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Quantum Teleportation is a very useful scheme for
transferring quantum information. Given that the quantum information
is encoded in a state of a system of distinguishable particles, and
given that the shared bi-partite entangled state is also that of a
system of distinguishable particles, the optimal teleportation
fidelity of the shared state is known to be $(F_{max}d+1)/(d+1)$ with
$F_{max}$ being the `maximal singlet fraction' of the shared state. In
the present work, we address the question of optimal teleportation
fidelity given that the quantum information to be teleported is
encoded in Fermionic modes while a $2N$-mode state of a system of
Fermions (with maximum $2N$ no. of Fermions -- in the second
quantization language) is shared between the sender and receiver with
each party possessing N modes of the $2N$-mode state. Parity
Superselection Rule (PSSR) in Fermionic Quantum Theory (FQT) puts
constraint on the allowed set of physical states and operations, and
thereby, leads to a different notion of Quantum Teleportation. Due to
PSSR, we introduce restricted Clifford twirl operations that
constitute the Unitary 2-design in case of FQT, and show that the
structure of the canonical form of Fermionic invariant shared state
differs from that of the isotropic state -- the corresponding
canonical invariant form for teleportation in Standard Quantum Theory
(SQT). We provide a lower bound on the optimal teleportation fidelity
in FQT and compare the result with teleportation in SQT. Surprisingly,
we find that, under separable measurements on a bipartite Fermionic
state, input and output states of the Fermionic teleportation channel
cannot be distinguished operationally, even if a particular kind of
resource state with `maximal singlet fraction' being less than unity
is used.
Ref.: arXiv:2312.04240 [quant-ph] |