1205.3294 (T. Subeesh et al.)

Phase-space based operator valued measure for the quantum optical phase    [PDF]

T. Subeesh, Vivishek Sudhir

The Wigner Phase Operator (WPO) is identified as an operator valued measure (OVM) and its eigen states are obtained. An operator satisfying the canonical commutation relation with the Wigner phase operator is also constructed and this establishes a Wigner distribution based operator formalism for the quantum phase. The operator satisfying the canonical commutation relation with the Wigner Phase Operator valued measure (WP-OVM) is found to be not the usual number operator. We show a way to overcome the non-positivity problem of the WP-OVM by defining a positive OVM by means of a proper filter function, based on the view that phase measurements are coarse-grained in phase space, leading to the well known Q-distribution.The identification of Q phase operator as a POVM is in good agreement with the earlier observation regarding the relation between operational phase measurement schemes and the Q-distribution.

View original: http://arxiv.org/abs/1205.3294