Coherency Matrices and Quantum

G. A. Bochkin, Alexander Ivanovich Zenchuk

We show that quantum states of a certain structure can be transferred from the sender to the receiver without mixing the matrix elements. The only effect of such a state transfer is scaling { of the} certain blocks (MQ-coherence matrices) of the transferred matrix. In addition, equal scaling of these blocks is also possible. We consider the transfer of two-qubit states along a homogeneous spin-1/2 chain and find the states admitting perfect transfer of their zero-order coherence matrices.

José Tito Mendonça, Hugo Terças

Tiberiu S. Tudor, Istvan Vinkler

The problem of spectral analyses, in terms of optical observables, of the time-varying spinorial fields encountered in optics is presented. Time-varying coherency matrices and spectral coherency matrices are introduced. The spectral analyses of the output of a KDP electro-optical modulator is presented as an example. The paper is conceived as a contribution to the development of the language of the optics of observables.

Karen Southwell

Ashutosh S. Marwah, Norbert Lütkenhaus

Quantum communication protocols are typically formulated in terms of abstract qudit states and operations, leaving the question of an experimental realization open. Direct translations of these protocols, say, into single photons with some $d$-dimensional degree of freedom, are typically challenging to realize. Multimode coherent states, on the other hand, can be easily generated experimentally. Reformulation of protocols in terms of these states has been a successful strategy for implementation of quantum protocols. Quantum key distribution and the quantum fingerprinting protocol have both followed this route. In this paper, we characterize the Gram matrices of multimode coherent states in an attempt to understand the class of communication protocols which can be implemented using these states. As a side product, we are able to use this characterization to show that the Hadamard exponential of a Euclidean distance matrix is positive semidefinite. We also derive the closure of the Gram matrices, which can be implemented in this way, so that we also characterize those matrices, which can be approximated arbitrarily well using multimode coherent states.

W. Pötz, Ulrich Hohenester, Jaroslav Fabian