Measuring Nonclassicality of Bosonic Field Quantum States via Operator Ordering Sensitivity

Nonclassicality and entanglement as a quantifiable measure for phase estimation

We establish an approach to measure the nonclassicality of a two-mode quantum state by extending the method of quantifying nonclassicality for a single-mode quantum state. We then discuss the nonclassicality and entanglement properties of several different quantum states, and determine the optimal phase estimation for entangled coherent states (ecs) in the form of nonclassicality and concurrence. Accordingly, a new interferometer (linear and nonlinear) scheme is proposed by modifying a traditional interferometer. Specially, we specify a new normal ordering form of the evolution operator of nonlinear interferometer (NI) using the techniques of integration within an ordered product of operators (IWOP), and obtain the parity signal based on representation of the coherent state. By inputting several common quantum states, we further study the phase sensitivity of the linear interferometer (LI) and NI with parity detection, and perform a detailed comparison among the different input states schemes. Furthermore, we quantitatively investigated the effect of nonclassicality and entanglement on the phase sensitivity of two interferometers. These results show that nonclassicality or entanglement is very crucial but not a necessary condition for improving the phase sensitivity of interferometers.

Phase-Space Inequalities Beyond Negativities

We derive a family of inequalities involving different phase-space distributions of a quantum state which have to be fulfilled by any classical state. The violation of these inequalities is a clear signature of nonclassicality. Our approach combines the characterization of nonclassical effects via negativities in phase-space distributions with inequality conditions usually being formulated for moments of physical observables. Importantly, the obtained criteria certify nonclassicality even when the involved phase-space distributions are non-negative. Moreover, we show how these inequalities are related to correlation measurements. The strength of the derived conditions is demonstrated by different examples, including squeezed states, lossy single-photon states, and even coherent states.

Negativity of Quasiprobability Distributions as a Measure of Nonclassicality

We demonstrate that the negative volume of any s-parametrized quasiprobability, including the Glauber-Sudashan P function, can be consistently defined and forms a continuous hierarchy of nonclassicality measures that are linear optical monotones. These measures belong to an operational resource theory of nonclassicality based on linear optical operations. The negativity of the Glauber-Sudashan P function, in particular, can be shown to have an operational interpretation as the robustness of nonclassicality. We then introduce an approximate linear optical monotone, and we show that this nonclassicality quantifier is computable and is able to identify the nonclassicality of nearly all nonclassical states.

Quadrature Coherence Scale Driven Fast Decoherence of Bosonic Quantum Field States

We introduce, for each state of a bosonic quantum field, its quadrature coherence scale (QCS), a measure of the range of its quadrature coherences. Under coupling to a thermal bath, the purity and QCS are shown to decrease on a timescale inversely proportional to the QCS squared. The states most fragile to decoherence are therefore those with quadrature coherences far from the diagonal. We further show a large QCS is difficult to measure since it induces small scale variations in the state's Wigner function. These two observations imply a large QCS constitutes a mark of "macroscopic coherence." Finally, we link the QCS to optical classicality: optical classical states have a small QCS and a large QCS implies strong optical nonclassicality.