In a previous paper [1] an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov’s volume formula for SU(N) [2,3] will also be derived. As an example of this parameterization’s usefulness, the density matrix paramete...

Recently a pair of experiments [1, 2] demonstrated a simulation of Abelian anyons in a spin network of single photons. The experiments were based on an Abelian discrete gauge theory spin lattice model of Kitaev [3]. Here we describe how to use linear optics and single photons to simulate non-Abelian anyons. The scheme makes use of joint qutrit-qubit encoding of the spins and the resources requi...

Abstract A 9×9 unitary R̆−matrix, solution of the Yang-Baxter Equation, is obtained in this paper. The entanglement properties of R̆−matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via R̆-matrix acting on the standard basis. A Yang-Baxter Hamiltonian can be constructed from unitary R̆−matrix. Then the geometric properties of this sys...

Classical to quantum decoherence transition, an issue existing for incoherent superposition of Bell-diagonal states is studied for three dimensional bipartite AB mixed quantum systems. Depending on the initial conditions, the dynamics of classical and quantum correlations can exhibit a sudden transition between classical to quantum decoherence. This result is calculated numerically by using ent...

Non-separable superpositions of polarization and spatial mode of a single photon produce a state that has a polarization that depends on the transverse position, and contains all states of polarization represented on the Poincaré sphere. We have done measurements of the space-dependent state of polarization of single photons prepared in distinct 2×2 (qubit-qubit) and 2×3 (qubit-qutrit) non-sepa...

Eigenstates of permutation gates are either stabilizer states (for gates in the Pauli group) or magic states, thus allowing universal quantum computation (Planat, Rukhsan-Ul-Haq 2017 Adv. Math. Phys. 2017, 5287862 (doi:10.1155/2017/5287862)). We show in this paper that a subset of such magic states, when acting on the generalized Pauli group, define (asymmetric) informationally complete POVMs. ...

We present a way to transfer maximally- or partially-entangled states of n single-photon-state (SPS) qubits onto coherent-state (CS) qubits, by employing 2n microwave cavities coupled superconducting flux qutrit. The two logic SPS qubit here are represented the vacuum state and single-photon cavity, while CS encoded with coherent cavity. Because using only one qutrit as coupler, circuit archite...

A general protocol in quantum information and communication relies in the ability of producing, transmitting, and reconstructing, in general, qunits. In this Letter we show for the first time the experimental implementation of these three basic steps on a pure state in a three-dimensional space, by means of the orbital angular momentum of the photons. The reconstruction of the qutrit is perform...

In a previous paper [1] an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov’s volume formula for SU(N) [2,3] will also be derived. As an example of this parameterization’s usefulness, the density matrix paramete...

In this paper, three quantum key distribution protocols will be presented. The first protocol considered is the Ekert protocol for qubit systems based on the famous Einstein-Podolsky-Rosen experiment, and using the Bell inequality as a test of channel security. The Ekert protocol will then be extended to a qutrit system for our second protocol. Finally, a protocol based on mutually complementar...