Related papers: Noiseless subsystems for collective rotation chann…
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 case. The fixed point set and noise commutant…
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…
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 terms of the superoperator perspective,…
Noiseless subsystems offer a general and efficient method for protecting quantum information in the presence of noise that has symmetry properties. A paradigmatic class of error models displaying non-trivial symmetries emerges under…
Quantum channels describe subsystem or open system evolution. Using the classical Koopman operator that evolves functions on phase space, 4 classical Koopman channels are identified that are analogs of the 4 possible quantum channels in a…
Moments of ensembles of unitaries play a central role in quantum information theory as they capture the statistical properties of dynamics of systems with some form of randomness. Indeed, concepts such as approximate $t$-designs arise when…
The dynamical-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…
This survey article is concerned with the modeling of the kinematical structure of quantum systems in an algebraic framework which eliminates certain conceptual and computational difficulties of the conventional approaches. Relying on the…
Operator quantum error-correction is a technique for robustly storing quantum information in the presence of noise. It generalizes the standard theory of quantum error-correction, and provides a unified framework for topics such as quantum…
We construct C*-dynamical systems for the dynamics of classical infinite particle systems describing harmonic oscillators interacting with arbitrarily many neighbors on lattices, as well on more general structures. Our approach allows…
The Ahtekar-Isham C*-algebra known from Loop Quantum Gravity is the algebra of continuous functions on the space of (generalized) connections with a compact structure Lie group. The algebra can be constructed by some inductive techniques…
We study noiseless subsystems on collective rotation channels of qudits, i.e., quantum channels with operators in the set ${\mathcal E}(d,n) = \{ U^{\otimes n}: U \in {\mathrm{SU}}(d)\}.$ This is done by analyzing the decomposition of the…
Estimating the information transmission capability of a quantum channel remains one of the fundamental problems in quantum information processing. In contrast to classical channels, the information-carrying capability of quantum channels is…
A pair of quantum channels are said to be incompatible if they cannot be realized as marginals of a single channel. This paper addresses the general structure of the incompatibility of completely positive channels with a fixed quantum input…
We present a unified approach to quantum error correction, called operator quantum error correction. This scheme relies on a generalized notion of noiseless subsystems that is not restricted to the commutant of the interaction algebra. We…
When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free…
Many quantum mechanical experiments can be viewed as multi-round interactive protocols between known quantum circuits and an unknown quantum process. Fully quantum "coherent" access to the unknown process is known to provide an advantage in…
Quantum simulation is of great importance in quantum information science. Here, we report an experimental quantum channel simulator imbued with an algorithm for imitating the behavior of a general class of quantum systems. The reported…
In the present work we review and refine some results about fixed points of semigroups of quantum channels. Noncommutative potential theory enables us to show that the set of fixed points of a recurrent semigroup is a W*-algebra; aside from…
This paper introduces quantum circuit $C^*$-algebra net, which provides a connection between $C^*$-algebra nets proposed in classical machine learning and quantum circuits. Using $C^*$-algebra, a generalization of the space of complex…