A Fixed-Phase Quantum Search Algorithm with More Flexible Behavior

When the Grover’s algorithm is applied to search an unordered database, the probability of success usually decreases with the increase of marked items. To address this phenomenon, a fixed-phase quantum search algorithm with more flexible behavior is proposed. In proposed algorithm, the phase shifts can be fixed at the different values to meet the needs of different practical problems. If research requires a relatively rapid speed, the value of the phase shifts should be appropriately increased, if search requires a higher success probability, the value of the phase shifts should be appropriately decreased. When the phase shifts are fixed at , the success probability of at least 99.38% can be obtained in iterations.

Detecting the quantum phase transition from the perspective of quantum information in the Aubry–André model

We investigate the effectiveness of entropic uncertainty, entanglement and steering in discerning quantum phase transitions(QPTs). Specifically, we observe significant fluctuations in entropic uncertainty as the driving parameter traverses the phase transition point. It is observed that the entropic uncertainty, entanglement and quantum steering, based on the electron distribution probability, can serve as indicators for detecting QPTs. Notably, we reveal an intriguing anticorrelation relationship between entropic uncertainty and entanglement in the Aubry–André model. Moreover, we explore the feasibility of detecting a QPT when the period parameter is a rational number. These observations open up new and efficient avenues for probing QPTs.

First-order quantum phase transition and entanglement in the Jaynes-Cummings model with a squeezed light

We study the quantum phase transition and entanglement in the Jaynes-Cummings model with squeezed light,utilize a special transformation method to obtain the analytical ground state of the model within the near-resonance regime,and numerically verify the validity of the analytical ground state.It is found that the ground state exhibits a first-order quantum phase transition at the critical point linearly induced by squeezed light,and the ground state entanglement reaches its maximum when the qubit-field coupling strength is large enough at the critical point.

Floquet dynamical quantum phase transitions in transverse XY spin chains under periodic kickings

Floquet dynamical quantum phase transitions(DQPTs),which are nonanalytic phenomena recuring periodically in time-periodic driven quantum many-body systems,have been widely studied in recent years.In this article,the Floquet DQPTs in transverse XY spin chains under the modulation ofδ-function periodic kickings are investigated.We analytically solve the system,and by considering the eigenstate as well as the ground state as the initial state of the Floquet dynamics,we study the corresponding multiple Floquet DQPTs emerged in the micromotion with different kicking moments.The rate function of return amplitude,the Pancharatnam geometric phase and the dynamical topological order parameter are calculated,which consistently verify the emergence of Floquet DQPTs in the system.

Phase transition in bilayer quantum Hall system with opposite magnetic field

We construct a mapped bilayer quantum Hall system to realize the proposal that two nearly flatbands have opposite Chern numbers.For the C=±1 case,the two Landau levels of the bilayer experience opposite magnetic fields.We consider a mapped bilayer quantum Hall system at total fillingν_(t)=1/2+1/2where the intralayer interaction is repulsive and the interlayer interaction is attractive.We take exact diagonalization(ED)calculations on a torus to study the phase transition when the separation distance d/l_(B)is driven.The critical point at d_(c)/l_(B)=0.68 is characterized by a collapse of degeneracy and a crossing of energy levels.In the region d/l_(B)<d_(c)/l_(B),the states of each level are highly degenerate.The pair-correlation function indicates electrons with opposite pseudo-spins are strong correlated at r=0.We find an exciton stripe phase composed of bound pairs.The ferromagnetic ground state is destroyed by the strong effective attractive potential.An electron composite-Fermion(eCF)and a hole composite Fermion(hCF)are tightly bound.In the region d/lB>d_(c)/l_(B),a crossover from the d→d_(c)limit to the large d limit is observed.The electron and hole composite Fermion liquids(CFL)are realized by composite Fermions(CF)which attach opposite fluxes,respectively.

Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.

Where Is Phase Velocity in Minkowski Space?

