International Journal of Quantum Information

We investigate schemes to securely distribute and reconstruct single-qubit and two-qubit arbitrary quantum states between two parties via tripartite GHZ states in cavity QED without joint measurement. Our schemes offer a simple way of demonstrating quantum state sharing in cavity QED. We also consider the generalization of our schemes to distribute and reconstruct a quantum state among many parties.

We propose an experimentally feasible scheme to implement the optimal general 1→2 phase-covariant quantum cloning machine based on cavity QED. In the scheme, the cavity is only virtually excited and thus the scheme is insensitive to the cavity field states and cavity decay.

Based on entanglement swapping between two Bell states, two novel quantum key distribution protocols are proposed. One is for two-level systems, where there is no need for classical communication before each entanglement swapping. This feature is essential to its practical realization. Furthermore, to establish an arbitrarily long key, the protocol needs only two Bell states. The other is for d-level (d > 2) systems, in which higher security and higher source capacity are achieved. Using the theory of quadratic residue, we prove that in the two-qudit systems, each Bell state is a uniform superposition of all basis states in the dual basis, which is different to the situation in two-qubit systems. This difference means our two-level protocol cannot be generalized to the d-level situation directly. On the other hand, it results in higher security of our d-level protocol and is instructive to design quantum cryptography protocols.

We propose a theoretical scheme for teleportation of a general wave function of a quantum object. In principle, this protocol provides teleportation of discrete N-level spatial states of an object with various degrees of freedom, e.g. spin, in ordinary three-dimensional space. All necessary Bell states and their corresponding operators to measure and reconstruct the initial state are represented.

Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are compared and found to be very similar for both discrete and continuous time walks. The role of the oracle, and how it changes if more prior information about the graph is available, is also discussed.

Entropy squeezing is examined in the framework of Shannon information entropy for a degenerate Raman process involving two degenerate Rydberg energy levels of an atom interacting with a single-mode cavity field. Quantum squeezing in entropy is exhibited via the entropic uncertainty relation.

Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any system that allows superposition of states. A physical realization of this algorithm is described using coupled simple harmonic oscillators, which can be exactly solved in both classical and quantum domains. Classical wave algorithms are far more stable against decoherence compared to their quantum counterparts. In addition to providing convenient demonstration models, they may have a role in practical situations, such as catalysis.

We study the entanglement of formation and quantum phase transition in a one-dimensional quantum dot system with disorder modeled by the Hubbard Hamiltonian. The entanglement for three different cases is studied: the homogeneous case, the impurity case of symmetric electron hopping, and asymmetric electron hopping. We find that the local entanglement of the system can be tuned by introducing different impurities characterized by the physical parameters of the system. In particular, for certain parameters, the entanglement is negligible up to a critical point U_c, where a quantum phase transition occurs, and is different from zero above U_c.

We present a physical scheme for entanglement concentration of atomic entangled states via cavity QED. In our scheme cavity decay and atomic spontaneous emission are taken into consideration, and the atomic qubit is used as stationary qubit and photonic qubit as flying qubit, thus it is more practical to discuss entanglement concentration.

Results are presented of a large-scale simulation of the quantum adiabatic search (QuAdS) algorithm in the presence of noise. The algorithm is applied to the NP-Complete problem N-Bit Exact Cover 3 (EC3). The noise is assumed to Zeeman-couple to the qubits and its effects on the algorithm's performance is studied for various levels of noise power, and for four different types of noise polarization. We examine the scaling relation between the number of bits N (EC3 problem-size) and the algorithm's noise-averaged median run-time 〈T(N)〉. Clear evidence is found of the algorithm's sensitivity to noise. Two fits to the simulation results were done: (i) power-law scaling 〈T(N)〉 = aN^b; and (ii) exponential scaling 〈T(N)〉 = a[exp(bN) - 1]. Both types of scaling relations provided excellent fits, although the scaling parameters a and b varied with noise power, and with the type of noise polarization. The sensitivity of the scaling exponent b to noise polarization allows a relative assessment of which noise polarizations are most problematic for quantum adiabatic search. We demonstrate how the noise leads to decoherence in QuAdS, and estimate the amount of decoherence present in our simulations. An upper bound is also derived for the noise-averaged QuAdS success probability in the limit of weak noise that is appropriate for our simulations.

An analytical method to calculate the sub-entropies and entanglement for the mixed state as an initial field is presented. Also, we investigate the effects of the atomic motion and the field-mode structure on sub-entropies and phase properties of the coherent superposition state and a statistical mixture of coherent states as initial field states taking into account different forms of the intensity-dependent coupling. The initial state, the atomic motion and the field-mode structure play important roles in the time evolution of the entropies, entanglement and phase properties.

We investigate the possibility of having someone carry out the work of executing a function for you, but without letting him learn anything about your input. Say Alice wants Bob to compute some known function f upon her input x, but wants to prevent Bob from learning anything about x. The situation arises for instance if client Alice has limited computational resources in comparison with mistrusted server Bob, or if x is an inherently mobile piece of data. Could there be a protocol whereby Bob is forced to compute ,f(x)blindly, i.e. without observing x? We provide such a blind computation protocol for the class of functions which admit an efficient procedure to generate random input–output pairs, e.g. factorization. The cheat-sensitive security achieved relies only upon quantum theory being true. The security analysis carried out assumes the eavesdropper performs individual attacks.