Modular values and weak values of quantum observables


  Yaron Kedem  ,  Lev Vaidman  
Tel Aviv University

We will introduce a new concept, the modular value of an observable of a pre- and post-selected quantum system [1]:  

Am = <ψ| Exp(-i k A)  |φ> / <ψ|φ>.

The modular value completely characterizes the effect of a pre- and post-selected quantum system on a qubit that is coupled via an observable A. For some observables, modular values yield weak values  Aw = <ψ| A |φ> / <ψ|φ>, universal properties of pre- and post-selected quantum system weakly coupled to other systems introduced by Aharonov, Albert and Vaidman in 1988. Measurements of modular values, which do not require weak coupling, provide an efficient method of measuring certain weak values. This is particularly important for measuring weak values of nonlocal observables.  Modular values have a potential for useful applications in devising and engineering novel quantum protocols.

[1] Y. Kedem, L. Vaidman, e-print arXiv:1007.5281v1, to be published in Phys. Rev. Lett.