Chen Li-Bing

Simple Algorithm for Deterministic Entanglement Concentration

We first present the general solution and the simplest special solution of the doubly stochastic matrix used in deterministic entanglement concentration. Then, we give a better scheme to realize deterministic entanglement concentration. Under this scheme, the concentration is realized, and more importantly, two partially entangled pairs concentrate to four-particle Greenberger–Horne–Zeilinger (GHZ) states with a certain probability.

Generation of GHZ States via Deterministic Entanglement Concentration

We present the generation of six-particle Greenberger–Horne–Zeilinger (GHZ) states via deterministic entanglement concentration and generalize the scheme to the case of 2N particles. We show that arbitrary 2N-particle GHZ states can be obtained with certain probability via entanglement concentration. This may provide a new perspective for the preparation of multi-particle GHZ states. This study is also an exploration on the theory of deterministic entanglement concentration.

Implementation of non-local multiple qubits controlled-not operation via partially entangled channels

We propose two different schemes for probabilistic implementing a non-local multiple qubits controlled-not operation via partially entangled quantum channels. The overall physical resources required for accomplishing these schemes are different and the successful implementation probabilities are also different.

Nonlocal multi-target controlled–controlled gate using Greenberger–Horne–Zeilinger channel and qutrit catalysis*

We present a scheme for implementing locally a nonlocal N-target controlled–controlled gate with unit probability of success by harnessing two (N+1)-qubit Greenberger–Horne–Zeilinger (GHZ) states as quantum channel and N qutrits as catalyser. The quantum network that implements this nonlocal (N+2)-body gate is built entirely of local single-body and two-body gates, and has only (3N+2) two-body gates. This result suggests that both the computational depth of quantum network and the quantum resources required to perform this nonlocal gate might be significantly reduced. This scheme can be generalized straightforwardly to implement a nonlocal N-target and M-control qubits gate.

Permutation Matrix Method for Dense Coding Using GHZ States

We present a new method called the permutation matrix method to perform dense coding using Greenberger–Horne–Zeilinger (GHZ) states. We show that this method makes the study of dense coding systematically and regularly. It also has high potential to be realized physically.

Controlled Implementation of Non-local CNOT Operation Using Three-Qubit Entanglement

We investigate the controlled implementation of a non-local CNOT operation using a three-qubit entangled state. Firstly, we show how the non-local CNOT operation can be implemented with unit fidelity and unit probability by using a maximally entangled GHZ state as controlled quantum channel. Then, we put forward two schemes for conclusively implementing the non-local operation with unit fidelity by employing a partially entangled pure GHZ state as quantum channel. The feature of these schemes is that a third side is included, who may participate the process of quantum non-local implementation as a supervisor. Furthermore, when the quantum channel is partially entangled, the third one can rectify the state distorted by imperfect quantum channel. In addition to the GHZ class state, the W class state can also be used to implement the same non-local operation probabilistically. The probability of successful implementation using the W class state is always less than that using the GHZ class state.

Quantum networks for implementing effiently a nonlocal N -qubit controlled unitary gate via non-symmetric quantum channels: Designing and optimizing

We show how a nonlocal N -qubit controlled unitary gate can be implemented locally and effectively by using non-symmetric quantum channels. We construct respectively two quantum networks for realizing conclusively this nonlocal quantum gate. The first one hires ( N –2) symmetric qubit-qubit Bell states and a non-symmetric qubit-qudit Bell state as quantum channels. The basic idea of this scheme is to use ( N –2) additional levels of this qudit to “hide” certain computational states of ( N –1) nonlocal control states from the conditional dynamics, which results in an effective nonlocal N -qubit controlled unitary gate design. In this scheme, however, either the number of the additional levels or that of 1-qudit gates needs to increase with N . The other one can improve significantly the local implementation of this nonlocal gate if we harness ( N –1) non-symmetric qubit-qutrit Bell states as quantum channels. This scheme uses respectively ( N –1) qutrits’s additional levels to expose one and only one initial computational state of ( N –1) nonlocal control states to the conditional dynamics. In comparison with the first one, the procedure is greatly simplified, and the total gate time is reduced. The fact that the quantum network that does the proposed implementation is built entirely of local single-body and two-body gates, and has only (3 N –4) two-body gates is notable.

Quantum networks for implementing locallyand conclusively a nonlocal qudit Toffoli gate: Designing and optimizing

Local implementation of a nonlocal d -dimensional quantum Toffoli gate is considered. We construct respectively two quantum networks for realizing this nonlocal quantum gate conclusively. The first one is based on Eisert’s insight but follow a different pathway which results in a nonlocal d -dimensional Toffoli gate design. This scheme involves a local d -dimensional three-body interaction, which does not appear naturally in physical system. The other one can improve significantly the local implementation of this nonlocal gate if the target node harnesses a qutrit as a catalyser. In its simplest form this quantum network that does the improved scheme is built entirely of local single-body and two-body elementary gates, and with only 3 two-body elementary gates at the target node. The latter is simpler but conclusive, and more efficient but with less resource, which will make it more feasible with the current experimental technology and more suitable for large-scale quantum network.

Teleporting a quantum controlled-Not with one target/two targets gate using two partially entangled states

This paper considers the teleportation of quantum controlled-Not (CNOT) gate by using partially entangled states. Different from the known probability schemes, it presents a method for teleporting a CNOT gate with unit fidelity and unit probability by using two partially entangled pairs as quantum channel. The method is applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients μ and v are (2μ + 2v – 2μv – 1) ≥ 0. In this scheme, the senders local generalized measurement described by a positive operator valued measurement (POVM) lies at the heart. It constructs the required POVM. It also puts forward a scheme for teleporting a CNOT with two targets gate with unit fidelity by using same quantum channel. With assistance of local operations and classical communications, three spatially separated users are able to complete the teleportation of a CNOT with two targets gate with probability of (2μ + 2v – 1). With a proper value of μ and v, the probability could reach nearly 1.

General and Optimal Scheme for Local Conversion of Pure States

We present general and optimal schemes for local conversion of pure states, via one specific example. First, we give the general solution of the doubly stochastic matrix. Then, we find the general and optimal positive-operator-valued measure (POVM) to realize the local conversion of pure states. Lastly, the physical realization of the POVM is discussed. We show that our scheme has a more general and better effect than other schemes.