Optical implementation of a unitarily correctable code (2009)
Schreiter, Kurt M., Pasieka, Aron, Kaltenbaek, Rainer, Resch, Kevin J., Kribs, David W.
Noise poses a challenge for any real-world implementation in quantum information science. The theory of quantum error correction deals with this problem via methods to encode and recover quantum...
Man-duen Choi, John A. Holbrook, David W. Kribs, P. Halmos, D. Van Nostr
Abstract. We verify a conjecture on the structure of higher-rank numerical ranges for a wide class of unitary and normal matrices. Using analytic and geometric techniques, we show precisely how the...
Entropy of a quantum error correction code (2008)
Kribs, David W., Pasieka, Aron, Zyczkowski, Karol
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the...
The multiplicative domain in quantum error correction (2008)
Choi, Man-Duen, Johnston, Nathaniel, Kribs, David W.
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...
Quantum error correction on infinite-dimensional Hilbert spaces (2008)
Bény, Cédric, Kempf, Achim, Kribs, David W.
We present a generalization of quantum error correction to infinite-dimensional Hilbert spaces. The generalization yields new classes of quantum error correcting codes that have no finite-dimensional...
Computing Stabilized Norms for Quantum Operations via the Theory of Completely Bounded Maps (2007)
Johnston, Nathaniel, Kribs, David W., Paulsen, Vern I.
The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences of...
Kretschmann, Dennis, Kribs, David W., Spekkens, Robert W.
We make an explicit connection between fundamental notions in quantum cryptography and quantum error correction. Error-correcting subsystems (and subspaces) for quantum channels are the key vehicles...
Experimentally scalable protocol for identification of correctable codes (2007)
Silva, Marcus, Magesan, Easwar, Kribs, David W., Emerson, Joseph
The task of finding a correctable encoding that protects against some physical quantum process is in general hard. Two main obstacles are that an exponential number of experiments are needed to gain...
Quantum Error Correction of Observables (2007)
Beny, Cedric, Kempf, Achim, Kribs, David W.
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the...
Higher-Rank Numerical Ranges of Unitary and Normal Matrices (2006)
Choi, Man-Duen, Holbrook, John A., Kribs, David W., Zyczkowski, Karol
We verify a conjecture on the structure of higher-rank numerical ranges for a wide class of unitary and normal matrices. Using analytic and geometric techniques, we show precisely how the higher-rank...
Generalization of Quantum Error Correction via the Heisenberg Picture (2006)
Beny, Cedric, Kempf, Achim, Kribs, David W.
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. The resulting theory describes the...
Quantum Error Correcting Subsystems are Unitarily Recoverable Subsystems (2006)
Kribs, David W., Spekkens, Robert W.
We show that every correctable subsystem for an arbitrary noise operation can be recovered by a unitary operation, where the notion of recovery is more relaxed than the notion of correction insofar...
Decoherence-Insensitive Quantum Communication by Optimal C^*-Encoding (2006)
Bodmann, Bernhard G., Kribs, David W., Paulsen, Vern I.
The central issue in this article is to transmit a quantum state in such a way that after some decoherence occurs, most of the information can be restored by a suitable decoding operation. For this...
Decoherence-insensitive quantum communications by optimal C ∗ -encoding, preprint (2006)
Bernhard G. Bodmann, David W. Kribs, Vern I. Paulsen
The central issue in this article is to transmit a quantum state in such a way that after some decoherence occurs, most of the information can be restored by a suitable decoding operation. For this...
Higher-Rank Numerical Ranges and Compression Problems (2005)
Choi, Man-Duen, Kribs, David W., Zyczkowski, Karol
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...
Quantum Error Correcting Codes From The Compression Formalism (2005)
Choi, Man-Duen, Kribs, David W., Zyczkowski, Karol
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels...
Geometry from quantum particles (2005)
Kribs, David W., Markopoulou, Fotini
We investigate the possibility that a background independent quantum theory of gravity is not a theory of quantum geometry. We provide a way for global spacetime symmetries to emerge from a...
A method to find quantum noiseless subsystems (2005)
Choi, Man-Duen, Kribs, David W.
We develop a structure theory for decoherence-free subspaces and noiseless subsystems that applies to arbitrary (not necessarily unital) quantum operations. The theory can be alternatively phrased in...
A brief introduction to operator quantum error correction (2005)
We give a short introduction to operator quantum error correction. This is a new protocol for error correction in quantum computing that has brought the fundamental methods under a single umbrella,...
