Quantum state tomography relies on the ability to perform well-characterized unitary operations, which are not always available. This places restrictions on which physical systems can be characterized using such techniques. We develop a formalism that circumvents the requirement for well-characterized unitary operations by treating unknown parameters in the state and unitary process on the same...

We introduce a 3 x 3 matrix for the study of unitary optical systems. This 3 x 3 matrix is a submatrix of the 4 x 4 Mueller matrix. The elements of this 3 x 3 matrix are real, and thus complex-number calculations can be avoided. The 3 x 3 matrix is useful for illustrating the polarization state of an optical system. One can also use it to derive the conditions for linear and circular polarizati...

Quantum Logic Processors can be implemented with Mach Zehnder Interferometer(MZI) configurations for the Quantum logic operations and gates. In this paper, its implementation for both optical and electronic system has been presented. The correspondence between Jones matrices for photon polarizations and Pauli spin matrices for electrons gives a representation of all the unitary matrices for the...

We consider the problem of digital communication in a Rayleigh flat fading environment using a multiple-antenna system, when the channel state information is available neither at the transmitter nor at the receiver. It is known that at high SNR, or when the coherence interval is much larger than the number of transmit antennas, a constellation of unitary matrices can achieve the capacity of the...

We consider a Markovian approximation, of weak coupling type, to an open system perturbation involving emission, absorption and scattering by reservoir quanta. The result is the general form for a quantum stochastic flow driven by creation, annihilation and gauge processes. A weak matrix limit is established for the convergence of the interaction-picture unitary to a unitary, adapted quantum st...

Governed by locality, we explore a connection between unitary braid group representations associated to a unitary R-matrix and to a simple object in a unitary braided fusion category. Unitary R-matrices, namely unitary solutions to the Yang-Baxter equation, afford explicitly local unitary representations of braid groups. Inspired by topological quantum computation, we study whether or not it is...

The reliable and precise generation of quantum unitary transformations is essential to the realization of a number of fundamental objectives, such as quantum control and quantum information processing. Prior work has explored the optimal control problem of generating such unitary transformations as a surface optimization problem over the quantum control landscape, defined as a metric for realiz...

The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite size may be expressed in terms of a solution of the fifth Painlevé transcendent. The generating function of a certain discontinuous linear statistic of the Laguerre unitary ensemble can similarly be expressed in terms of a solution of the fifth Painlevé equation. The methodology used to derive ...

We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schrödinger equation in the continuum limit, in any number of dimensions. There is a simple mathematical relationship between the mass of the Schrödinger particle and the eigenvalues of a unitary matrix describing the local evolution of t...