QIC Abstracts

 Vol.11 No.11&12, November 1, 2011

Research Articles:

Complexity of commuting Hamiltonians on a square lattice of qubits (pp0901-0912)
Norbert Schuch

We consider the computational complexity of Hamiltonians which are sums of commuting terms acting on plaquettes in a square lattice of qubits, and we show that deciding whether the ground state minimizes the energy of each local term individually is in the complexity class NP. That is, if the ground states has this property, this can be proven using a classical certificate which can be efficiently verified on a classical computer. Different to previous results on commuting Hamiltonians, our certificate proves the existence of such a state without giving instructions on how to prepare it.

Passively self-error-rejecting qubit transmission over a collective-noise channel (pp0913-0924)
Fu-Guo Deng, Xi-Han Li, and Hong-Yu Zhou
We propose a passively self-error-rejecting single-qubit transmission scheme for an arbitrary polarization state of a single qubit over a collective-noise channel, without resorting to additional qubits and entanglement. By splitting a single qubit into some wavepackets with some Mach-Zehnder interferometers, we can obtain an uncorrupted state with a success probability approaching 100% via postselection in different time bins, independent of the parameters of collective noise. It is simpler and more flexible than the schemes utilizing decoherence-free subspace and those with additional qubits. One can directly apply this scheme to almost all quantum communication protocols based on single photons or entangled photon systems against a collective noise.

Low temperature dynamics of netral atoms for quantum logic (pp0925-0936)
Fang-Yu Hong, Yang Xiang, Z.Y. Zhu, and W.H. Tang

We study from the point of view of quantum logic the properties of the collective oscillations of two Rydberg atoms in two harmonic traps. The difference in the frequency of two normal modes of motion expands with the difference in the mass of the two atoms. The probability of excitation of the motional quanta due to the strong dipole-dipole interaction can be made to be sufficiently small. Based on the normal modes of motion we present a scheme for quantum state transfer which is useful for quantum information process and for precision spectroscopy of atoms that lack suitable transitions for efficient laser cooling, internal state preparation, and detection.

Security of quantum key distribution with state-dependent imperfections (pp0937-0947)
Hong-Wei Li, Zhen-Qiang Yin, Shuang Wang, Wan-Su Bao, Guang-Can Guo, and Zheng-Fu Han
In practical quantum key distribution system, the state preparation and measurement have state-dependent imperfections comparing with the ideal BB84 protocol. If the state-dependent imperfection can not be regarded as an unitary transformation, it should not be considered as part of quantum channel noise introduced by the eavesdropper, the commonly used secret key rate formula GLLP can not be applied correspondingly. In this paper, the unconditional security of quantum key distribution with state-dependent imperfections will be analyzed by estimating upper bound of the phase error rate in the quantum channel and the imperfect measurement. Interestingly, since Eve can not control all phase error in the quantum key distribution system, the final secret key
rate under constant quantum bit error rate can be improved comparing with the perfect quantum key distribution protocol.

Bound on genuine multipartite correlations from the principle of information causality (pp0948-0956)
Yang Xiang and Wei Ren
Quantum mechanics is not the unique no-signaling theory which is endowed with stronger-than-classical correlations, and there exists a broad class of no-signaling theories allowing even stronger-than-quantum correlations. The principle of information causality has been suggested to distinguish quantum theory from these nonphysical theories, together with an elegant information-theoretic proof of the quantum bound of two-particle correlations. In this work, we extend this to genuine $N$-particle correlations that cannot be reduced to mixtures of states in which a smaller number of particles are entangled. We first express Svetlichny's inequality in terms of multipartite no-signaling boxes, then prove that the strongest genuine multipartite correlations lead to the maximal violation of information causality. The maximal genuine multipartite correlations under the constraint of information causality is found to be equal to the quantum mechanical bound. This result consolidates information causality as a physical principle defining the possible correlations allowed by nature, and provides intriguing insights into the limits of genuine multipartite correlations in quantum theory.

Relativity of mixed entangled states (pp0957-0967)
Shahpoor Moradi
We obtain the necessary and sufficient separability and distillability conditions of mixtures of a maximally entangled state and the completely separable state in relativistic setting. In an inertial frame we study the entanglement under Wigner rotations induced by Lorentz transformations. We also investigate the mixed state entanglement of scalar and Dirac fields as seen by two relatively accelerated observers. For scalar field we show that in infinite acceleration limit the state has no longer distillable entanglement. For dirac field the entanglement in the infinite acceleration limit is finite. In both cases we show that there are states that will change from entangled into separable for a certain value of velocity or acceleration. We conclude that distillability is a relative concept, depending on the frame in which it is observed.

