Nonlinearity as a resource for nonclassicality in anharmonic systems

Abstract

Nonclassicality is a key ingredient for quantum enhanced technologies and experiments involving macroscopic quantum coherence. Considering various exactly-solvable quantum-oscillator systems, we address the role played by the anharmonicity of their potential in the establishment of nonclassical features. Specifically, we show that a monotonic relation exists between the the entropic nonlinearity of the considered potentials and their ground state nonclassicality, as quantified by the negativity of the Wigner function. In addition, in order to clarify the role of squeezing -which is not captured by the negativity of the Wigner function -we focus on the Glauber-Sudarshan P-function and address the nonclassicality/nonlinearity relation using the entanglement potential. Finally, we consider the case of a generic sixth-order potential confirming the idea that nonlinearity is a resource for the generation of nonclassicality and may serve as a guideline for the engineering of quantum oscillators. II. NONCLASSICALITY OF A STATE AND NONLINEARITY OF A POTENTIALA. Nonclassicality of a Single-mode Bosonic StateWe consider a bosonic system with a single degree of freedom, such as a one-dimensional oscillator or a single-mode of

Resource theory of quantum non-Gaussianity and Wigner negativity

“…Furthermore, in this and in the following examples we observe that, as long as both the WLN W and the non-Gaussianity δ are functions of a single effective parameter, the two measures are monotonic and thus display the same qualitative behavior. We remark that the same fact has also been observed for ground states of anharmonic potentials [84]. Given this heuristic argument, we also expect the WLN of the cubic phase state to be a monotonically increasing function of its effective parameter, with a behavior similar to the measure δ; this is indeed what we observe from a numerical evaluation [85], see Fig.…”

Operational Resource Theory of Continuous-Variable Nonclassicality

“…They have been instrumental in understanding quantum reference frames [30], thermodynamics [31][32][33][34], coherence [35][36][37], contextuality [38], steering [39], and non-Gaussianity [40][41][42][43]. Resourcetheoretic terminology in continuous variables has appeared in a number of recent works [44][45][46][47][48][49][50][51][52], but these ideas are still in their infancy.…”

Quantum state engineering by nondeterministic noiseless linear amplification

“…Interestingly, for families of pure non-Gaussian states where only a single parameter is varied, quantifiers of nG and W -nC were always found to be in a monotonic relationship. In particular, this observation has been made for ground states of anharmonic oscillators [57], where the behavior of the two quantities is also qualitatively very similar. However, note that in some cases the behavior can be wildly different, while retaining monotonicity, e.g., when varying the amplitude of cat states the measure δ nC saturates to a finite value, while δ nG diverges [27].…”