Noiseless Quantum Codes
نویسنده
چکیده
In this paper we study a model quantum register R made of N replicas (cells) of a given finitedimensional quantum system S. Assuming that all cells are coupled with a common environment with equal strength we show that, for N large enough, in the Hilbert space of R there exists a linear subspace CN which is dynamically decoupled from the environment. The states in CN evolve unitarily and are therefore decoherence-dissipation free. The space CN realizes a noiseless quantum code in which information can be stored, in principle, for arbitrarily long time without being affected by errors.
منابع مشابه
Stabilizing Quantum Information
The algebraic structure underlying all the schemes for quantum information stabilization is argued to be fully contained in the reducibility of the operator algebra describing the interaction with the environment of the coding quantum system. This property amounts to the existence of a non-trivial group of symmetries for the global dynamics. We provide a unified framework which allows us to bui...
متن کاملOn subsystem codes beating the quantum Hamming or Singleton bound
Subsystem codes are a generalization of noiseless subsystems, decoherence-free subspaces and stabilizer codes. We generalize the quantum Singleton bound to Fq-linear subsystem codes. It follows that no subsystem code over a prime field can beat the quantum Singleton bound. On the other hand, we show the remarkable fact that there exist impure subsystem codes beating the quantum Hamming bound. A...
متن کاملQuantum error correction via less noisy qubits.
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit any classical linear codes over the binary or quaternary finite field. However, the known entanglement-assisted scheme requires noiseless qubits that help co...
متن کاملar X iv : q ua nt - p h / 07 03 21 3 v 1 2 2 M ar 2 00 7 On Subsystem Codes Beating the Hamming or Singleton Bound
Subsystem codes are a generalization of noiseless subsystems, decoherence free subspaces, and quantum error-correcting codes. We prove a Singleton bound for Fqlinear subsystem codes. It follows that no subsystem code over a prime field can beat the Singleton bound. On the other hand, we show the remarkable fact that there exist impure subsystem codes beating the Hamming bound. A number of open ...
متن کاملar X iv : q ua nt - p h / 05 04 18 9 v 2 2 8 Se p 20 05 OPERATOR QUANTUM ERROR CORRECTION
This paper is an expanded and more detailed version of the work [1] in which the Operator Quantum Error Correction protocol was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known techniques — i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method— as special cases, and relies...
متن کامل