Measuring Nonclassicality of Bosonic Field Quantum States via Operator Ordering Sensitivity

Abstract

We introduce a new distance-based measure for the nonclassicality of the states of a bosonic field, which outperforms the existing such measures in several ways. We define for that purpose the operator ordering sensitivity of the state which evaluates the sensitivity to operator ordering of the Renyi entropy of its quasi-probabilities and which measures the oscillations in its Wigner function. Through a sharp control on the operator ordering sensitivity of classical states we obtain a precise geometric image of their location in the density matrix space allowing us to introduce a distance-based measure of nonclassicality. We analyse the link between this nonclassicality measure and a recently introduced quantum macroscopicity measure, showing how the two notions are distinct.

Quadrature Coherence Scale Driven Fast Decoherence of Bosonic Quantum Field States

“…Indeed, |ξ|χ 2 2 / χ 2 2 is the mean of |ξ| 2 with respect to the probability density |χ(ξ)| 2 / χ 2 2 . Hence, a large value of the QCS corresponds to a characteristic function with a wide spread in at least some directions in the ξ-plane, a manifestation of the well known link between the characteristic function and the coherences [29]: On the other hand, a large QCS implies the gradient of W is large, which means the graph of W must has steep slopes, at least in some places of the phase plane, a signature either of oscillations or of sharp peaks [15,23]. For Gaussian states, this phenomenon manifests itself in that the variance of the probability distribution of one of the quadratures is of order C −2 (more details in Appendix B).…”

“…We show here a quantitative link between optical (non)classicality, the presence of coherences, and (fast) decoherence. Our analysis is based on the optical nonclassicality distance d(ρ, C cl ) defined in [23] using a quantity denoted S o (ρ), which measures the sensitivity of the state to operator ordering. It has a number of equivalent expressions, the primary one being In other words, the QCS provides a new physical interpretation of the ordering sensitivity in terms of quadrature coherences, and the associated physical phenomena described above.…”

Bell inequality violation and operator ordering in quantum theory

“…This can be accomplished with the following polarization settings: θ = 0, θ = π/4, φ = π/8 e φ = 3π/8 , for example. We next check the CHSH inequality in each operator ordering by plugging (21) and (22) into (23) and (24). Note that the ordering dependent terms in Eqs.…”

“…Note that the ordering dependent terms in Eqs. (21) and (22) cancel out in the numerator of (23) but they do contribute to the denominator. As we show below, it drastically affects the violation of the CHSH criterion in the thin crystal limit gτ 1 , usually valid in actual experimental conditions.…”

Thermal-difference states of light: Quantum states of heralded photons

“…We are interested in including high-gain PDC in our consideration and exploring if a similar tradeoff exists between the brightness and the nonclassicality. For that purpose we use several measures of nonclassicality, including a recently introduced one, the ordering sensitivity (OS) of a quantum state [35]. The main results of our approach have been reported on the QTech'2018 conference [36].…”