Quantum convolutional coding with shared entanglement: general structure
Mark M. Wilde,Todd A. Brun +1 more
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Citations
Entanglement-assisted quantum turbo codes
TL;DR: It is proved that entanglement is the resource that enables a convolutional encoder to be both non-catastrophic and recursive because an encoder acting on only information qu bits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them.
Trading Classical Communication, Quantum Communication, and Entanglement in Quantum Shannon Theory
Min-Hsiu Hsieh,Mark M. Wilde +1 more
TL;DR: A “unit-resource” capacity theorem is proved that applies to the scenario where only the above three noiseless resources are available for consumption or generation, and the optimal strategy mixes the three fundamental protocols of teleportation, superdense coding, and entanglement distribution.
94
Entanglement-Assisted Quantum Turbo Codes
TL;DR: In this article, an entanglement-assisted quantum convolutional encoder for quantum turbo codes is proposed, which can achieve both recursive and non-catastrophic decoding.
•Journal Article
Encoding One Logical Qubit Into Six Physical Qubits
TL;DR: In this paper, it was shown that a six-qubit code without entanglement assistance cannot simultaneously possess a Calderbank-Shor-Steane CSS stabilizer and correct an arbitrary single qubit error.
29
Minimal-memory, non-catastrophic, polynomial-depth quantum convolutional encoders
TL;DR: This paper elucidate a general technique for finding an encoder of an arbitrary quantum convolutional code such that the encoder possesses these desirable properties and provides an elementary proof that these encoders are nonrecursive.
21
References
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Quantum Computation and Quantum Information
Michael A. Nielsen,Isaac L. Chuang +1 more
- 01 Jan 2000
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Communication via One- and Two-Particle Operators on Einstein-Podolsky-Rosen States
TL;DR: The set of states accessible from an initial EPR state by one-particle operations are characterized and it is shown that in a sense they allow two bits to be encoded reliably in one spin-1/2 particle.
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Stabilizer Codes and Quantum Error Correction
TL;DR: In this paper, the authors give an overview of the field of quantum error correction and the formalism of stabilizer codes, discuss a number of known codes, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation.
2.2K
Quantum error correction via codes over GF(4)
A.R. Calderbank,Eric M. Rains,Peter W. Shor,Neil J. A. Sloane +3 more
- 29 Jun 1997
TL;DR: In this article, the problem of finding quantum error-correcting codes is transformed into one of finding additive codes over the field GF(4) which are self-orthogonal with respect to a trace inner product.
The private classical capacity and quantum capacity of a quantum channel
TL;DR: In this paper, the capacity of a quantum channel for transmitting private classical information is derived, which is shown to be equal to the capacity for generating a secret key, and neither capacity is enhanced by forward public classical communication.
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