Entanglement in dissipative dynamics of identical particles

Abstract

Entanglement of identical massive particles recently gained attention, because of its relevance in highly controllable systems, e.g. ultracold gases. It accounts for correlations among modes instead of particles, providing a different paradigm for quantum information. We prove that the entanglement of almost all states rarely vanishes in the presence of noise, and analyse the most relevant noise in ultracold gases: dephasing and particle losses. Furthermore, when the particle number increases, the entanglement decay can turn from exponential into algebraic.Quantum correlations were proved to be a key resource in quantum information processing [1, 2, 3] and a useful tool for studying condensed matter systems [4,5]. Many of these studies were developed in the framework of distinguishable particles, where particles are manipulated locally. The peculiarity of identical particles is that they cannot be individually addressed, unless particles are effectively distinguished employing additional degrees of freedom [6,7,8], e.g. confining them in different positions.The behaviour of truly identical particles is of practical importance, since they are the elementary constituents of several physical systems in atomic and condensed matter physics. For instance, ultracold gases [9,10,11,12] can be controlled with a very high precision, and are a promising arena for the study of many-body physics and applications in quantum information [13,14,15,16,17,18]. However, these systems are unavoidably affected by noise, typically dephasing and particle losses [9].Despite different approaches [19,20,21,22,8], only a few of them are relevant for observable predictions. The characterization of quantum correlations with identical particles cannot rely on the tensor product structure of single particle Hilbert spaces, but must be reformulated in terms of subsets of locally manipulable observables [23,24,25,26,16,27,28]. This powerful approach generalizes the theory of entanglement of distinguishable particles. Moreover, when applied to identical particles, it accounts for quantum correlations of occupations of orthogonal modes, like wells in optical lattices or hyperfine levels of molecules, which are individually addressable in actual experiments [29,30,31].Within this framework, we shall prove that entanglement of almost all the states is never completely dissipated by noise under minimal assumptions including any Markovian noise, contrary to the case of distinguishable particles. Moreover, entanglement is easily generated by tunneling even in the presence of noise. We shall show with concrete examples that entanglement can decay exponentially in time but is never lost. Interestingly, when the number of particles is very large the exponential decay can turn into an algebraic decay.Beyond the characterization of the dynamics itself, the non-vanishing entanglement of many replicas of states discussed here, though small, can be distilled into a fewer copies of more entagled states via local operations and classical communiation, w...

Quantum teleportation with identical particles

“…In fact, this kind of entanglement cannot be washed out by any mixtures with separable states, and mixtures with entangled states can erase such entanglement only under very special conditions [45]. On the other hand, local noisy dynamics cannot completely dissipate entanglement at finite times [46], contrary to what happens to distinguishable particles [78][79][80]. All these phenomena reflect the fact that the set of separable states has zero measure.…”

“…Therefore, V (α) G 4 ,G 5 has to preserve the norm of the state (49). Comparing the state after the measurement (49) and the initial state (46), in order to maximize the fidelity, the state of the set G 4 that multiplies |k,σ G 1 should be transformed into |N − k,τ G 4 . Since these properties must be satisfied for all the initial states, i.e., for all the coefficients c k,σ,τ , the operator V (α) G 4 ,G 5 must transform the states…”

“…where |ψ G 1 ,G 4 is the same as the initial state (46) with the only difference that the set of modes G 2 is replaced by G 4 . Equation (54) is the average of | ψ|ψ (α) | 2 ψ (α) |ψ (α) with probability ψ (α) |ψ (α) .…”

“…Recalling the notation (4), and considering, among all possible initial states (46), (57) with 0 < c < 1, the condition (55) can be rewritten, after some simple algebra, as…”

Quantum correlations of identical particles subject to classical environmental noise

“…In real physical systems, QWs are subject to environmental noise, whose effect is to destroy quantum correlations among the walkers [58]. Therefore, the study of decoherence is of vital importance for the realization of devices that are able to implement robust quantum information protocols, in order to preserve correlations against the action of the environment.…”