78 research outputs found
Mixed quantum state detection with inconclusive results
We consider the problem of designing an optimal quantum detector with a fixed
rate of inconclusive results that maximizes the probability of correct
detection, when distinguishing between a collection of mixed quantum states. We
develop a sufficient condition for the scaled inverse measurement to maximize
the probability of correct detection for the case in which the rate of
inconclusive results exceeds a certain threshold. Using this condition we
derive the optimal measurement for linearly independent pure-state sets, and
for mixed-state sets with a broad class of symmetries. Specifically, we
consider geometrically uniform (GU) state sets and compound geometrically
uniform (CGU) state sets with generators that satisfy a certain constraint.
We then show that the optimal measurements corresponding to GU and CGU state
sets with arbitrary generators are also GU and CGU respectively, with
generators that can be computed very efficiently in polynomial time within any
desired accuracy by solving a semidefinite programming problem.Comment: Submitted to Phys. Rev.
Quantum Convolutional Coding with Shared Entanglement: General Structure
We present a general theory of entanglement-assisted quantum convolutional
coding. The codes have a convolutional or memory structure, they assume that
the sender and receiver share noiseless entanglement prior to quantum
communication, and they are not restricted to possess the
Calderbank-Shor-Steane structure as in previous work. We provide two
significant advances for quantum convolutional coding theory. We first show how
to "expand" a given set of quantum convolutional generators. This expansion
step acts as a preprocessor for a polynomial symplectic Gram-Schmidt
orthogonalization procedure that simplifies the commutation relations of the
expanded generators to be the same as those of entangled Bell states (ebits)
and ancilla qubits. The above two steps produce a set of generators with
equivalent error-correcting properties to those of the original generators. We
then demonstrate how to perform online encoding and decoding for a stream of
information qubits, halves of ebits, and ancilla qubits. The upshot of our
theory is that the quantum code designer can engineer quantum convolutional
codes with desirable error-correcting properties without having to worry about
the commutation relations of these generators.Comment: 23 pages, replaced with final published versio
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