In the special theory of relativity, massive particles can travel at neither the speed of light c nor faster. Meanwhile, since the photon was quantized, many have thought of it as a point particle. How pointed? The idea could be a mathematical device or physical simplification. By contrast, the preceding notion of wave-group duality has two velocities: a group velocity vg and a phase velocity vp. In light vp = vg = c;but it follows from special relativity that, in massive particles, vp > c. The phase velocity is the product of the two best measured variables, and so their product constitutes internal motion that travels, verifiably, faster than light. How does vp then appear in Minkowski space? For light, the spatio-temporal Lorentz invariant metric is s2=c2t2−x2−y2−z2, the same in whatever frame it is viewed. The space is divided into 3 parts: firstly a cone, symmetric about the vertical axis ct > 0 that represents the world line of a stationary particle while the conical surface at s = 0 represents the locus for light rays that travel at the speed of light c. Since no real thing travels faster than the speed of light c, the surface is also a horizon for what can be seen by an observer starting from the origin at time t = 0. Secondly, an inverted cone represents, equivalently, time past. Thirdly, outside the cones, inaccessible space. The phase velocity vp, group velocity vg and speed of light are all equal in free space, vp = vg = c, constant. By contrast, for particles, where causality is due to particle interactions having rest mass mo > 0, we have to employ the Klein-Gordon equation with s2=c2t2−x2−y2−z2+mo2c2. Now special relativity requires a complication: vp.vg = c2 where vg c and therefore vp > c. In the volume outside the cones, causality due to light interactions cannot extend beyond the cones. However, since vp > c and even vp >> c when wavelength λ is long, extreme phase velocities are then limited in their causal effects by the particle uncertainty σ, i.e. to vgt ± σ/ω, where ω is the particle angular frequency. This is the first time the phase range has been described for a massive particle.

A scheme for conditional quantum phase gate via bimodal cavity and a∧-type three-level atom

We propose a scheme to implement a two-qubit conditional quantum phase gate for the intracavity field via a single three-level ∧-type atom driven by two modes in a high-Q cavity. The quantum inforraation is encoded on the Fock states of the bimodal cavity. The gate＇s averaged fidelity is expected to reach 99.8%.

Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems

We investigate the role of quantum correlation around the quantum phase transitions by using quantum renormalization group theory. Numerical analysis indicates that quantum correlation as well as quantum nonlocality can efficiently detect the quantum critical point in the two-dimensional XY systems. The nonanalytic behavior of the first derivative of quantum correlation is observed at the critical point as the size of the model increases. Furthermore, we discuss the quantum correlation distribution in this system based on the square of concurrence（SC） and square of quantum discord（SQD）. The monogamous properties of SC and SQD are obtained. Particularly, we prove that the quantum critical point can also be achieved by monogamy score.

Quantum phase transition and entanglement in Heisenberg XX spin chain with impurity

In this paper, we study the quantum phase transition and the effect of impurity on the thermal entanglement between any two lattices in three-qubit Heisenberg XX chain in a uniform magnetic field. We show that the quantum phase transition always appears when impurity parameter is an arbitrary constant and unequal to zero, the external magnetic field and impurity parameters have a great effect on it. Also, there exists a relation between the quantum phase transition and the entanglement. By modulating the temperature, magnetic field and the impurity parameters, the entanglement between any two lattices can exhibit platform-like behaviour, which can be used to realize entanglement switch.

Discord under the influence of a quantum phase transition

This paper studies the discord of a bipartite two-level system coupling to an XY spin-chain environment in a transverse field and investigates the relationship between the discord property and the environment＇s quantum phase transition. The results Show that the quantum discord is also able to characterize the quantum phase transitions. We also discuss the difference between discord and entanglement, and show that quantum discord may reveal more general information than quantum entanglement for characterizing the environment＇s quantum phase transition.

Entanglement and quantum phase transition in the Heisenberg-Ising model

We use the quantum renormalization-group（QRG） method to study the entanglement and quantum phase transition（QPT） in the one-dimensional spin-1/2 Heisenberg-Ising model [Lieb E,Schultz T and Mattis D 1961 Ann.Phys.（N.Y.） 16 407].We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations.We also investigate the scaling behavior of the system close to the quantum critical point,which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size.Also,the first derivative of concurrence between two blocks diverges at the quantum critical point,which is directly associated with the divergence of the correlation length.

Implementation of quantum phase gate between two atoms via Rydberg antiblockade and adiabatic passage

Combining adiabatic passage and Rydberg antiblockade, we propose a scheme to implement a two-qubit phase gate between two Rydberg atoms. Detuning parameters between frequencies of atomic transitions and those of the corresponding driving lasers are carefully chosen to offset the blockade effect of two Rydberg atoms, so that an effective Hamiltonian,representing a single-photon detuning L-type three-level system and concluding the quantum state of two Rydberg atoms excited simultaneously, is obtained. The adiabatic-passage technique, based on the effective Hamiltonian, is adopted to implement a two-atom phase gate by using two time-dependent Rabi frequencies. Numerical simulations indicate that a high-fidelity two-qubit p-phase gate is constructed and its operation time does not have to be controlled accurately. Besides,owing to the long coherence time of the Rydberg state, the phase gate is robust against atomic spontaneous emission.

