Optimal entanglement witnesses in a split spin-squeezed Bose-Einstein condensate

Abstract

How do we detect quantum correlations in bipartite scenarios using a split many-body system and collective measurements on each party? We address this question by deriving entanglement witnesses using either only first-order or both first-and second-order moments of local collective spin components. In both cases, we derive optimal witnesses for spatially split spin-squeezed states in the presence of local white noise. We then compare the two optimal witnesses with respect to their resistance to various noise sources operating either at the preparation or at the detection level. We finally evaluate the statistics required to estimate the value of these witnesses when measuring a split spin-squeezed Bose-Einstein condensate. Our results can be seen as a step toward Bell tests with many-body systems.

Bipartite nonlocality with a many-body system

“…k is a vector having the 3 Pauli matrices as components and a  is a unit length vector with components α x , While entanglement witnesses have been intensively studied in this scenario with first order moments [12][13][14], few results are known with respect to Bell inequality violations. One noticeable exception is [15,16] where authors showed that bipartite correlations issued from first order collective measurements can be reproduced by a local model if the number of measurement settings is smaller or equal to n A for Alice and n B for Bob.…”

Split spin-squeezed Bose–Einstein condensates

“…In this work we study the quantum correlations between the two BECs obtained from this protocol, and discuss methods for detecting entanglement using correlations of observables. Recently, Oudot, Sangouard, and coworkers examined entanglement witnesses for such entangled BECs in the presence of local white noise [45]. Our physical model differs from this work and those experimental results in [30][31][32] as we consider the spatial separations to be large enough such that particle number superpositions on the left and right wells collapse to a fixed number.…”

“…We note that in comparison with the criterion proposed in [45], the criteria for entanglement based on variances adopted in our work should be experimentally more practical. This is because the use of the second order moments of the collective spin operator along y and z directions would require the first order ones along these two axis to be (at least very close to) zero, which is experimentally very challenging to achieve.…”

“…We now construct a model for the splitting of a spin-squeezed BEC illustrated in figure 1. Our model has general similarities to that considered in [45], but with differing treatments of the splitting procedure. The basic assumptions are that each trap in figure 1 can be approximated by two bosonic modes.…”

Stroboscopic quantum nondemolition measurements for enhanced entanglement generation between atomic ensembles

“…The closest demonstration has been the observation of entanglement between spatially separate regions of a single cloud [21,22,47,48]. Numerical theoretical proposals for entanglement between BECs have been proposed, using a variety of techniques ranging from cavity QED [49][50][51][52][53], Rydberg excitations [54], state dependent forces [55], adiabatic transitions [51], and others [53,56,57]. Such entanglement is fundamental to performing various quantum information tasks based on atomic ensembles, such as quantum teleportation [58,59], remote state preparation and clock synchronization [60,61], and quantum computing [62,63].…”