arXiv subjects
Publications and source records attributed to B. Zeng.
We prove a new impossibility for quantum information (the no-splitting theorem): an unknown quantum bit (qubit) cannot be split into two complementary qubits. This impossibility, together with the no-cloning theorem, demonstrates that an unknown qubit state is a single entity, which cannot be cloned or split. This sheds new light on quantum computation and quantum information.
We investigate quantum correlations of the $N$-qubit states via a collective pseudo-spin interaction ($\propto J_y^2$) on arbitrary pure separable states for a given interval of time. Based on this dynamical generation of the $N$-qubit maximal entangled states, a quantum secret sharing protocol with $N$ continuous classical secrets is developed.
We present a scheme for a projective measurement of the parity operator $P_z=\prod_{i=1}^N σ_z^{(i)}$ of $N$-qubits. Our protocol uses a single ancillary qubit, or a probe qubit, and involves manipulations of the total spin of the $N$ qubits without requiring individual addressing. We illustrate our protocol in terms of an experimental implementation with atomic ions in a two-zone linear Paul trap, and further discuss its extensions to several more general cases.
We discuss the canonical form for a pure state of three identical bosons in two modes, and classify its entanglement correlation into two types, the analogous GHZ and the W types as well known in a system of three distinguishable qubits. We have performed a detailed study of two important entanglement measures for such a system, the concurrence $\mathcal{C}$ and the triple entanglement measure $τ$. We have also calculated explicitly the spin squeezing parameter $ξ$ and the result shows that the W state is the most ``anti-squeezing'' state, for which the spin squeezing parameter cannot be regarded as an entanglement measure.
We propose two protocols to encode a logical qubit into physical qubits relying on common types of qubit-qubit interactions in as simple forms as possible. We comment on its experimental implementation in several quantum computing architectures, e.g. with trapped atomic ion qubits, atomic qubits inside a high Q optical cavity, solid state Josephson junction qubits, and Bose-Einstein condensed atoms.
The concept of qudit (a d-level system) cluster state is proposed by generalizing the qubit cluster state (Phys. Rev. Lett. \textbf{86}, 910 (2001)) according to the finite dimensional representations of quantum plane algebra. We demonstrate their quantum correlations and prove a theorem which guarantees the availability of the qudit cluster states in quantum computation. We explicitly construct the network to show the universality of the one-way computer based on the defined qudit cluster states and single-qudit measurement. And the corresponding protocol of implementing one-way quantum computer can be suggested with the high dimensional "Ising" model which can be found in many magnetic systems.
We find that a class of entanglement measures for bipartite pure state can be expressed by the average values of quantum operators, which are related to any complete basis of one partite operator space. Two specific examples are given based on two different ways to generalize Pauli matrices to $d$ dimensional Hilbert space and the case for identical particle system is also considered. In addition, applying our measure to mixed state case will give a sufficient condition for entanglement.
We revisit the criterion of multi-particle entanglement based on the overlaps of a given quantum state $ρ$ with maximally entangled states. For a system of $m$ particles, each with $N$ distinct states, we prove that $ρ$ is $m$-particle negative partial transpose (NPT) entangled, if there exists a maximally entangled state $|{\rm MES}>$, such that $<{\rm MES}|ρ|{\rm MES}>>{1}/{N}$. While this sufficiency condition is weaker than the Peres-Horodecki criterion in all cases, it applies to multi-particle systems, and becomes especially useful when the number of particles ($m$) is large. We also consider the converse of this criterion and illustrate its invalidity with counter examples.
A protocol of quantum communication is proposed in terms of the multi-qubit quantum teleportation through cluster states (Phys. Rev. Lett. \textbf{86}, 910 (2001)). Extending the cluster state based quantum teleportation on the basic unit of three qubits (or qudits), the corresponding multi-qubit network is constructed for both the qubits and qudits (multi-level) cases. The classical information costs to complete this communication task is also analyzed. It is also shown that this quantum communication protocol can be implemented in the spin-spin system on lattices.