# 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…

## 6 Citations

Thermodynamic Constraints on Quantum Information Gain and Error Correction: A Triple Trade-Off

- Physics
- 2022

Quantum error correction (QEC) is a procedure by which the quantum state of a system is protected against a known type of noise, by preemptively adding redundancy to that state. Such a procedure is…

Revisiting thermodynamics in computation and information theory

- Physics, Computer Science
- 2021

The progress of the thermodynamic cost of computation starting from Landauer’s principle to the latest model, which simulates the modern complex computation mechanism is reviewed.

The correlation functions of the Heisenberg chain in the case of zero or infinite anisotropy, and random walks of vicious walkers

- Physics, Mathematics
- 2011

The XXZ Heisenberg chain is considered for two specific limits of the anisotropy parameter: � ! 0 and � ! −1 . The corresponding wave functions are expressed by means of the symmetric Schur…

## References

SHOWING 1-10 OF 35 REFERENCES

Error Correcting Codes in Quantum Theory.

- PhysicsPhysical review letters
- 1996

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

- Physics
- 2001

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

- Computer Science
- 1997

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

- PhysicsProceedings 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

- Physics, Computer Science
- 2000

This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.

Topological Quantum Computation

- Physics
- 2001

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

- Physics, Computer Science
- 2001

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

- Computer Science
- 1997

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)

- Computer Science, PhysicsIEEE Trans. Inf. Theory
- 1998

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

- Physics, Computer Science
- 2001

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.