We demonstrate the feasibility to completely characterize entanglement by negativities of quasiprobabilities. This requires the complete solution of a sophisticated mathematical problem, the so-called separability eigenvalue problem. Its solution is obtained for a non-Gaussian continuous variable quantum state, a two-mode squeezed state undergoing dephasing. This is a standard scenario for experiments with quantum-correlated radiation fields.
We demonstrate the feasibility to completely characterize entanglement by negativities of quasiprobabilities. This requires the complete solution of a sophisticated mathematical problem, the so-called separability eigenvalue problem. Its solution is obtained for a non-Gaussian continuous variable quantum state, a two-mode squeezed state undergoing dephasing. This is a standard scenario for experiments with quantum-correlated radiation fields.
Regular quasiprobabilities are introduced for the aim of characterizing quantum correlations of multimode radiation fields. Negativities of these quantum-correlation quasiprobabilities are necessary and sufficient for any quantum correlation encoded in the multimode Glauber-Sudarshan P function. The strength of the method is demonstrated for a two-mode, phase-randomized, squeezed-vacuum state. It has no entanglement, no quantum discord, a positive Wigner function, and a classical reduced single-mode representation. Our method clearly visualizes the quantum correlations of this state.
Continuous-variable (CV) entanglement is a valuable resource in the field of quantum information. One source of CV entanglement is the correlations between the position and momentum of photons in a two-mode squeezed state of light. In this paper, we theoretically study the generation of squeezed states, via spontaneous parametric down conversion, inside a two-mode lossy cavity that is pumped with a classical optical pulse. The dynamics of the density operator in the cavity is modeled using the Lindblad master equation, and we show that the solution to this model is the density operator for a two-mode squeezed thermal state, with a time-dependent squeezing amplitude and average thermal photon number for each mode. We derive an expression for the minimum correlation variance inside the cavity that depends crucially on the difference in the losses between the two modes. We apply our analytic solution to the important example of a microring resonator that is pumped with a Gaussian pulse. The expressions that we derive will help researchers optimize CV entanglement in lossy cavities.
The characterisation of quantum correlations, also known as entanglement, is central to quantum information theory. Operationally, entanglement gives rise to the notion of quantum non-locality, which challenges the ‘reality’ of quantum mechanics (adopting the terminology of Einstein, Podolski and Rosen) and arguably represents its most distinctive feature, in the sense that it calls for a departure from certain foundational tenets of classical physics. It should thus not come as a surprise that entanglement turns out to be a key resource for the implementation of a number of quantum communication protocols and also necessary to achieve computational speed-ups with quantum hardware, in the sense that accessing regions of the Hilbert space with entangled states allows one to shorten the computational depth of certain algorithms. Not surprisingly, generating and maintaining entanglement is generally difficult in practice, as it requires strong interactions between selected components of a system that must at the same time be isolated from the environment. Thanks to the techniques developed in quantum optical set-ups to achieve squeezed light, entanglement is, however, comparatively accessible with optical quantum continuous variables. As we shall see, in fact, continuous variable entanglement is closely related to the notion of squeezing. It is therefore of the utmost importance to be able to qualify and quantify the entanglement of quantum continuous variables, which is the subject matter of the present chapter. The first part of the chapter is devoted to techniques and criteria based on second moments to detect the entanglement of Gaussian states and also to the description of possible ways to quantify such quantum correlations, bearing in mind that the determination of entanglement monotones of clear operational significance is still an open problem, even in the restricted arena of Gaussian states. Although the criteria based on second moments are sufficient, but not necessary, for the detection of non-Gaussian entanglement too, we will push our analysis further by introducing more general criteria based on higher order statistical moments, which will be put to use to detect, on paper, the quantum correlations of an entangled cat-like state. We will also address the issues of entanglement distillation and quantum non-locality tests, in whose contexts we shall encounter other non-Gaussian operations and states, such as photon-subtracted states.
We present an effort to find a measure of non-Gaussianity of non-Gaussian states. We compute the difference between the logarithmic negativities of a non-Gaussian state and its Gaussified form as a non-Gaussian entanglement resource. We use the latter to assess the resource content of non-Gaussianity of experimentally relevant state - two- mode squeezed vacuum with a subtracted photon. We also used symplectic analysis to discard the Gaussian entanglement. Therefore the measure is reduced to the logarithmic negativity of a non-Gaussian state only. We compare the measure with the Wigner distribution and its negativity and discuss the results. 1
We use quantum entanglement witnesses derived from Gaussian operators to study the separable criteria of continuous variable states. We transform the validity of a Gaussian witness to a Bosonic Gaussian channel problem. It follows that the maximal means of two-mode and some four-mode Gaussian operators over product pure states are achieved by vacuum (or coherent states and squeezed states) according to the properties of Bosonic Gaussian channels. Then we have necessary and sufficient criteria of separability not only for Gaussian quantum states, but also for non-Gaussian states prepared by photon adding to or/and subtracting from Gaussian states. The criterion can be further explicitly expressed with covariance matrix of the Gaussian state or covariance matrix of Gaussian kernel of the non-Gaussian state. This opens a way for precise detection of non-Gaussian entanglement.
Entangled quantum states, such as NOON states, are of major importance for quantum technologies due to their quantum-enhanced performance. At the same time, their quantum correlations are relatively vulnerable when they are subjected to imperfections. Therefore, it is crucial to determine under which circumstances their distinct quantum features can be exploited. In this paper, we study the entanglement property of noisy NOON states. This class of states is a generalization of NOON states including various attenuation effects, such as mixing, constant or fluctuating losses, and dephasing. To verify their entanglement, we pursue two strategies: detection-based entanglement witnesses and entanglement quasiprobabilities. Both methods result from our solution of so-called separability eigenvalue equations. In particular, the entanglement quasiprobabilities allow for a full entanglement characterization. As examples of our general treatment, the cases of NOON states subjected to Gaussian dephasing and fluctuating atmospheric losses are explicitly studied. In any correlated fluctuating loss channel, entanglement is found to survive for nonzero transmissivity. In addition, an extension of our approach to multipartite systems is given, and the relation to the quantum-optical nonclassicality in phase space is discussed.