arXiv subjects

Jian Cui

Publications and source records attributed to Jian Cui.

79 records · Page 5Linked to original sources

arXiv2013

Local characterization of 1d topologically ordered states

We consider 1d Hamiltonian systems whose ground states display symmetry protected topological order. We show that ground states within the topological phase cannot be connected with each other through LOCC between a bipartition of the system. Our claim is demonstrated by analyzing the entanglement spectrum and Renyi entropies of different physical systems providing examples for symmetry protected topological phases. Specifically, we consider spin-1/2 Cluster-Ising model and a class of spin-1 models undergoing quantum phase transitions to the Haldane phase. Our results provide a probe for simmetry-protected topological order, that holds true even at the system's local scale. Therefore our analysis can serve as as local experimental test for topological order.

quant-ph↗

arXiv2012

Entanglement-assisted local operations and classical communications conversion in the quantum critical systems

Conversions between the ground states in quantum critical systems via entanglement-assisted local operations and classical communications (eLOCC) are studied. We propose a new method to reveal the different convertibility by local operations when a quantum phase transition occurs. We have studied the ground state local convertibility in the one dimensional transverse field Ising model, XY model and XXZ model. It is found that the eLOCC convertibility sudden changes at the phase transition points. In transverse field Ising model the eLOCC convertibility between the first excited state and the ground state are also distinct for different phases. The relation between the order of quantum phase transitions and the local convertibility is discussed.

quant-ph↗

arXiv2012

Quantum phases with differing computational power

The observation that concepts from quantum information has generated many alternative indicators of quantum phase transitions hints that quantum phase transitions possess operational significance with respect to the processing of quantum information. Yet, studies on whether such transitions lead to quantum phases that differ in their capacity to process information remain limited. Here We show that there exist quantum phase transitions that cause a distinct qualitative change in our ability to simulate certain quantum systems under perturbation of an external field by local operations and classical communication. In particular, we show that in certain quantum phases of the XY model, adiabatic perturbations of the external magnetic field can be simulated by local spin operations, whereas the resulting effect within other phases results in coherent non-local interactions. We discuss the potential implications to adiabatic quantum computation, where a computational advantage exists only when adiabatic perturbation results in coherent multi-body interactions.

quant-ph↗

arXiv2011

Two questions of L. Va${\rm \check{\textbf{s}}}$ on *-clean rings

A ring $R$ with an involution * is called (strongly) *-clean if every element of $R$ is the sum of a unit and a projection (that commute). All *-clean rings are clean. Va${\rm \check{s}}$ [L. Va${\rm \check{s}}$, *-Clean rings; some clean and almost clean Baer *-rings and von Neumann algebras, J. Algebra 324 (12) (2010) 3388-3400] asked whether there exists a *-ring that is clean but not *-clean and whether a unit regular and *-regular ring is strongly *-clean. In this paper, we answer both questions by several examples. Moreover, some characterizations of unit regular and *-regular rings are provided.

math.RA↗

arXiv2010

Critical behaviors and local transformation properties of wave function

We investigate crossing behavior of ground state entanglement Renyi entropies of quantum critical systems. We find a novel property that the ground state in one quantum phase cannot be locally transferred to that of another phase, that means a global transformation is necessary. This also provides a clear evidence to confirm the long standing expectation that entanglement Renyi entropy contains more information than entanglement von Neumann entropy. The method of studying crossing behavior of entanglement Renyi entropies can distinguish different quantum phases well. We also study the excited states which still give interesting results.

quant-ph↗

arXiv2010

Quantum information approach to the quantum phase transition in the Kitaev honeycomb model

Kitaev honeycomb model with topological phase transition at zero temperature is studied using quantum information method. Based on the exact solution of the ground state, the mutual information between two nearest sites and between two bonds with longest distance are obtained. It is found that the mutual information show some singularities at the critical point where the ground state of the system transits from gapless phase to gapped phase. The finite-size effects and scalar behavior are also studied. The mutual information can serve as good indicators of the topological phase transition, since the mutual information catches some global correlation properties of the system. Meanwhile, this method has other advantages such that the phase transition can be determined easily and the order parameters are not required previously, for the order parameters of some topological phase transitions are hard to know.

quant-ph↗

arXiv2009

Correlations in Grover search

Grover search is a well-known quantum algorithm that outperforms any classical search algorithm. It is known that quantum correlations such as entanglement are necessary for the power of quantum computation. But entanglement is not the only kind of quantum correlations. Other quantum correlations such as quantum discord are also useful to capture some aspects of the nonclassical correlation. We investigate several kinds of correlations including both quantum and classical in the whole process of Grover search algorithm. These correlations are the concurrence, entanglement of formation, quantum discord, classical correlation and mutual information. The behaviors of quantum discord, classical correlation and mutual information are almost the same while the concurrence is different. When the search is over, all kinds of correlations are zero, we argue that this is necessary for the final step in the search.

quant-ph↗