We study the entanglement R{e}nyi $alpha$-entropy (ER$alpha $E) as the measure of entanglement. Instead of a single quantity in standard entanglement quantification for a quantum state by using the von Neumann entropy for the well-accepted entangleme
nt of formation (EoF), the ER$alpha $E gives a continuous spectrum parametrized by variable $alpha $ as the entanglement measure, and it reduces to the standard EoF in the special case $alpha rightarrow 1$. The ER$alpha $E provides more information in entanglement quantification, and can be used such as in determining the convertibility of entangled states by local operations and classical communication. A series of new results are obtained: (i) we can show that ER$alpha $E of two states, which can be mixed or pure, may be incomparable, in contrast to the fact that there always exists an order for EoF of two states; (ii) similar as the case of EoF, we study in a fully analytical way the ER$alpha $E for arbitrary two-qubit states, the Werner states and isotropic states in general d-dimension; (iii) we provide a proof of the previous conjecture for the analytical functional form of EoF of isotropic states in arbitrary d-dimension.
We propose a quantum method to judge whether two spatially separated clocks have been synchronized within a specific accuracy $sigma$. If the measurement result of the experiment is obviously a nonzero value, the time difference between two clocks is
smaller than $sigma$; otherwise the difference is beyond $sigma$. On sharing the 2$N$-qubit bipartite maximally entangled state in this scheme, the accuracy of judgement can be enhanced to $sigmasim{pi}/{(omega(N+1))}$. This criterion is consistent with Heisenberg scaling that can be considered as beating standard quantum limit, moreover, the unbiased estimation condition is not necessary.
We propose a scenario to create topological superfluid in a periodically driven two-dimensional square optical lattice. We study the phase diagram of a spin-orbit coupled s-wave pairing superfluid in a periodically driven two-dimensional square optic
al lattice. We find that a phase transition from a trivial superfluid to a topological superfluid occurs when the potentials of the optical lattices are periodically changed. The topological phase is called Floquet topological superfluid and can host Majorana fermions.
We propose a scheme to implement quantum computation in decoherence-free subspace with superconducting devices inside a cavity by unconventional geometric manipulation. Universal single-qubit gates in encoded qubit can be achieved with cavity assiste
d interaction. A measurement-based two-qubit Controlled-Not gate is produced with parity measurements assisted by an auxiliary superconducting device and followed by prescribed single-qubit gates. The measurement of currents on two parallel devices can realize a projective measurement, which is equivalent to the parity measurement on the involved devices.
We study theoretically the localization of relativistic particles in disordered one-dimensional chains. It is found that the relativistic particles tend to dislocation in comparison with the non-relativistic particles with the same disorder strength.
More intriguingly, we reveal that the massless Dirac particles are entirely delocalized for any energy due to the inherent chiral symmetry, leading to a well-known result that particles are always localized in one-dimensional system for arbitrary weak disorders to break down. Furthermore, we propose a feasible scheme to simulate and detect the delocalization feature of the Dirac particles with cold atoms..
A two-component fermion model with conventional two-body interactions was recently shown to have anyonic excitations. We here propose a scheme to physically implement this model by transforming each chain of two two-component fermions to the two capa
citively coupled chains of superconducting devices. In particular, we elaborate how to achieve the wanted operations to create and manipulate the topological quantum states, providing an experimentally feasible scenario to access the topological memory and to build the anyonic interferometry.
We design an ingenious scheme to realize the Haldanes quantum Hall model without Landau level by using ultracold atoms trapped in an optical lattice. Three standing-wave laser beams are used to construct a wanted honeycomb lattice, where different on
-site energies in two sublattices required in the Haldanes model can be implemented through tuning the phase of one of the laser beams. The staggered magnetic field is generated from the Berry phase associated with the atom moving in a region with other three standing-wave laser beams. Moreover, we establish a relation between the Hall conductivity and the equilibrium atomic density upon turning on a stimulated uniform magnetic field, which enables us to detect the topological Chern number with the density profile measurement technique that is typically used in ultracold atoms experiments.
