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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 derived… Expand

Unified and generalized approach to quantum error correction.

- D. Kribs, R. Laflamme, D. Poulin
- Computer Science, Medicine
- Physical review letters
- 9 December 2004

TLDR

Generalization of quantum error correction via the Heisenberg picture.

TLDR

Quantum error correction of observables

- C. Bény, Achim Kempf, D. Kribs
- Physics
- 11 May 2007

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

- E. Katsoulis, D. Kribs
- Mathematics
- 22 September 2003

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. For… Expand

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 on… Expand

Operator quantum error correction

- D. Kribs, R. Laflamme, D. Poulin, M. Lesosky
- Computer Science, Physics
- Quantum Inf. Comput.
- 26 April 2005

TLDR

Higher-rank numerical ranges and compression problems

- Man-Duen Choi, D. Kribs, K. Życzkowski
- Mathematics, Physics
- 10 November 2005

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 theory… Expand

Tensor algebras of C∗-correspondences and their C∗-envelopes

- E. Katsoulis, D. Kribs
- Mathematics
- 8 June 2005

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 ∗ -algebras… Expand

The multiplicative domain in quantum error correction

- Man-Duen Choi, N. Johnston, D. Kribs
- Mathematics, Physics
- 6 November 2008

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 that… Expand

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