Effect of interaction and temperature on quantum phase transition in anisotropic square-octagon lattice

We investigate the effect of interaction, temperature, and anisotropic parameter on the quantum phase transitions in an anisotropic square-octagon lattice with fermions under the framework of the single band Hubbard model through using the combination of cellular dynamical mean field theory and a continuous time Monte Carlo algorithm. The competition between interaction and temperature shows that with the increase of the anisotropic parameter, the critical on-site repulsive interaction for the metal-insulator transition increases for fixed temperature. The interaction-anisotropic parameter phase diagram reveals that with the decrease of temperature, the critical anisotropic parameter for the Mott transition will increase for fixed interaction cases.

Quantum Phase Transitions and Dimerized Phases in Frustrated Spin Ladder

In this paper, we study the phase diagram of a frustrated spin ladder model by applying the bosonization technique and the density-matrix renormalization-group （DMRG） algorithm. Effect of the intra-ehain next-nearest- neighbor （NNN） super-exchange interaction is investigated in detail and the order parameters are calculated to detect the emergence of the dimerized phases. We find that the intra-chain NNN interaction plays a key role in inducing dimerized phases.

Fidelity spectrum:A tool to probe the property of a quantum phase

Fidelity measures the similarity between two states and is widely adapted by the condensed matter community as a probe of quantum phase transitions in many-body systems. Despite its success in witnessing quantum critical points, information about the fine structure of a quantum phase one can get from this approach is still limited. Here, we proposed a scheme called fidelity spectrum, By studying the fidelity spectrum, one can obtain information about the characteristics of a phase. In particular, we investigated the spectra in the one-dimensional transverse-field Ising model and the two- dimensional Kitaev model on a honeycomb lattice. It was found that the sPectra have qualitative differences in the critical and non-critical regions of the two models. From the distributions of them, the dominating k modes in a particular phase could also be captured.

Scheme for the implementation of 1 → 3 optimal phase-covariant quantum cloning in ion-trap systems

This paper proposes a scheme for the implementation of 1→ 3 optimal phase-covariant quantum cloning with trapped ions. In the present protocol, the required time for the whole procedure is short due to the resonant interaction, which is important in view of decoherence. Furthermore, the scheme is feasible based on current technologies.

Influence of multi-photon pulses on practical differential-phase-shift quantum key distribution

The influence of multi-photon pulses on practical differcBtial-phase-shift quantum key distribution （DPS-Qt（D） is analysed. We have estimated the information which Eve obtained by PNS （photon-number splitting） attack and BS （beam splitting） attack. The result indicates that the PNS attack and BS attack will not limit the transmission distance as long as we select an appropriate mean photon number. Also, the maximum mean photon number under BS attack in practical DPS-QKD system and the set of practical assumptions about Eve＇s capabilities are presented.

Geometric phases and quantum phase transitions in inhomogeneous XY spin-chains:Effect of the Dzyaloshinski-Moriya interaction

We study geometric phases of the ground states of inhomogeneous XY spin chains in transverse fields with Dzyaloshinski--Moriya （DM） interaction, and investigate the effect of the DM interaction on the quantum phase transition （QPT） of such spin chains. The results show that the DM interaction could influence the distribution of the regions of QPTs but could not produce new critical points for the spin-chain. This study extends the relation between geometric phases and QPTs.

Phase diagram characterized by transmission in a triangular quantum dot

We propose a theoretical model to detect the quantum phase transition in a triangular quantum dot molecule with frustration. The boundaries of the phase diagram are accurately determined by the transmission. For small frustration t, as the interdot Coulomb repulsion V increases, the system undergoes a Kosterlitz–Thouless（KT） transition from the Kondo resonance state with a transmission peak at zero energy to the Coulomb blocked state with zero transmission, which is followed by a first transition to the V-induced resonance（VIR） state with unitary transmission. For large frustration t, as V increases, the orbital spin singlet without transmission transits to the VIR state through a KT transition.