Abstract
Quantum teleportation is considered a basic primitive in many quantum information processing tasks and has been experimentally confirmed in various photonic and matter-based setups. Here, we consider teleportation of quantum information encoded in modes of a fermionic field. In fermionic systems, superselection rules lead to a more differentiated picture of entanglement and teleportation. In particular, one is forced to distinguish between single-mode entanglement swapping, and qubit teleportation with or without authentication via Bell inequality violation, as we discuss here in detail. We focus on systems subject to parity superselection where the particle number is not fixed, and contrast them with systems constrained by particle number superselection which are relevant for possible practical implementations. Finally, we analyze the consequences for the operational interpretation of fermionic mode entanglement and examine the usefulness of so-called mixed maximally entangled states for teleportation.
Highlights
Quantum teleportation refers to the transference of quantum information encoded in the complex amplitudes of an unknown quantum state of a localized system to a remote system solely via initially entangled, local operations and exchange of classical information
We focus on systems subject to parity superselection where the particle number is not fixed, and contrast them with systems constrained by particle number superselection which are relevant for possible practical implementations
We aim to extend previous work [59] in this direction and identify if and how quantum information encoded in fermionic modes can be teleported, which resources need to be shared, and which information needs to be communicated, before we return to a discussion of the implications for fermionic entanglement in Sec
Summary
Quantum teleportation refers to the transference of quantum information encoded in the complex amplitudes of an unknown quantum state of a localized system to a remote system solely via initially entangled, local operations and exchange of classical information. Fermionic systems with variable or indefinite numbers of particles (but subject to superselection rules) allow for different ways of quantifying entanglement; see, e.g., [30,31] What do these quantifiers tell us about the usefulness of the corresponding states in practical tasks? For a single fermionic mode that is not entangled with any other mode(s), the parity SSR implies that the encoded information is classical Teleporting such a state requires no shared entanglement in principle. We consider the potential of fermionic Gaussian states and operations for teleportation, as well as the limitations imposed by particle number superselection, which is highly relevant for potential experimental implementations (in particular, using state-of-the-art methods in electron quantum optics [65]).
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