International Journal of Quantum Information

We show how mapping techniques inherent to N²-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the modified Lipkin–Meshkov–Glick (LMG) model in order to obtain the time evolution of certain special parameters related to the Robertson–Schrödinger (RS) uncertainty principle and some particular proposals of entanglement measure based on collective angular-momentum generators. Our results reinforce the connection between both the squeezing and entanglement effects, as well as allow to investigate the basic role of spin correlations through the discrete representatives of quasiprobability distribution functions. Entropy functionals are also discussed in this context. The main sequence correlations ↦ entanglement ↦ squeezing of quantum effects embraces a new set of insights and interpretations in this framework, which represents an effective gain for future researches in different spin systems.

We consider the power of various quantum complexity classes with the restriction that states and operators are defined over a real, rather than complex, Hilbert space. It is well known that a quantum circuit over the complex numbers can be transformed into a quantum circuit over the real numbers with the addition of a single qubit. This implies that BQP retains its power when restricted to using states and operations over the reals. We show that the same is true for QMA(k), QIP(k), QMIP and QSZK.

Given two bipartite quantum states and the convex linear combination of them, we discuss the relation between the entanglement of the convex linear combination state and the entanglement of states being combined. This is achieved by characterizing quantum states quantitatively via the positive partial transpose (PPT) criterion and the computable cross-norm or realignment (CCNR) criterion. Inspired by the Horodecki's 3 ⊗ 3 quantum states, we also give explicit examples to illustrate all possible cases of convex linear combination. Finally, as an application of this method, we show how to construct new bipartite PPT entangled states from known PPT entangled states by convex linear combination.

We investigate thermal properties of quantum correlations in the thermodynamic limit with reference to the XY-model and the finite two-qubit Heisenberg model. Although this model has been the subject of active entanglement-research, the bulk of the pertinent work refers to finite instantiations. As a consequence, the temperature cannot be properly defined in such circumstances, a problem that is overcome here. Our effort should be of interest because quantum discord notion.

A scheme that probabilistically realizing hierarchical quantum state sharing of an arbitrary unknown qubit state with a nonmaximally four-qubit cluster state is presented in this paper. In the scheme, the sender Alice distributes a quantum secret with a Bell-state measurement and publishes her measurement outcomes via a classical channel to three agents who are divided into two grades. One agent is in the upper grade while other two agents are in the lower grade. Then introducing an ancillary qubit, the agent of the upper grade only needs the assistance of any one of the other two agents for probabilistically getting the secret, while an agent of the lower grade needs the help of all the other two agents by implementing a controlled-NOT operation and a proper positive operator-valued measurement instead of usual projective measurement. In other words, the agents of two different grades have different authorities to reconstruct Alice's secret by a probabilistic manner. Moreover, the total success probability and the maximum success probability of the scheme are also worked out.

Recently, quantum key distribution (QKD) with classical Bob has been suggested and proven completely robust by Boyer et al. [Phys. Rev. Lett.99 (2007) 140501] in which quantum Alice has a fully-fledged quantum power, while classical Bob is restricted to preparing and measuring a particle in the computational basis, reflecting or reordering the particles. In this paper, we describe two related but simpler semi-quantum key distribution protocol that exempts classical Bob from measurement (hereafter called limited classical Bob for convenience) and, prove them completely robust. As limited classical Bob can deterministically prepare the qubits, we exploit this feature to construct a semi-quantum secure direct communication protocol, which is the direct communication of secret messages without first producing a shared secret key.

By a careful analysis on cyclotomic cosets, the maximal designed distance δ_new of narrow-sense imprimitive Euclidean dual containing q-ary BCH code of length is determined, where q is a prime power and l is odd. Our maximal designed distance δ_new of dual containing narrow-sense BCH codes of length n improves upon the lower bound δ_max for maximal designed distances of dual containing narrow-sense BCH codes given by Aly et al. [IEEE Trans. Inf. Theory53 (2007) 1183]. A series of non-narrow-sense dual containing BCH codes of length n, including the ones whose designed distances can achieve or exceed δ_new, are given, and their dimensions are computed. Then new quantum BCH codes are constructed from these non-narrow-sense imprimitive BCH codes via Steane construction, and these new quantum codes are better than previous results in the literature.

This paper provides an analysis of patent activity in the field of quantum information processing. Data from the PatentScope database from the years 1993–2011 was used. In order to predict the future trends in the number of filed patents time series models were used.

Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose we have additional k qubits available. Given such a constraint k, we propose an approach for the phase estimation for an eigenphase of exactly n-bit precision. This approach adopts the standard recursive circuit for quantum Fourier transform (QFT) in [R. Cleve and J. Watrous, Fast parallel circuits for quantum fourier transform, Proc. 41st Annual Symp. on Foundations of Computer Science (2000), pp. 526–536.] and adopts classical bits to implement such a task. Our algorithm has the complexity of O(n log k), instead of O(n²) in the conventional QFT, in terms of the total invocation of rotation gates. We also design a scheme to implement the factorization algorithm by using k available qubits via either the continued fractions approach or the simultaneous Diophantine approximation.

We study the effect of external electric bias on the quantum correlations in the array of optically excited three coupled semiconductor quantum dots. The correlations are characterized by the quantum discord and concurrence and are observed using excitonic qubits. We employ the lower bound of concurrence for thermal density matrix at different temperatures. The effect of the Förster interaction on correlations will be studied. Our theoretical model detects nonvanishing quantum discord when the electric field is on while concurrence dies, ensuring the existence of nonclassical correlations as measured by the quantum discord.

Recently, a protocol is proposed for the quantum state sharing (QSTS) of an arbitrary three-photon state using four sets of W-class states. Unfortunately, its security analysis is inadequate. In this paper, we find the security loophole of this QSTS protocol. It is mainly caused by the fake quantum channel, whose security is not guaranteed by the legal participants. We present a simple but feasible strategy, by which an eavesdropper can successfully steal the exact secret. Furthermore, a secure QSTS protocol is put forward. The security of our improved protocol is analyzed in details.

Two three-party schemes of qubit operation sharing proposed by Zhang and Cheung [J. Phys. B44 (2011) 165508] are generalized by utilizing partially entangled states as quantum channels instead of maximally entangled ones. Their quantum and classical resource consumptions, necessary-operation complexities, success probabilities and efficiencies are calculated and compared with each other. Moreover, it is revealed that the success probabilities are completely determined by the shared entanglement.

Quantum correlations (QC) are generally considered to be the crucial resource for quantum information processing, however, in practice, the inevitable interaction of the quantum systems with the environment can cause decoherence and thus destroy the QC. In this paper, by comparatively studying the model of a two-qubit system in a common environment with and without dynamical control, we show that dynamical control can be exploited to protect QC from being completely destroyed for a long time. For certain product states, the dynamical control can even be used to generate the QC.

Due to some ambiguity in the definition of mutual Tsallis entropy in classical probability theory, its generalization to quantum theory is discussed and, as a consequence, two types of generalized quantum discords, called q-discords, are defined in terms of quantum Tsallis entropy. Both q-discords for two-qubit Werner and isotropic states are determined and compared and it is shown that one of them is non-negative, at least for states under investigation, for all q > 0. Finally, an analytical expression for q-discord of certain family of two-qubit X-states is presented. Using this example, we show that both types of q-discords can take negative values for some q > 1, hence their use as correlations measures is rather limited.

In this paper, we compute the various bipartite quantum correlations in the presence of the (4 + n)-dimensional Schwarzschild black hole. In particular, we focus on the n-dependence of various bosonic bipartite entanglements. For the case between Alice and Rob, where the former is free falling observer and the latter is at the near-horizon region, the quantum correlation is degraded compared to the case in the absence of the black hole. The degradation rate increases with decreasing n. We also compute the physically inaccessible correlations. It is found that there is no creation of quantum correlation between Alice and AntiRob. For the case between Rob and AntiRob the quantum entanglement is created although they are separated in the causally disconnected regions. It is found that contrary to the physically accessible correlation the entanglement between Rob and AntiRob decreases with increasing n.

A general scheme is presented to decompose a d-by-d unitary matrix as the product of two-level unitary matrices with additional structure and prescribed determinants. In particular, the decomposition can be done by using two-level matrices in d - 1 classes, where each class is isomorphic to the group of 2 × 2 unitary matrices. The proposed scheme is easy to apply, and useful in treating problems with the additional structural restrictions. A Matlab program is written to implement the scheme, and the result is used to deduce the fact that every quantum gate acting on n-qubit registers can be expressed as no more than 2^n-1(2ⁿ-1) fully controlled single-qubit gates chosen from 2ⁿ-1 classes, where the quantum gates in each class share the same n - 1 control qubits. Moreover, it is shown that one can easily adjust the proposed decomposition scheme to take advantage of additional structure evolving in the process.