International Journal of Quantum Information

We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the possibility of developing fast decoders for them. Codes based on the homology of embeddings of graphs, such as Kitaev's toric code, have been discussed widely in the literature and our class of codes generalize these. We use embedded hypergraphs, which are a generalization of graphs that can have edges connected to more than two vertices.

We develop theorems and examples of our hypermap-homology codes, especially in the case that we choose a special type of basis in our homology chain complex. In particular the most straightforward generalization of the m × m toric code to hypermap-homology codes gives us a [(3/2)m², 2, m] code as compared to the toric code which is a [2m², 2, m] code. Thus we can protect the same amount of quantum information, with the same error-correcting capability, using less physical qubits.

A quantum private comparison (QPC) protocol based on W states [W. Liu et al., Opt. Commun.284, 3160 (2011)] has pointed out there is a flaw of information leak [Y. B. Li et al., Eur. Phys. J. D.66, 110 (2012)]. In order to solve the problem, a special kind of W-class state is introduced, and its construction framework of quantum circuits is sketched. Based on this kind of W-class states, an improvement on Liu et al.'s protocol is presented. Analysis shows the improvement can not only hold the characteristics of original protocol, but also avoid the information leak that Li et al. pointed out.

A recurrence scheme is presented to decompose an n-qubit unitary gate to the product of no more than N(N - 1)/2 single qubit gates with small number of controls, where N = 2ⁿ. Detailed description of the recurrence steps and formulas for the number of k-controlled single qubit gates in the decomposition are given. Comparison of the result to a previous scheme is presented, and future research directions are discussed.

The entanglement of different classes of initially entangled qubit pair is investigated in the presence of short laser pulses of rectangular and exponential shapes with either one or both qubits are excited. For the rectangular pulse, the detuning parameter protects the entanglement from degradation and controls its upper and lower bounds. We show that the upper bounds of entanglement decrease if both particles are excited, but the lower bounds are much better if only one particle is excited. The phenomena of entanglement degradation, sudden-death and -birth are shown for small initial time. Long-lived entanglement behavior, but with a variable degree, appears in the presence of rectangular pulse. However, in the case of the exponential pulse one obtains an invariably long-lived entanglement. For the combined case (rectangular + exponential), we show that one can generate a long-lived entanglement with small variable by increasing the strength of the rectangular pulse area and decreasing the Rabi-frequency of the exponential pulse.

The effect of filtering operation with respect to purification and concentration of entanglement in quantum states are discussed in this paper. It is shown, through examples, that the local action of the filtering operator on a part of the composite quantum state allows for purification of the remaining part of the state. The redistribution of entanglement in the subsystems of a noise affected state is shown to be due to the action of local filtering on the non-decohering part of the system. The varying effects of the filtering parameter, on the entanglement transfer between the subsystems, depending on the choice of the initial quantum state is illustrated.

We investigate the two-mode optomechanical cavity coupled with the three-level cascade atom. We propose a scheme to enhance the cooling of optomechanical oscillator by introducing atomic medium. Our results show that the existence of the atom can lead to a lower effective temperature of mechanical oscillator comparing to the case without atom. The coherence of the injected atomic affects the population of the photon, which can lead to the change in the radiation pressure on the movable mirror. We also show that the cooling of the mechanical oscillator is affected by initial state of inserting atom.

In this paper, we investigate Yangian symmetry for the three-spin-1/2 and four-spin-1/2 Heisenberg XXX models. Applying Yangian Y(sl(2)) theory to three-spin-1/2 and four-spin-1/2 systems, we construct Yangian Y(sl(2)) realizations for these systems. We show that these Yangian realizations can be used to describe three-spin-1/2 and four-spin-1/2 Heisenberg XXX models. The Yangian operators as shift operators are also studied in this paper.

The paper concerns some optical phenomena where quantum correlations take place: two-photon and three-photon interference, the photon antibunching, squeezed vacuum. The main properties of quantum correlations are: they do not depend on the distance, do not consume energy, take place for quantum entities both with zero and with nonzero rest mass, take place in the physical vacuum, that is, it is not necessary for the quantum entities to be detected simultaneously. A physical process is discussed which is responsible for quantum correlations in such macrosystem as superfluid ³He–B. An analogy is shown between the properties of spin supercurrents in superfluid ³He–B and the above properties of quantum correlations for quantum entities. The important feature of spin supercurrents is that they are not accompanied by any mass transfer.

The improvement and extension of quantum secret sharing (QSS) using orthogonal product states (OPS) are studied in this paper. Based on such three typical schemes, a quantitative analysis on security is provided. The paper also discusses the simplification measures and their effect on security, and then the possibility to extend is proved. Finally, several conclusions about the methods to improve the security, simplify the schemes and extend to one-to-many situation are given.

We present an efficient method to generate Einstein–Podolsky–Rosen (EPR) entanglement of two microwave photons with different frequencies in two superconducting resonators. Our scheme is based on the sideband couplings of two resonators with a single gap-tunable superconducting quantum circuits driven by a controlled field. By the proper choice of the physical parameters, the nonlinear interaction of parametric down-conversion occurs between two resonators while the superconducting qubit remains in the original state, which is responsible for the entanglement generation. The present scheme would provide a promising alternative approach to scalable quantum information processing in solid-state systems.