Geometric discord for non-X states

The level surfaces of geometric discord for a class of two-qubit non-X states are investigated when the Bloch vectors are in arbitrary directions. The level surfaces of constant geometric discord are formed by three intersecting open tubes along three orthogc^nal directions. When Bloch vectors increase, the tubes along one or two directions shrink towards the center and may either totally disappear or the open tubes may become closed tubes when the Bloch vectors reach a critical value. In the generalized amplitude damping channel, the evolution of geometric discord shows double sudden changes when the parameter γ, increases. In the phase damping channel, the freezing phenomenon of geometric discord also exists.

Geometrical representation of coherent tunneling process in two-waveguide and three-waveguide coupler

We propose an identical geometrical representation scheme for both Landau-Zener （LZ） tunneling process in two-waveguide coupler with a cubically bent structure and stimulated Raman adiabatic passage （STIRAP） in three-waveguide coupler, similar to the geometrical representation of sum frequency process. The results show that although the two-waveguide coupler with a cubically bent axis has not aperiodic structure, it acts as a chirped quasi-phase-matching （QPM） grating and corrects the relative phase between the two supermodes in the curved coupler system. We present a scheme about how to choose the parameters to design the curved beam splitter.

Nonlinear and non-CP gates for Bloch vector amplification

Any state r=(x,y,z)of a qubit,written in the Pauli basis and initialized in the pure state r=(0,0,1),can be prepared by composing three quantum operations:two unitary rotation gates to reach a pure state r=(x^(2)+y^(2)+z^(2))-1/2×(x,y,z)on the Bloch sphere,followed by a depolarization gate to decrease|r|.Here we discuss the complementary state-preparation protocol for qubits initialized at the center of the Bloch ball,r=0,based on increasing or amplifying|r|to its desired value,then rotating.Bloch vector amplification increases purity and decreases entropy.Amplification can be achieved with a linear Markovian completely positive trace-preserving(CPTP)channel by placing the channel’s fixed point away from r=0,making it nonunital,but the resulting gate suffers from a critical slowing down as that fixed point is approached.Here we consider alternative designs based on linear and nonlinear Markovian PTP channels,which offer benefits relative to linear CPTP channels,namely fast Bloch vector amplification without deceleration.These gates simulate a reversal of the thermodynamic arrow of time for the qubit and would provide striking experimental demonstrations of non-CP dynamics.