In Section 1 we introduce the notion of lifting as a generalization of the notion of compound state introduced in [21] and [22] and we show that this notion allows a unified approach to the problems of quantum measurement and of signal transmission through quantum channels The dual of a linear lifting is a transition expectation in the sense of [3] and we characterize those transition expectations which arise from compound states in the sense of [22]

/pdf/compound-channels-transition-expectations-and-liftings-101g3z1a8v.pdf

Compound Channels, Transition Expectations, and Liftings

A new theoretical description of identical particle entanglement frames it as a useful quantum resource in frequently encountered real-world experimental settings and not just a mathematical quirk.

Entanglement between Identical Particles Is a Useful and Consistent Resource

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 quasiprobabilities 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 analyze the link between this nonclassicality measure and a recently introduced quantum macroscopicity measure, showing how the two notions are distinct

https://hal.archives-ouvertes.fr/hal-01865597/document

Measuring Nonclassicality of Bosonic Field Quantum States via Operator Ordering Sensitivity.

The diverse range of resources which underlie the utility of quantum states in practical tasks motivates the development of universally applicable methods to measure and compare resources of different types. However, many of such approaches were hitherto limited to the finite-dimensional setting or were not connected with operational tasks. We overcome this by introducing a general method of quantifying resources for continuous-variable quantum systems based on the robustness measure, applicable to a plethora of physically relevant resources such as optical nonclassicality, entanglement, genuine non-Gaussianity, and coherence. We demonstrate in particular that the measure has a direct operational interpretation as the advantage enabled by a given state in a class of channel discrimination tasks. We show that the robustness constitutes a well-behaved, bona fide resource quantifier in any convex resource theory, contrary to a related negativity-based measure known as the standard robustness. Furthermore, we show the robustness to be directly observable---it can be computed as the expectation value of a single witness operator---and establish general methods for evaluating the measure. Explicitly applying our results to the relevant resources, we demonstrate the exact computability of the robustness for several classes of states.

Operational Quantification of Continuous-Variable Quantum Resources.

We revisit the notion of nonclassical distance of states of bosonic quantum systems introduced in Phys. Rev. A 35, 725 (1987) in a general multimode setting. After reviewing its definition, we establish some of its general properties. We obtain new upper and lower bounds on the nonclassical distance in terms of the supremum of the Husimi function of the state. Considering several examples, we elucidate the cases for which our lower bound is tight, which include the multimode number states and a class of multimode NOON states. The latter provide examples of states of definite photon number $n\ensuremath{\ge}2$ whose nonclassical distance can be made arbitrarily close to the upper limit of 1 by increasing the number of modes. We show that the nonclassical distance of the even and odd Schr\"odinger cat states is bounded away from unity regardless of how macroscopic the superpositions are, and that the nonclassical distance is not necessarily monotonically increasing with respect to macroscopicity.

Nonclassical distance in multimode bosonic systems

It is shown that the convex set of classical states of the quantum harmonic oscillator is a simplex generated as the closed convex hull of the coherent states in the weak topology of the Banach space of trace class operators.

/pdf/the-simplex-structure-of-the-classical-states-of-the-quantum-3u3srsyd2n.pdf

U. Lüxmann-Ellinghaus

Papers

The simplex structure of the classical states of the quantum harmonic oscillator