A. Ekert and C. Macchiavello, "Error correction in quantum communication", quantph /9602022. Home/Search Document Not in Database Summary APS Related Articles Check |
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Efficient Computations of Encodings for Quantum Error Correction - Cleve, Gottesman (1996) (3 citations) (Correct)
.... in the development of error correction schemes for quantum information systems [1 10] This includes methods for converting classical error correcting codes to into quantum error correcting codes [2,3] formalizations of necessary and sufficient conditions for sets of states to form quantum codes [11,7,12], and a mathematical framework for a large class of quantum codes, known as stabilizer codes [8,9] In order to actually use quantum codes in quantum information systems, constructive methods for performing encodings, error correction, and decodings are required. Towards this end, gate arrays that ....
A. Ekert and C. Macchiavello, "Error correction in quantum communication", quantph /9602022.
Quantum Stabilizer Codes and Classical Linear Codes - Cleve (1996) (1 citation) (Correct)
....an external environment , thereby simulating the effect of decoherence . An apparently weaker definition limits the unitary operations to being among: oe x , oe y , and oe z , the standard Pauli spin matrices, and I, the unit matrix. It turns out that, by reasoning similar to that in [6,10,11], these three definitions of alter can be shown to be equivalent, in the sense that a code that is t error correcting with respect to the apparently weaker one will automatically be t error correcting with respect to the apparently stronger one. A quantum analog of the binary symmetric channel ....
.... Gamma 4ffi bound in [11] though the latter bound has the advantage that it applies to nonstabilizer codes as well. It is noteworthy that all of the quantum codes proposed to date for the channels described above are stabilizer codes. Other upper bounds exist for nondegenerate quantum codes (see [10] for a definition of nondegenerate) One is 1 Gamma H(ffi) Gamma p log 2 3, and is based on an analogue of the classical sphere packing bound [10] and another asserts that the asymptotic capacity is zero if ffi 1=6 [20] It remains an open question whether the 1 Gamma H(ffi) Gamma ffi ....
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A. Ekert and C. Macchiavello, "Error correction in quantum communication," Phys. Rev. Lett. Vol. 77, No. 12, pp 2585--2588 (1996).
Quantum Error Correction Via Codes Over GF(4) - Calderbank, Rains, Shor, Sloane (1996) (27 citations) (Correct)
....x oe z , describes the possible errors in n qubits. For the purposes of quantum error correction, we need consider only the three types of errors oe x , oe z and oe x oe z , since any error correcting code which corrects t of these errors will be able to correct arbitrary errors in t qubits [3] [20]. Our codes will thus be tailored for the error model in which each qubit undergoes independent errors, and the three errors oe x , oe z and oe x oe z are all equally likely. The results of [3] 20] show that any code which corrects these types of quantum errors will be able to correct errors in ....
....code which corrects t of these errors will be able to correct arbitrary errors in t qubits [3] 20] Our codes will thus be tailored for the error model in which each qubit undergoes independent errors, and the three errors oe x , oe z and oe x oe z are all equally likely. The results of [3] [20] show that any code which corrects these types of quantum errors will be able to correct errors in arbitrary error models, assuming the errors are not correlated among large numbers of qubits and that the error rate is small. It may be possible for other error models to find codes which correct ....
A. Ekert and C. Macchiavello, "Error correction in quantum communication," LANL e-print quant-ph/9602022.
Projective Plane And Planar Quantum Codes - Freedman, Meyer (1998) (1 citation) (Correct)
.... Meyer Kitaev has constructed a class of quantum error correcting codes using qubits arranged on the edges of square lattices embedded in the two dimensional torus [1] While these toric codes are not particularly efficient they do not come close to saturating the quantum Hamming bound [2] they are nevertheless interesting for several reasons: Toric codes have local stabilizers, which means that the code subspace can be identified as the (degenerate) ground state subspace of a local Hamiltonian; thus there would be some level of automatic error correction in such a quantum ....
A. Ekert and C. Macchiavello, "Error correction in quantum communication", Phys. Rev. Lett. 77 (1996) 2585--2588.
quant-ph/9607030 31 Jul 1996 - Calt- Quic- Efficient (Correct)
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A. Ekert and C. Macchiavello, "Error correction in quantum communication", quantph /9602022.
quant-ph/9612048 - Dec Quantum Stabilizer (Correct)
No context found.
A. Ekert and C. Macchiavello, "Error correction in quantum communication," Phys. Rev. Lett. Vol. 77, No. 12, pp 2585--2588 (1996).
The Art of Signaling: Fifty Years of Coding Theory - Calderbank (1998) (6 citations) (Correct)
No context found.
A. Ekert and C. Macchiavello, "Error correction in quantum communication, " Phys. Rev. Lett., vol. 77, pp. 2585--2588, 1996.
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