Scattering of Spin-$\frac{1}{2}$ Particles from a $\cal PT$-symmetric Complex Potential

Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential

We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schrödinger (FNLS) equation with focusing saturable nonlinearity and PT-symmetric potential. The continuous asymmetric soliton branch bifurcates from the fundamental symmetric one as the power exceeds some critical value. Intriguingly, the symmetry of fundamental solitons is broken into two branches of asymmetry solitons (alias ghost states) with complex conjugate propagation constants, which is solely in fractional media. Besides, the dipole (antisymmetry) and tripo…

量子图着色的对称归约技术

Symmetric Reduction Techniques for Quantum Graph Colouring

本文提出面向特殊图着色问题的量子对称归约方法，通过利用轴穿节点或边的对称性减少着色矩阵、量子态、量子比特、门、迭代次数和运行时间。

Exact Quantum Query Algorithms Outperforming Parity -- Beyond The Symmetric functions

In Exact Quantum Query model, almost all of the Boolean functions for which non-trivial query algorithms exist are symmetric in nature. The most well known techniques in this domain exploit parity decision trees, in which the parity of two bits can be obtained by a single query. Thus, exact quantum query algorithms outperforming parity decision trees are rare. In this paper we first obtain optimal exact quantum query algorithms ($Q_{algo}(f)$) for a direct sum based class of $Ω\left( 2^{\frac{\sqrt{n}}{2}} \right)$ non-symmetric functions. We construct these algorithms by analyzing the algebra…

Symmetric Halves of the 8/33-Probability that the Joint State of Two Quantum Bits is Disentangled

Compelling evidence-though yet no formal proof--has been adduced that the probability that a generic two-qubit state ($ρ$) is separable is $\frac{8}{33}$ (arXiv:1301.6617, arXiv:1109.2560, arXiv:0704.3723). Proceeding in related analytical frameworks, using a further determinantal moment formula of C. Dunkl (Appendix), we reach the conclusion that one-half of this probability arises when the determinantal inequality $|ρ^{PT}|>|ρ|$, where $PT$ denotes the partial transpose, is satisfied, and, the other half, when $|ρ|>|ρ^{PT}|$. These probabilities are taken with respect to the flat, Hilbert-Sc…

$\mathcal{P}\mathcal{T}$-symmetric $-gφ^4$ theory

The scalar field theory with potential $V(φ)=\textstyle{\frac{1}{2}} m^2φ^2-\textstyle{\frac{1}{4}} gφ^4$ ($g>0$) is ill defined as a Hermitian theory but in a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric framework it is well defined, and it has a positive real energy spectrum for the case of spacetime dimension $D=1$. While the methods used in the literature do not easily generalize to quantum field theory, in this paper the path-integral representation of a $\mathcal{P}\mathcal{T}$-symmetric $-gφ^4$ theory is shown to provide a unified formulation for general $D$. A new conjectural relat…