Tensor algebras of C*-correspondences and their C*-envelopes (2005)
Katsoulis, Elias G., Kribs, David W.
We show that the $\ca$-envelope of the tensor algebra of an arbitrary $\ca$-correspondence $\X$ coincides with the Cuntz-Pimsner algebra $\O_{\X}$, as defined by Katsura \cite{Ka}. This improves...
Operator quantum error correction (2005)
Kribs, David W., Laflamme, Raymond, Poulin, David, Lesosky, Maia
This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of...
A unified framework for graph algebras and quantum causal histories (2005)
We present a mathematical framework that unifies the quantum causal history formalism from theoretical high energy physics and the directed graph operator framework from the theory of operator...
Inductive limit algebras from periodic weighted shifts on Fock space (2004)
Non-commutative multivariable versions of weighted shift operators arise naturally as `weighted' left creation operators acting on the Fock space Hilbert space. We identify a natural notion of...
Isometric dilations of non-commuting finite rank $n$-tuples (2004)
Davidson, Kenneth R., Kribs, David W., Shpigel, Miron E.
A contractive $n$-tuple $A=(A_1,...,A_n)$ has a minimal joint isometric dilation $S=(S_1,...,S_n)$ where the $S_i$'s are isometries with pairwise orthogonal ranges. This determines a representation...
A class of limit algebras associated with directed graphs (2004)
Kribs, David W., Solel, Baruch
Every directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C*-algebras. We prove...
The $H^\infty$ algebras of higher rank graphs (2004)
Kribs, David W., Power, Stephen C.
We begin the study of a new class of operator algebras that arise from higher rank graphs. Every higher rank graph generates a Fock space Hilbert space and creation operators which are partial...
Universal collective rotation channels and quantum error correction (2004)
Junge, Marius, Kim, Peter T., Kribs, David W.
We present and investigate a new class of quantum channels, what we call `universal collective rotation channels', that includes the well-known class of collective rotation channels as a special...
A quantum computing primer for operator theorists (2004)
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We...
Katsoulis, Elias, Kribs, David W.
Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the...
Ideal Structure in Free Semigroupoid Algebras from Directed Graphs (2003)
Jury, Michael T., Kribs, David W.
A free semigroupoid algebra is the weak operator topology closed algebra generated by the left regular representation of a directed graph. We establish lattice isomorphisms between ideals and...
Partially Isometric Dilations of Noncommuting $N$-tuples of Operators (2003)
Jury, Michael T., Kribs, David W.
Given a row contraction of operators on Hilbert space and a family of projections on the space which stabilize the operators, we show there is a unique minimal joint dilation to a row contraction of...
Factoring in Non-commutative Analytic Toeplitz Algebras (2003)
The non-commutative analytic Toeplitz algebra is the weak operator topology closed algebra generated by the left regular representation of the free semigroup on $n$ generators. The structure theory...
The Curvature Invariant of a Non-commuting $N$-tuple (2003)
Non-commutative versions of Arveson's curvature invariant and Euler characteristic for a commuting $n$-tuple of operators are introduced. The non-commutative curvature invariant is sensitive enough...
Quantum Channels, Wavelets, Dilations and Representations of $O_n$ (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...
Partly Free Algebras from Directed Graphs (2003)
Kribs, David W., Power, Stephen C.
We say that a nonselfadjoint operator algebra is partly free if it contains a free semigroup algebra. Motivation for such algebras occurs in the setting of what we call free semigroupoid algebras....
Free Semigroupoid Algebras (2003)
Kribs, David W., Power, Stephen C.
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...
On Bilateral Weighted Shifts in Noncommutative Multivariable Operator Theory (2003)
We present a generalization of bilateral weighted shift operators for the noncommutative multivariable setting. We discover a notion of periodicity for these shifts, which has an appealing...
Non-selfadjoint Operator Algebras generated by Weighted Shifts on Fock Space (2003)
Noncommutative multivariable versions of weighted shifts arise naturally as `weighted' left creation operators acting on Fock space. We investigate the unital weak operator topology closed algebras...
Isometric Dilations of noncommuting finite rank n-tuples (1999)
Kenneth R. Davidson, David W. Kribs, E. Shpigel
Abstract. A contractive n-tuple A = (A1,..., An) has a minimal joint isometric dilation S = (S1,..., Sn) where the Si’s are isometries with pairwise orthogonal ranges. This determines a...