International Journal of Quantum Information

In this paper, we investigate the convergence behavior of the fixed-point search algorithm with two arbitrary equal phase shifts for any number of iterations. We show that no matter what the initial deviation is, the algorithm converges to the target state with certainty for phase shifts between 0 and π∕2, and to the target state with the success probabilities of at least 80% and at least 66% for phase shifts between π∕2 and arccos(-1/4) and between arccos(-1/4) and 2π/3, respectively, while the algorithm does not converge for phase shifts between 2π/3 and π.

Shannon entropies of the Wigner function are calculated for ground and excited stationary states of the Particle-In-A-Box and Harmonic Oscillator model systems and examined as a measure of the localization of the phase-space distribution. We show that their behavior is consistent with that of the sum of the position and momentum space entropies as a function of quantum number. Position-momentum correlation is then analyzed in these systems by defining mutual information between position and momentum variables. This mutual information yields non-zero values, in contrast to the quantum covariance, and increases with quantum number.

We present two quantum key distribution (QKD) schemes over a collective-noise channel. Each logical qubit, composed of two physical qubits with a decoherence-free subspace, is immune to a collective noise and can carry one bit of information in theory. Although the receiver should prepare entangled two-photon quantum systems, he can read out the information encoded by the sender with two unitary operations on two photons, resorting to only two single-photon measurements, not Bell-state measurements, which makes these protocols simpler than others in experiment. These two QKD protocols are deterministic, not random, which makes the classical information exchanged be reduced largely. Also, they have a high intrinsic efficiency.

The transfer of entanglement from source particles (SPs) to target particles (TPs) via the Heisenberg interaction H = s₁ ⋅ s₂ has been investigated. In our research, TPs are two qubits and SPs are two qubits or qutrits. When TPs are two qubits, we find that no matter what state the TPs are initially prepared in, at the specific time t = π the quantity of entanglement of the TPs can attain 1 after interaction with the SPs which stay on the maximally entangled state. When TPs are two qutrits, the maximal quantity of entanglement of the TPs is proportional to the quantity of entanglement of the initial state of the TPs and cannot attain 1 for almost all the initial states of the TPs. Here we propose an iterated operation which can make the TPs go to the maximal entangled state.

In this paper, we have presented some results of entanglement between two moving atoms, when the multi-photon transition occurs. We obtain the general solution of the system using the unitary operator approach. It is shown that the center-of-mass motion plays an important role on the entanglement dynamics. It is also shown that the initial state settings have an impact on the evaluation.

We investigate the entanglement dynamics and coherence loss of a two-level atom dispersively interacting with two coherent fields in a dissipative cavity by using the concurrence and linear entropy, respectively. It is shown that the atomic coherence can lead to entanglement between the atom and one mode while the two modes are always separable. We also find that there is long-lived coherence loss as the system evolves.

Quantum entanglement is an important element of quantum information processing. Sharing entangled quantum states between two remote parties is a precondition of most quantum communication schemes. We will show that the protocol proposed by Yamamoto et al. (Phys. Rev. Lett.95 (2005) 040503) for transmitting single quantum qubit against collective noise with linear optics is also suitable for distributing the components of entanglements with some modifications. An additional qubit is introduced to reduce the effect of collective noise, and the receiver can take advantage of the time discrimination and the measurement results of the assistant qubit to reconstruct a pure entanglement with the sender. Although the scheme succeeds probabilistically, the fidelity of the entangled state is almost unity in principle. The resource used in our protocol to get a pure entangled state is finite, which establishes entanglement more easily in practice than quantum entanglement purification. Also, we discuss its application in quantum key distribution over a collective channel in detail.

We present a mathematical formulation of old teleportation protocol (original teleportation protocol introduced by Bennett et al.) for mixed state and study in detail the role of mixedness of the two-qubit quantum channel in a teleportation protocol. We show that maximally entangled mixed state described by the density matrix of rank-4 will be useful as a two-qubit teleportation channel to teleport a single qubit mixed state when the teleportation channel parameter p₁ > 1/2. Also we discuss the case when p₁ ≤ 1/2.

We propose a new way of description of the global entanglement property of a multi-partite pure state quantum system. Based on the idea of bipartite concurrence, by dividing the multi-partite quantum system into two subsystems, a combination of all the bipartite concurrences of a multi-partite quantum system is used to describe the entanglement property of the multi-partite system. We derive the analytical results for GHZ-state, W-state with arbitrary number of qubits, and cluster state with the number of particles no greater than 6.

Based on finite field and combinatorics theory, an elementary recursive construction is used to construct Hermitian self-orthogonal codes over 𝔽₉, the Galois field with nine elements, with dual distance three for all n ≥ 4. Consequently, good ternary linear quantum codes of minimum distance three for such length n are obtained. These ternary linear quantum codes are optimal or near optimal according to the quantum Singleton bound and quantum Hamming bound.

We present an S-matrix, a solution of the braid relation. A matrix representation of specialized Birman-Wenzl-Murakami algebra is obtained. Based on which, a unitary -matrix is generated via the Yang-Baxterization approach. Then we construct a Yang-Baxter Hamiltonian through the unitary -matrix. Berry phase of this Yang-Baxter system is investigated in detail.

We demonstrate a linear optical protocol to generate W state in terms of optical elements within a network. The proposed setup involves simple linear optical elements, N-photon polarization entangled state, and conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states. We show that with local operations, single-photon measurement, and one way classical communication, the protocol can be successfully realized with a certain probability.

In this paper, we present the explicit transformations of the optimal 1 → 3 universal quantum and the phase-covariant cloning in 3 dimensions (qutrits). The fidelities of two types of cloners reach the theoretical bounds.

Utilizing the notation in Refs. 10 and 11, we revisit general bipartite Bell state for any (d × d) dimensional systems. In particular, we bring out the conditions for general bipartite Bell state and find out the relation between general Bell states and the u(d) group. Furthermore, we construct local unitary complete set for quantum dense coding based on general Bell states.

Quantum and reversible logic circuits have found emerging attentions in nanotechnology, optical computing, quantum computing, and low power CMOS design. In this paper, we propose some new quantum and reversible compressors using our new genetic algorithm-based simulator, analyzer, and synthesizer software. The proposed quantum 4:2 and 6:2 compressor circuits are compared with the existing counterparts in terms of number of constant inputs, number of garbage outputs, delay and the quantum cost (QC). We have also designed quantum 7:2 compressor for the first time. The proposed quantum compressors are optimized in terms of QC and delay. The proposed designs can be used as a basic block in complex systems like multipliers, and can execute complicated operations better than the existing designs in literature.