Universal nonclassicality witnesses for harmonic oscillators

It is shown that a nonclassicality witness, whose expectation value can be measured for all quantum states, can be constructed from every nonclassicality filter. This finding leads to a set of universal witnesses, parameterized by only three real numbers, for the detection of nonclassicality of any quantum state of a harmonic oscillator. An explicit operator expression is given for such a universal witness. The application of the witnesses is demonstrated for a nontrivial example, and its experimental measurement is briefly considered.

Figure 1

Experimental setup. The beam splitter displaces the initial state, followed by a photon-number resolving detection. The filter width is introduced by application of Eq. (26).

Figure 2

Dependence of the expectation value of the witness ${\widehat{W}}_{\mathit{w}}\left(0\right)$ on the filter width, for SPATSs of different mean thermal photon number $\overline{n}$ and quantum efficiency $\eta =0.5$. Nonclassicality is indicated by negative expectation values, which appear for sufficiently large $\mathit{\text{w}}$ for all states.