Fidelity Matters: The Birth of Entanglement in the Mixing of Gaussian States

Abstract

We address the interaction of two Gaussian states through bilinear exchange Hamiltonians and analyze the correlations exhibited by the resulting bipartite systems. We demonstrate that entanglement arises if and only if the fidelity between the two input Gaussian states falls under a threshold value depending only on their purities, first moments and on the strength of the coupling. Our result clarifies the role of quantum fluctuations (squeezing) as a prerequisite for entanglement generation and provides a tool to optimize the generation of entanglement in linear systems of interest for quantum technology. [2] and because they may be generated with current technology, in particular in the quantum optics context [3][4][5]. As a consequence, much attention have been dedicated to the characterization of Gaussian entanglement [6][7][8][9][10][11][12][13][14]. Among the possible mechanisms to generate Gaussian entanglement, the one consisting in mixing squeezed states [15][16][17][18][19][20][21] is of special interest in view of its feasibility, which indeed had been crucial to achieve continuous variable teleportation [22]. The entangling power of bilinear interactions has been widely analyzed, either to optimize the generation of entanglement [23,24] or to find relations between their entanglement and purities [25] or teleportation fidelity [26,27].In this Letter we address bilinear, energy conserving, i.e., exchange, interactions described by Hamiltonians of the form [32], all of which are of interest for the quantum technology. Our analysis can be applied to all these systems and lead to very general results about the resources needed for Gaussian entanglement generation.The bilinear Hamiltonians H I generally describe the action of simple passive interactions and, in view of this simplicity, their fundamental quantum properties are often overlooked. Actually, the exchange amplitudes for the quanta of one of the systems strongly depend on the statistics of the quanta of the other one and on the particle indistinguishability. This mechanism gives rise to interference and, thus, to the birth of correlations in the output bipartite system. A question arises about the nature of these correlations, depending on the parameters of the input signals and coupling constant. In this Letter, motivated by recent results on the dynamics of bipartite GS through bilinear interactions [33,34] and by their experimental demonstration [35], we investigate the relation between the properties of two input GS and the correlations exhibited by the output state. Our main result is that entanglement arises if and only if the fidelity between the two input states falls under a threshold value depending only on their purities, first-moment values and on the strength of the coupling. Our analysis provides a direct link between the mismatch in the quantum properties of the input signals and the creation of entanglement, thus providing a better understanding of the process leading to the generation of nonclassical correlations. In fact, if,...

Experimental pre-assessing of two-mode entanglement in Gaussian state mixing

“…They may be exploited to assess whether entanglement has been produced after a given interaction took place. On the other hand, an a priori criterion has been recently introduced [19] to assess the entanglement capability of a pair of distinct Gaussian states interacting at a BS. The criterion is based on the mutual fidelity of two uncorrelated Gaussian states, c and d , describing the preparation of two bosonic modes c and d, and is able to predict whether the state obtained by mixing them at a BS, will be entangled or not.…”

“…In Section II we introduce the notation and the tools to describe entanglement generation by Gaussian states mixing. We also review the fidelity criterion proposed in [19]. In Section III we describe Gaussian states propagation in lossy and noisy channels.…”

The second-order interference between laser and thermal light

“…However, there is an important difference between these two situations. It is predicted [28] and experimentally verified [17,29] that g (2) (0) equals 1 for two thermal light beams in a HOM interferometer. This conclusion is true no matter what is the ratio between the intensities of these two input thermal light beams.…”

Dynamics of Quantum Correlations of Two Interfering Bipartite Gaussian States

“…11 The properties of the correlated states emerging from a beam splitter have been thoroughly investigated in the past years, either to optimize the generation of entanglement 12,13 or to find relations between their entanglement and purities 14 or teleportation fidelity. 15 Furthermore, a recent work 16 has proved that there exists a strict relation between the fidelity (similarity) of the Gaussian states interacting through a beam-splitter Hamiltonian and the birth of entanglement at the output.…”