On the "Security analysis and improvements of arbitrated quantum signature schemes"

Recently, Zou et al. [Phys. Rev. A 82, 042325 (2010)] pointed out that two arbitrated quantum signature (AQS) schemes are not secure, because an arbitrator cannot arbitrate the dispute between two users when a receiver repudiates the integrity of a signature. By using a public board, they try to propose two AQS schemes to solve the problem. This work shows that the same security problem may exist in their schemes and also a malicious party can reveal the other party's secret key without being detected by using the Trojan-horse attacks. Accordingly, two basic properties of a quantum signature, i.e. unforgeability and undeniability, may not be satisfied in their scheme

Continuous topological phase transitions between clean quantum Hall states

Continuous transitions between states with the {\em same} symmetry but different topological orders are studied. Clean quantum Hall (QH) liquids with neutral quasiparticles are shown to have such transitions. For clean bilayer (nnm) states, a continous transition to other QH states (including non-Abelian states) can be driven by increasing interlayer repulsion/tunneling. The effective theories describing the critical points at some transitions are derived.Comment: 4 pages, RevTeX, 2 eps figure

Gapless Fermions and Quantum Order

Using 2D quantum spin-1/2 model as a concrete example, we studied the relation between gapless fermionic excitations (spinons) and quantum orders in some spin liquid states. Using winding number, we find the projective symmetry group that characterizes the quantum order directly determines the pattern of Fermi points in the Brillouin zone. Thus quantum orders provide an origin for gapless fermionic excitations.Comment: 23 pages. LaTeX. Homepage http://dao.mit.edu/~we

Quantum orders in an exact soluble model

We find all the exact eigenstates and eigenvalues of a spin-1/2 model on square lattice: $H=16g \sum_i S^y_i S^x_{i+x} S^y_{i+x+y} S^x_{i+y}$. We show that the ground states for $g0$ have different quantum orders described by Z2A and Z2B projective symmetry groups. The phase transition at $g=0$ represents a new kind of phase transitions that changes quantum orders but not symmetry. Both the Z2A and Z2B states are described by $Z_2$ lattice gauge theories at low energies. They have robust topologically degenerate ground states and gapless edge excitations.Comment: 4 pages, RevTeX4, More materials on topological/quantum orders and quantum computing can be found in http://dao.mit.edu/~we

Binding Transition in Quantum Hall Edge States

We study a class of Abelian quantum Hall (QH) states which are topologically unstable (T-unstable). We find that the T-unstable QH states can have a phase transition on the edge which causes a binding between electrons and reduces the number of gapless edge branches. After the binding transition, the single-electron tunneling into the edge gains a finite energy gap, and only certain multi-electron co-tunneling (such as three-electron co-tunneling for $\nu=9/5$ edges) can be gapless. Similar phenomenon also appear for edge state on the boundary between certain QH states. For example edge on the boundary between $\nu=2$ and $\nu=1/5$ states only allow three-electron co-tunneling at low energies after the binding transition.Comment: 4 pages, RevTeX, 1 figur

Fidelity and quantum phase transitions

It is shown that the fidelity, a basic notion of quantum information science, may be used to characterize quantum phase transitions, regardless of what type of internal order is present in quantum many-body states. If the fidelity of two given states vanishes, then there are two cases: (1) they are in the same phase if the distinguishability results from irrelevant local information; or (2) they are in different phases if the distinguishability results from relevant long-distance information. The different effects of irrelevant and relevant information are quantified, which allows us to identify unstable and stable fixed points (in the sense of renormalization group theory). A physical implication of our results is the occurrence of the orthogonality catastrophe near the transition points.Comment: 5 pages, 2 figure

Bulk and Edge excitations in a ν=1\nu =1 quantum Hall ferromagnet

In this article, we shall focus on the collective dynamics of the fermions in a $\nu = 1$ quantum Hall droplet. Specifically, we propose to look at the quantum Hall ferromagnet. In this system, the electron spins are ordered in the ground state due to the exchange part of the Coulomb interaction and the Pauli exclusion principle. The low energy excitations are ferromagnetic magnons. To provide a means for describing these magnons, we shall discuss a method of introducing collective coordinates in the Hilbert space of many-fermion systems. These collective coordinates are bosonic in nature. They map a part of the fermionic Hilbert space into a bosonic Hilbert space. Using this technique, we shall interpret the magnons as bosonic collective ex citations in the Hilbert space of the many-electron Hall system. By considering a Hall droplet of finite extent, we shall also obtain the effective Lagrangian governing the spin collective excitations at the edge of the sample.Comment: Plain TeX 18 Pages Proceedings for the Y2K conference on strongly c orrelated fermionic systems, Calcutta, Indi