Security analysis of the time-coding quantum key distribution protocols (pp0968-0987)
Thierry Debuisschert and Simon Fossier

We report the security analysis of time-coding quantum key distribution protocols. The protocols make use of coherent single-photon pulses. The key is encoded in the photon time-detection. The use of coherent superposition of states allows to detect eavesdropping of the key. We give a mathematical model of a first protocol from which we derive a second, simpler, protocol. We derive the security analysis of both protocols and find that the secure rates can be similar to those obtained with the BB84 protocol. We then calculate the secure distance for those protocols over standard fibre links. When using low-noise superconducting single photon detectors, secure distances over 200 km can be foreseen. Finally, we analyse the consequences of photon-number splitting attacks when faint pulses are used instead of single photon pulses. A decoy states technique can be used to prevent such attacks.

Polarization-entanglement purification and concentration using cross-Kerr nonlinearity (pp0988-1002)
Chuan Wang, Yong Zhang, and Guang-Sheng Jin

We present an entanglement purification protocol and an entanglement concentration protocol in this paper, resorting to cross-Kerr nonlinearities and interference of two coherent beams. Our purification protocol can be used to purify photon pairs not only from an ideal entangled source but also from a parametric down-conversion source by the measurement on the interference of two coherent beams without giant cross-Kerr media. Our quantum nondemolition detection can also used to concentrate photon pairs in less entangled pure states efficiently. Our protocols are more flexibilities in distinguishing the phases of the coherent states during homodyne detection.

Universal quantum computation and leakage reduction in the 3-Qubit decoherence free subsystem  (pp1003-1018)
Bryan H. Fong and Stephen M. Wandzura

We describe exchange-only universal quantum computation and leakage reduction in the 3-qubit decoherence free subsystem (DFS). We discuss the angular momentum structure of the DFS, the proper forms for the DFS CNOT and leakage reduction operators in the total angular momentum basis, and new exchange-only pulse sequences for the CNOT and leakage reduction operators. Our new DFS CNOT sequence requires 22 pulses in 13 time steps. The DFS leakage reduction sequence, the first explicit leakage reduction sequence of its kind, requires 30 pulses in 20 time steps. Although the search for sequences was performed numerically using a genetic algorithm, the solutions presented here are exact, with closed-form expressions.

A note about a partial no-go theorem for quantum PCP (pp1019-1027)
Itai Arad

This is not a disproof of the quantum PCP conjecture! In this note we use perturbation on the commuting Hamiltonian problem on a graph, based on results by Bravyi and Vyalyi, to provide a very partial no-go theorem for quantum PCP. Specifically, we derive an upper bound on how large
the promise gap can be for the quantum PCP still to hold, as a function of the non-commuteness of the system. As the system becomes more and more commuting, the maximal promise gap shrinks. We view these results as possibly a preliminary step towards disproving the quantum PCP conjecture posed in \cite{ref:Aha09}. A different way to view these results is actually as indications
that a critical point exists, beyond which quantum PCP indeed holds; in any case, we hope that these results will lead to progress on this important open problem.

Local extrema of entropy functions under tensor products (pp1028-1044)
Shmuel Friedland, Gilad Gour, and Aidan Roy

We show that under a certain condition of local commutativity the minimum von-Neumann entropy output of a quantum channel is locally additive. We also show that local minima of the 2-norm entropy functions are closed under tensor products if one of the subspaces has dimension 2.

Non-demolition Adiabatic Measurement of the Phase Qubit State (pp1045-1065)
G.P. Berman, A.A. Chumaka,b, D.I. Kameneva, D. Kinionc, and V.I. Tsifrinovichd

An adiabatic method for a single-shot non-demolition measurement of the phase qubit is suggested. The qubit is inductively coupled to a low-frequency resonator, which in turn is connected with a classical measurement device (phase meter). The resonator drives adiabatic oscillations of the supercurrent in the qubit loop. The back reaction of the qubit loop on the resonator depends on the qubit state. Measuring the phase shift of the resonator’s oscillations one can determine the state of the qubit. Numerical computations with available experimental parameters show that the phase difference between the two qubit states increases at a rate of 0.0044 rad/ns with the fidelity of about 0.9989 and the measurement time of about 100 ns. The fidelity of the measurement is estimated taking into consideration possible quantum transitions inside and outside the qubit manifold. An increase of the phase difference is possible but it is linked to a reduction of the fidelity. The requirements for the reproducibility of the qubit and resonator parameters are formulated.

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