International Journal of Quantum Information

Let H(t) = (1 - t/T)H₀ + (t/T)H₁, t ∈ [0,T], be the Hamiltonian governing an adiabatic quantum algorithm, where H₀ is diagonal in the Hadamard basis and H₁ is diagonal in the computational basis. We prove that H₀ and H₁ must each have at least two large mutually-orthogonal eigenspaces if the algorithm's running time is to be subexponential in the number of qubits. We also reproduce the optimality proof of Farhi and Gutmann's search algorithm in the context of this adiabatic scheme; because we only consider initial Hamiltonians that are diagonal in the Hadamard basis, our result is slightly stronger than the original.

In this paper, we propose a new quantum algorithm for solving the minimum searching problem. This algorithm has the same order of time and space complexities as the algorithm proposed by Dürr and Høyer, but it provides a quadratic reduction in the number of measurements. In addition to the correctness and complexity analysis of the algorithm, we present simulation results considering an NP-hard problem.

The nonclassical properties of two spin-1/2 particles with Heisenberg exchange interaction in a single-mode vacuum field are investigated. By using the quantum reduced entropy, we demonstrate that the ratio k_a between Heisenberg exchange interaction constant difference (J - J_z) and the spin-field coupling constant Ω can affect the feature of the entanglement significantly. It is found that the entanglement of the system evolves periodically with time, the evolvement period of the entanglement between two spin-1/2 particles and the field increases with the increasing k_a, which is true for the single spin-field entanglement, but that is contrary for the entanglement between the two spin particles. Our results show that three entangled states of two spins-field, spin–spin, and spin-field can be prepared via two spin-1/2 particles interacting with a single-mode vacuum field. We also characterize the field state by using Mandel's Q parameter, it is proved that the nonclassical properties of the field state will get weaker with the increasing k_a and are dramatically different from those in the case of selective measurement for spin.

General n-qubit controlled unitary gates are frequently used in quantum information processing tasks. Barenco, Bennett, Cleve, Di Vincenzo, Margolus and Shor [Phys. Rev. A52 (1995) 3457] have given the general construction methods, and explicit results for up-to-four-qubits controlled unitary gates. We extended their calculation and gave two analytic expressions for the construction of general n-qubit controlled unitary gates in terms of one-qubit and two-qubit CNOT gates. There are two expressions – one is exponential in the qubit number which is efficient for up to ten qubits, and the other is polynomial in the qubit number, which is efficient for more than ten qubits.

We present a complete controlled quantum secure direct communication (CQSDC) protocol using a nonsymmetric quantum channel. We point out that the roles of controllers in two recent works^16,17 can be excluded due to their design. We also give a revised CQSDC protocol such that their original advantages are retained and the complete CQSDC can be realized. We then analyze the roles of the controllers in different CQSDC protocols with different purposes and these protocols' applicabilities.

It is shown that the two qubit CNOT (controlled NOT) gate can also be realized using q-deformed angular momentum states constructed via the Jordan–Schwinger mechanism. Thus, all the three gates necessary for universality i.e. Hadamard, Phase Shift and the two qubit CNOT gate are realizable with q-deformed oscillators.

We present a scheme of remote preparation of the two-particle state by using two Einstein–Podolsky–Rosen pairs or two partially entangled two-particle states as the quantum channel. The probability of the successful remote state preparation is obtained.

Two new deterministic secure quantum communication protocols are proposed in this paper. In these protocols, utilizing auxilians, no particle is transported between two authorized parties, who guarantee the safety of the protocols.

The quantum adiabatic algorithm is a Hamiltonian based quantum algorithm designed to find the minimum of a classical cost function whose domain has size N. We show that poor choices for the Hamiltonian can guarantee that the algorithm will not find the minimum if the run time grows more slowly than . These poor choices are nonlocal and wash out any structure in the cost function to be minimized, and the best that can be hoped for is Grover speedup. These failures tell us what not to do when designing quantum adiabatic algorithms.

We propose an experimentally feasible scheme for implementing quantum dense coding in cavity QED. In this scheme, the multi-atoms interact simultaneously with a highly detuned cavity mode, and are driven by a strong classical field. The scheme is insensitive to the cavity decay and the thermal field. Only one interaction between atoms and cavity is required. Multi-atom's GHZ-states can be exactly distinguished via detecting the atomic state, and the quantum dense coding can be realized in a simple way.

We study the relations between entanglement dynamics and energy distribution for multipartite systems. We show that if two blocks S and of a system have energy exchanges, the entanglement and energy distribution between them are closely related, and have definite relations.

In this paper, we proposed a protocol which can produce a perfect copy of an unknown bipartite d-dimension equatorial entangled state with assistance from a state preparer. In this protocol, the maximally and non-maximally entangled bipartite d-dimension states are used as the quantum channels, respectively. The first stage of the protocol requires usual teleportation. In the second stage of the protocol, with the assistance (two-qudit projective measurement) of the preparer, the perfect copy of an original unknown state can be produced.

Utilizing a partially entangled GHZ state, we propose a novel controlled quantum secure direct communication (QSDC) with quantum encryption. Under the supervision and help of the third side, the sender and the receiver can securely share the private quantum entanglement keys used to encrypt and decrypt the secret message. According to the results of checking the eavesdropping on decoy photons, communicators can decide whether the quantum keys are reused in the next round. Not only will eavesdropping inevitably disturb the states of the decoy photons and be detected, but arbitrary transmission errors can also be corrected.

A controlled quantum teleportation scheme of electron spin state in a quantum dot is proposed. With the entanglement generating through the interaction between the quantum dots in microcavities and a single photon, the controlled teleportation can be implemented using Faraday rotation and single photon measurements. The scheme can be easily generalized to multi-qubit system.

In this letter, we investigate the entanglement of superposition of multi-states. Three cases are considered when the states in the superposition are mutually biorthogonal, mutually orthogonal and nonorthogonal. The relations between the entanglement of superposition and the entanglements of the superposed states are explored.