International Journal of Quantum Information

By using representation theory and irreducible characters of the symmetric group, we introduce character dependent states and study their entanglement via geometric measure. We also present a geometric interpretation of generalized matrix functions via this entanglement analysis.

Quantum Cryptography is a rapidly developing field of research that benefits from the properties of Quantum Mechanics in performing cryptographic tasks. Quantum walks are a powerful model for quantum computation and very promising for quantum information processing. In this paper, we present a quantum public-key cryptographic system based on quantum walks. In particular, in the proposed protocol the public-key is given by a quantum state generated by performing a quantum walk. We show that the protocol is secure and analyze the complexity of public key generation and encryption/decryption procedures.

Simultaneous dense coding (SDC) guarantees that Bob and Charlie simultaneously receive their respective information from Alice in their respective processes of dense coding. The idea is to use the so-called locking operation to “lock” the entanglement channels, thus requiring a joint unlocking operation by Bob and Charlie in order to simultaneously obtain the information sent by Alice. We present some new results on SDC: (1) We propose three SDC protocols, which use different N-dimensional entanglement (Bell state, W state and GHZ state). (2) Besides the quantum Fourier transform, two new locking operators are introduced (the double controlled-NOT operator and the SWAP operator). (3) In the case that spatially distant Bob and Charlie have to finalize the protocol by implementing the unlocking operation through communication, we improve our protocol’s fairness, with respect to Bob and Charlie, by implementing the unlocking operation in series of steps. (4) We improve the security of SDC against the intercept–resend attack. (5) We show that SDC can be used to implement a fair contract signing protocol. (6) We also show that the N-dimensional quantum Fourier transform can act as the locking operator in simultaneous teleportation of N-level quantum systems.

A quantum circuit providing an undetectable eavesdropping of information in message mode, which compromises all two-state $\psi$-$\varphi$ quantum direct communication (QDC) protocols, has been recently proposed by Pavičić [Phys. Rev. A 87 (2013) 042326]. A modification of the protocol’s control mode is proposed, which improves users’ 25% detection probability of Eve to 50% at best, as that in ping-pong protocol. The modification also improves the detection probability of Wójcik’s attack [Phys. Rev. Lett 90 (2003) 157901] to 75% at best. The resistance against man-in-the-middle (MITM) attack as well as the discussion of security for four Bell state protocols is presented. As a result, the protocol security is strengthened both theoretically and practically, and quantum advantage of superdense coding is restored.

We study the nonlinear phenomena of the coupled semiconductor microcavities driven by coherent lasers in different coupling regimes. It is shown that the bistability and multistability in the strong-coupling regime are gradually generated or eliminated by properly adjusting the coupling strength or the amplitude of the input pump laser. The proposed system serves as a good candidate for the diverse control optical switch and the potential applications.

A return probability of random walks is one of the interesting subjects. As it is well known, the return probability strongly depends on the structure of the space where the random walker moves. On the other hand, the return probability of quantum walks, which are quantum models corresponding to random walks, has also been investigated to some extend lately. In this paper, we take care of a discrete-time three-state quantum walk on a hexagonal lattice from the view point of mathematics. The mathematical result shows a limit of the return probability when the walker starts off at the origin. The result of the limit tells us about a possibility of localization at the position and a dependence of localization on the initial state.

Entanglement is considered a basic physical resource for modern quantum applications as Quantum Information and Quantum Computation. Interactions based on specific physical systems able to generate and sustain entanglement are subject to deep research to get understanding and control on it. Atoms, ions or quantum dots are considered key pieces in quantum applications because they are elements in the development toward a scalable spin-based quantum computer through universal and basic quantum operations. Ising model is a type of interaction generating entanglement in quantum systems based on matter. In this work, a general bipartite anisotropic Ising model including an inhomogeneous magnetic field is analyzed in a non-local basis. This model summarizes several particular models presented in literature. When evolution is expressed in the Bell basis, it shows a regular block structure suggesting a $\mathrm{\text{SU}}(2)$ decomposition. Then, their algebraic properties are analyzed in terms of a set of physical parameters which define their group structure. In particular, finite products of pulses in this interaction are analyzed in terms of $\mathrm{\text{SU}}(4)$ covering. Thus, evolution denotes remarkable properties, in particular those related potentially with entanglement and control, which give a fruitful arena for further quantum developments and generalization.

An analytical description of a superconducting (SC) phase qubit coupled to a torsional resonator, which is damped by a dispersive reservoir, is presented based on the master equation. Therefore, the effect of the qubit phase damping on the dynamical behavior of the entanglement, purity loss and qubit inversion are investigated. It is found that the collapse and revival phenomena of qubit inversion are very sensitive not only to the damping parameter but also to the frequency detuning and the qubit distribution angle of the initial state. It is interesting to note that the purity of the state of the SC-qubit, which is measured by von Neumann entropy, can be completely lost due to the dispersive reservoir parameter. Because of the existence of dispersive reservoir, the von Neumann entropy cannot be a measure for the entanglement in open system. So, the negative eigenvalue of the partially transposed density matrix of qubit-resonator system is used to quantify the entanglement. For certain parameter sets, it is possible to control the degree and the dynamics of entanglement between the qubit and the torsional resonator.

The relationship between entanglement and anisotropy is studied in small spin chains with periodic boundary conditions. The Hamiltonian of the spin chains is given by a slight modification of the dipolar Hamiltonian. The effect of the anisotropy is analyzed using the concurrence shared by spin pairs, but the study is not restricted to nearest-neighbor (NN) entanglement. It is shown that, under rather general conditions, the inclusion of anisotropic terms diminishes the entanglement shared between the spins of the chain irrespective of its range or its magnetic character.

The quantum Fourier transform (QFT) is a key ingredient of several quantum algorithms and a qudit-specific implementation of the QFT is hence an important step toward the realization of qudit-based quantum computers. This work develops a circuit decomposition of the QFT for hybrid qudits based on generalized Hadamard and generalized controlled-phase gates, which can be implemented using selective rotations in NMR. We experimentally implement the hybrid qudit QFT on an NMR quantum emulator, which uses four qubits to emulate a single qutrit coupled to two qubits.