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Quantum Convolutional Coding with Shared Entanglement: General Structure (2008)
| Citations: | 3 - 0 self |
BibTeX
@MISC{Wilde08quantumconvolutional,
author = {Mark M. Wilde and Todd A. Brun},
title = { Quantum Convolutional Coding with Shared Entanglement: General Structure},
year = {2008}
}
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Abstract
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.
Keyphrases
general structure shared entanglement quantum convolutional coding commutation relation ancilla qubits receiver share noiseless entanglement general theory calderbank-shor-steane structure entangled bell state expansion step expanded generator significant advance previous work quantum code designer quantum convolutional generator original generator information qubits online encoding quantum convolutional coding theory equivalent error-correcting property memory structure entanglement-assisted quantum convolutional coding quantum convolutional code desirable error-correcting property polynomial symplectic gram-schmidt orthogonalization procedure
