A quantum algorithm for the dihedral hidden subgroup problem based on algorithm SV

To accelerate the algorithms for the dihedral hidden subgroup problem, we present a new algorithm based on algorithm SV(shortest vector). A subroutine is given to get a transition quantum state by constructing a phase filter function, then the measurement basis are derived based on the technique for solving low density subset problem. Finally, the parity of slope is revealed by the measurements on the transition quantum state. This algorithm takes O(n) quantum space and O(n^2) classical space, which is superior to existing algorithms, for a relatively small n(n<6400),it takes (n^0.5)*(log(max aij))^3 computation time, which is superior to 2^(O(n^0.5))

Rapidity dependent transverse momentum spectra of heavy quarkonia produced in small collision systems at the LHC

The rapidity dependent transverse momentum spectra of heavy quarkonia (J/psi and Upsilon mesons) produced in small collision systems such as proton-proton (pp) and proton-lead (p-Pb) collisions at center-of-mass energy (per nucleon pair) 5-13 TeV are described by a two-component statistical model which is based on the Tsallis statistics and inverse power-law. The experimental data measured by the LHCb Collaboration at the Large Hadron Collider (LHC) are well fitted by the model results. The related parameters are obtained and the dependences of parameters on rapidity are analyzed.Comment: 17 pages, 11 figures. Advances in High Energy Physics, accepte

A reduction from LWE problem to dihedral coset problem

Learning with Errors (LWE) problems are the foundations for numerous applications in lattice-based cryptography and are provably as hard as approximate lattice problems in the worst case. Here we present a reduction from LWE problem to dihedral coset problem(DCP). We present a quantum algorithm to generate the input of the two point problem which hides the solution of LWE. We then give a new reduction from two point problem to dihedral coset problem on D_{{{({n^{13}})}^{n\log n}}}. Our reduction implicate that any algorithm solves DCP in subexponential time would lead a quantum algorithm for LWE

Dependence of elliptic flow on transverse momentum in 200 GeV Au-Au and 2.76 TeV Pb-Pb collisions

We investigate the dependence of elliptic flows $v_2$ on transverse momentum $P_T$ for charged hadrons produced in nucleus-nucleus collisions at high energy by using a multi-source ideal gas model which includes the interaction contribution of the emission sources. Our calculated results are approximately in agreement with the experimental data over a wider $P_T$ range from the STAR and ALICE Collaborations. It is found that the expansion factor increases linearly with the impact parameter from most central (0-5%) to mid-peripheral (35-40%) collisions.Comment: 8 pages, 4 figure

Formulation of transverse mass distributions in Au-Au collisions at 200 GeV/nucleon

The transverse mass spectra of light mesons produced in Au-Au collisions at 200 GeV/nucleon are analyzed in Tsallis statistics. In high energy collisions, it has been found that the spectra follow a generalized scaling law. We applied Tsallis statistics to the description of different particles using the scaling properties. The calculated results are in agreement with experimental data of PHENIX Collaboration. And, the temperature of emission sources is extracted consistently.Comment: 8 pages, 11 figure

Kinetic freeze-out temperatures in central and peripheral collisions: Which one is larger?

The kinetic freeze-out temperatures, $T_0$, in nucleus-nucleus collisions at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies are extracted by four methods: i) the Blast-Wave model with Boltzmann-Gibbs statistics (the BGBW model), ii) the Blast-Wave model with Tsallis statistics (the TBW model), iii) the Tsallis distribution with flow effect (the improved Tsallis distribution), and iv) the intercept in $T=T_0+am_0$ (the alternative method), where $m_0$ denotes the rest mass and $T$ denotes the effective temperature which can be obtained by different distribution functions. It is found that the relative sizes of $T_0$ in central and peripheral collisions obtained by the conventional BGBW model which uses a zero or nearly zero transverse flow velocity, $\beta_T$, are contradictory in tendency with other methods. With a re-examination for $\beta_T$ in the first method in which $\beta_T$ is taken to be $\sim(0.40\pm0.07)c$, a recalculation presents a consistent result with others. Finally, our results show that the kinetic freeze-out temperature in central collisions is larger than that in peripheral collisions.Comment: 22 pages, 11 figures. Nuclear Science and Techniques, accepte

High-efficiency multipartite entanglement purification of electron-spin states with charge detection

We present a high-efficiency multipartite entanglement purification protocol (MEPP) for electron-spin systems in a Greenberger-Horne-Zeilinger state based on their spins and their charges. Our MEPP contains two parts. The first part is our normal MEPP with which the parties can obtain a high-fidelity N-electron ensemble directly, similar to the MEPP with controlled-not gates. The second one is our recycling MEPP with entanglement link from N'-electron subsystems (2 < N' < N). It is interesting to show that the N'-electron subsystems can be obtained efficiently by measuring the electrons with potential bit-flip errors from the instances which are useless and are just discarded in all existing conventional MEPPs. Combining these two parts, our MEPP has the advantage of the efficiency higher than other MEPPs largely for electron-spin systems.Comment: 15 pages, 5 figure

A classical postselected weak amplification scheme via thermal light cross-Kerr effect

In common sense, postselected weak amplification must be related to destructive interference effect of the meter system, and a single photon exerts no effect on thermal field via cross-phasemodulation (XPM) interaction. In this Letter we present, for the first time, a thermal light cross-Kerr effect. Through analysis, we reveal two unexpected results: i) postselection and weak amplification can be explained at a classical level without destructive interference, and ii) weak amplification and weak value are not one thing. After postselection a new mixed light can be generated which is nonclassical. This scheme can be realized via electromagnetically-induced transparency.Comment: Comments are welcome. 6 pages, 11 figure

Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities

Bell-state analysis (BSA) is essential in quantum communication, but it is impossible to distinguish unambiguously the four Bell states in the polarization degree of freedom (DOF) of two-photon systems with only linear optical elements, except for the case in which the BSA is assisted with hyperentangled states, the simultaneous entanglement in more than one DOF. Here, we propose a scheme to distinguish completely the 16 hyperentangled Bell states in both the polarization and the spatial-mode DOFs of two-photon systems, by using the giant nonlinear optics in quantum dot-cavity systems. This scheme can be applied to increase the channel capacity of long-distance quantum communication based on hyperentanglement, such as entanglement swapping, teleportation, and superdense coding. We use hyperentanglement swapping as an example to show the application of this HBSA.Comment: 11 pages (in one column), 5 figure

Complete deterministic multi-electron Greenberger-Horne-Zeilinger state analyzer for quantum communication

We present a scheme for the multi-electron Greenberger-Horne-Zeilinger (GHZ) state analyzer, resorting to an interface between the polarization of a probe photon and the spin of an electron in a quantum dot embedded in a microcavity. All the multi-spin GHZ states can be completely discriminated by using single-photon detectors and linear optical elements. Our scheme has some features. First, it is a complete GHZ-state analyzer for multi-electron spin systems. Second, the initial entangled states remain after being identified and they can be used for a successive task. Third, the electron qubits are static and the photons play a role of a medium for information transfer, which has a good application in quantum repeater in which the electron qubits are used to store the information and the photon qubits are used to transfer the information between others.Comment: 6 page, 3 figures, 1 tabl