Related papers: Environment and classical channels in categorical …

We define syntax and semantics of quantum circuits, allowing measurement gates and classical channels. We define circuit-based quantum algorithms and prove that, semantically, any such algorithm is equivalent to a single measurement that…

A quantum channel physically is a unitary interaction between the information carrying system and an environment, which is initialized in a pure state before the interaction. Conventionally, this state, as also the parameters of the…

We determine the capacity of compound classical-quantum channels. As a consequence we obtain the capacity formula for the averaged classical-quantum channels. The capacity result for compound channels demonstrates, as in the classical…

An assessment is given as to the extent to which pure unitary evolution, as distinct from environmental decohering interaction, can provide the transition necessary for an observer to interpret perceived quantum dynamics as classical. This…

The capacity of noisy quantum channels characterizes the highest rate at which information can be reliably transmitted and it is therefore of practical as well as fundamental importance. Capacities of classical channels are computed using…

State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under…

A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…

We propose a categorical foundation for the connection between pure and mixed states in quantum information and quantum computation. The foundation is based on distributive monoidal categories. First, we prove that the category of all…

A direct proof of the relation between the one-shot classical capacity and the minimal output entropy for covariant quantum channels is suggested. The structure of covariant channels is described in some detail. A simple proof of a general…

An expression is derived characterizing the set of admissible rate pairs for simultaneous transmission of classical and quantum information over a given quantum channel, generalizing both the classical and quantum capacities of the channel.…

We investigate whether certain non-classical communication channels can be simulated by a classical channel with a given number of states and a given `amount' of noise. It is proved that any noisy quantum channel can be simulated by a…

Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…

We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…

Contextuality is a defining feature that separates the quantum from the classical descriptions of physical systems. Within the marginal-scenario framework, noncontextual models are characterized by the existence of a single joint…

In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…

A variety of tasks in quantum control, ranging from purification and cooling, to quantum stabilization and open-system simulation, rely on the ability to implement a target quantum channel over a specified time interval within prescribed…

A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…

We give a sufficient condition for quantising integrable systems.

For a continuous-input-continuous-output arbitrarily distributed quantum channel carrying classical information, the channel capacity can be computed in terms of the distribution of the channel envelope, received signal strength over a…

We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…