Thermodynamic Interpretation of the Quantum Error Correcting Criterion

@article{Korepin2002ThermodynamicIO,
  title={Thermodynamic Interpretation of the Quantum Error Correcting Criterion},
  author={Vladimir E. Korepin and John Terilla},
  journal={Quantum Information Processing},
  year={2002},
  volume={1},
  pages={225-242}
}
AbstractShannon's fundamental coding theorems relate classical information theory to thermodynamics. More recent theoretical work has been successful in relating quantum information theory to thermodynamics. For example, Schumacher proved a quantum version of Shannon's 1948 classical noiseless coding theorem. In this note, we extend the connection between quantum information theory and thermodynamics to include quantum error correction. There is a standard mechanism for describing errors that… 
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References

SHOWING 1-10 OF 35 REFERENCES
Error Correcting Codes in Quantum Theory.
  • Steane
  • Physics
    Physical review letters
  • 1996
TLDR
It is shown that a pair of states which are, in a certain sense, “macroscopically different,” can form a superposition in which the interference phase between the two parts is measurable, providing a highly stabilized “Schrodinger cat” state.
Thermodynamical analogues in quantum information theory
TLDR
This work learns how to efficiently exploit entanglement by applying analogues of thermodynamical concepts, including reversibility, entropy, and the distinction between intensive and extensive quantities.
Theory of quantum error-correcting codes
TLDR
A general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions is developed and necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction are obtained.
Reliable quantum computers
  • J. Preskill
  • Physics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1998
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled
Quantum Computation and Quantum Information
TLDR
This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
Topological Quantum Computation
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones poly-
Balance of information in bipartite quantum-communication systems: Entanglement-energy analogy
TLDR
It is shown that in the closed bipartite quantum-communication systems, the information is conserved and the objectivity of quantum information in the context of information interpretation of quantum states and algorithmic complexity is discussed.
Stabilizer Codes and Quantum Error Correction
TLDR
An overview of the field of quantum error correction and the formalism of stabilizer codes is given and a number of known codes are discussed, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation are discussed.
Quantum Error Correction Via Codes Over GF(4)
TLDR
In the present paper 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 certain trace inner product.
Encoded Universality in Physical Implementations of a Quantum Computer
TLDR
A general Lie-algebraic framework is outlined which can be used to find the encoding for universality in quantum computing and several examples relevant to solid-state quantum computing are given.
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