Related papers: Quantum Complementarity and Operator Structures
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…
We propose an operational definition of complementarity, pinning down the concept originally introduced by Bohr. Two properties of a system are considered complementary if they cannot be simultaneously well defined. We further show that,…
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 generalize a recently discovered example of a private quantum subsystem to find private subsystems for Abelian subgroups of the $n$-qubit Pauli group, which exist in the absence of private subspaces. In doing so, we also connect these…
Quantum connections are defined by parallel transport operators acting on a Hilbert space. They transport tangent operators along paths in parameter space. The metric tensor of a Riemannian manifold is replaced by an inner product of pairs…
We present an "uncertainty principle" for quantum channels, showing a relationship between the dimensions of the range of a channel and the range of its complement. We examine some interesting specific cases, and discuss consequences for…
For certain situations we give a geometrical background for quasiclassical KP calculations based on an explicit connection to quantum mechanics and the collapse of coherent states to coadjoint orbits for classical operators.
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
We suggest that a certain one-to-one parametrization of completely positive maps on the matrix algebra might be useful in the study of quantum channels. This is illustrated in the case of binary quantum channels. While the algorithm is…
For a noisy quantum channel, a quantum error correcting code exists if and only if the joint higher rank numerical ranges associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint…
The relation between quantum systems associated to root systems and radial parts of Laplace operators on symmetric spaces is established. From this it follows the complete integrability of some quantum systems.
The quantum dimensions of modules for vertex operator algebras are defined and their properties are discussed. The possible values of the quantum dimensions are obtained for rational vertex operator algebras. A criterion for simple currents…
In many networks, including networks of protein-protein interactions, interdisciplinary collaboration networks, and semantic networks, connections are established between nodes with complementary rather than similar properties. While…
The dual picture of quantum geometry provided by a spin network state is discussed. From this perspective, we introduce a new operator in Loop Quantum Gravity - the length operator. We describe its quantum geometrical meaning and derive…
Quantum states are successfully reconstructed using the maximum likelihood estimation on the subspace where the measured projectors reproduce the identity operator. Reconstruction corresponds to normalization of incompatible observations.…
Problem of classification of parallel quantum channels for information transfer is studied by method of ladder operators. Detailed compared to http://arxiv.org/abs/quant-ph/0702076 presentation of method of ladder operators is given.…
Pivotal within quantum physics, the concept of quantum incompatibility is generally related to algebraic aspects of the formalism, such as commutation relations and unbiasedness of bases. Recently, the concept was identified as a resource…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.