arXiv subjects

D. W. Kribs

Publications and source records attributed to D. W. Kribs.

6 recordsLinked to original sources

arXiv2020

Nullspaces of Entanglement Breaking Channels and Applications

We investigate the nullspace structures of entanglement breaking channels, and related applications. We show that every operator space of trace zero matrices is the nullspace of an entanglement breaking channel. We derive a test for mixed unitarity of quantum channels based on complementary channel behaviour and entanglement breaking channel nullspaces. We identify conditions that guarantee the existence of private algebras for certain classes of entanglement breaking channels.

quant-ph↗

arXiv2019

Quantum Complementarity and Operator Structures

We establish operator structure identities for quantum channels and their error-correcting and private codes, emphasizing the complementarity relationship between the two perspectives. Relevant structures include correctable and private operator algebras, and operator spaces such as multiplicative domains and nullspaces of quantum channels and their complementary maps. For the case of privatizing to quantum states, we also derive related dimension inequalities that may be viewed as operator algebra uncertainty relations.

quant-ph↗

arXiv2014

Private quantum codes: introduction and connection with higher rank numerical ranges

We give a brief introduction to private quantum codes, a basic notion in quantum cryptography and key distribution. Private code states are characterized by indistinguishability of their output states under the action of a quantum channel, and we show that higher rank numerical ranges can be used to describe them. We also show how this description arises naturally via conjugate channels and the bridge between quantum error correction and cryptography.

math.OA↗

arXiv2004

Noiseless subsystems for collective rotation channels in quantum information theory

Collective rotation channels are a fundamental class of channels in quantum computing and quantum information theory. The commutant of the noise operators for such a channel is a C*-algebra which is equal to the set of fixed points for the channel. Finding the precise spatial structure of the commutant algebra for a set of noise operators associated with a channel is a core problem in quantum error prevention. We draw on methods of operator algebras, quantum mechanics and combinatorics to explicitly determine the structure of the commutant for the class of collective rotation channels.

math.OA↗

arXiv2004

Noiseless subsystems and the structure of the commutant in quantum error correction

The effect of noise on a quantum system can be described by a set of operators obtained from the interaction Hamiltonian. Recently it has been shown that generalized quantum error correcting codes can be derived by studying the algebra of this set of operators. This led to the discovery of noiseless subsystems. They are described by a set of operators obtained from the commutant of the noise generators. In this paper we derive a general method to compute the structure of this commutant in the case of unital noise.

quant-ph↗

arXiv2002

Wavelet representations and Fock space on positive matrices

We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly-cyclic subspaces. Further, motivated by these representations, we introduce a general Fock-space Hilbert space construction which yields creation operators containing the Cuntz--Toeplitz isometries as a special case.

math.CA↗