given by the positive operator measure ͉ ͗͘ ͉ where ͉ ͘ are the phase states [4,13,14],…”