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Free Semigroupoid Algebras
Every countable directed graph generates a Fock space Hilbert space and a family of partial isometries. These operators also arise from the left regular representations of free semigroupoids derivedExpand
Unified and generalized approach to quantum error correction.
We present a unified approach to quantum error correction which incorporates the known techniques--i.e., the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method. Expand
Generalization of quantum error correction via the Heisenberg picture.
We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. Expand
Quantum error correction of observables
A formalism for quantum error correction based on operator algebras was introduced by us earlier [Phys. Rev. Lett. 98, 10052 (2007)] via consideration of the Heisenberg picture for quantum dynamics.Expand
Isomorphisms of algebras associated with directed graphs
Abstract.Given countable directed graphs G and G′, we show that the associated tensor algebras (G) and (G′) are isomorphic as Banach algebras if and only if the graphs G are G′ are isomorphic. ForExpand
Quantum Channels, Wavelets, Dilations and Representations of $O_n$
  • D. Kribs
  • Mathematics, Physics
  • 23 September 2003
We show that the representations of the Cuntz C$^\ast$-algebras $O_n$ which arise in wavelet analysis and dilation theory can be classified through a simple analysis of completely positive maps onExpand
Operator quantum error correction
This paper is an expanded and more detailed version of the work [1] in which the Operator Quantum Error Correction formalism was introduced. Expand
Higher-rank numerical ranges and compression problems
We consider higher-rank versions of the standard numerical range for matrices. A central motivation for this investigation comes from quantum error correction. We develop the basic structure theoryExpand
Tensor algebras of C∗-correspondences and their C∗-envelopes
Abstract We show that the C ∗ -envelope of the tensor algebra of an arbitrary C ∗ -correspondence X coincides with the Cuntz–Pimsner algebra O X , as defined by Katsura [T. Katsura, On C ∗ -algebrasExpand
The multiplicative domain in quantum error correction
We show that the multiplicative domain of a completely positive map yields a new class of quantum error correcting codes. In the case of a unital quantum channel, these are precisely the codes thatExpand