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Teleportation of Indistinguishable Fermion Particles

Yan Feng-Li

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

It is more difficult to teleport indistinguishable particles than to teleport distinguishable particles. A scheme for teleporting indistinguishable Fermion particles is proposed in this paper,by introducing the spatial degrees of freedom of all the particles involved and the bell vectors including anti-symmetry property on the spins and the spatial degrees.

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•Dec 5, 2018•0 citations
It is more difficult to teleport indistinguishable particles than to teleport distinguishable particles. A scheme for teleporting indistinguishable Fermion particles is proposed in this paper,by introducing the spatial degrees of freedom of all the particles involved and the bell vectors including anti-symmetry property on the spins and the spatial degrees.
The teleportation of an unknown polarization state of one of the photons in a system of identical particles has been considered. It has been shown that the spatial degrees of freedom, which are various directions of the momentum of three photons, are of significant importance for teleportation in the system of identical particles. The inclusion of the spatial degrees of freedom increases the dimension of the space of single-particle states. In view of this increase, a four-dimensional subspace of two-particle states, which is similar to the space of states spanned on the Bell states in the system of two distinguishable qubits, can be separated in the experimental configuration.
We study teleportation with identical massive particles. Indistinguishability imposes that the relevant degrees of freedom to be teleported are not particles, but rather addressable orthogonal modes. We discuss the performances of teleportation under the constraint of conservation of the total number of particles. The latter inevitably decreases the teleportation fidelity. Moreover, even though a phase reference, given by the coupling to a reservoir, circumvents the constraint, it does not restore perfect deterministic teleportation. The latter is only achievable with some special resource entangled states and when the number of particles tends to infinity. Interestingly, some of such states are the many-particle atomic coherent states and the ground state of cold atoms loaded into a double well potential, which are routinely prepared in experiments.
We investigate indistinguishability of identical bosons and fermions undergoing arbitrary particle-number-preserving evolutions of their visible degrees of freedom. For the projective indistinguishability measure, defined by the projection of the visible state onto the symmetric/anti-symmetric subspace, we derive an equivalent expression in terms of the dynamically invariant internal state. We further generalize the textbook symmetrization/anti-symmetrization framework for bosons and fermions to arbitrary partial distinguishability by deriving an explicit reconstruction formula for the multiparticle visible state in terms of the indistinguishability function encoding the dynamical invariants. We give complete characterization of the class-functions of indistinguishability by projective measures on generalized symmetries. Finally, we reveal a strikingly counterintuitive effect: introducing additional particle label states can increase the multiparticle indistinguishability of identical particles. The effect originates from the cancellation of collective multiparticle phases.
When quantum teleportation is performed with truly identical massive particles, indistinguishability allows us to teleport addressable degrees of freedom which do not identify particles, but, for example, orthogonal modes. The key resource of the protocol is a state of entangled modes, but the conservation of the total number of particles does not allow for perfect deterministic teleportation unless the number of particles in the resource state goes to infinity. Here, we study the convergence of teleportation performances in the above limit and provide sufficient conditions for asymptotic perfect teleportation. We also apply these conditions to the case of resource states affected by noise.
Entanglement swapping represents an important protocol for transferring information within quantum networks. Here we present a scheme to implement entanglement swapping with independently-prepared identical particles (bosons or fermions), exploiting the indistinguishability due to their spatial overlap. In this protocol no initial entangled pairs are required and, for fermions, even Bell state measurements have not to be performed. These features constitute both a conceptual and practical advance compared to the standard procedure. The scheme is straightforwardly extended to multiple swapping, which is basic for quantum repeaters and relays in quantum information processing.