QIC Abstracts

 Vol.11 No.5&6 May 1, 2011

Research Articles:

Multi-Bloch vector representation of the qutrit (pp0361-0373)
          
Pawel Kurzynski
An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state. However, not every Bloch vector corresponds to a quantum state. It seems that only for two-dimensional quantum systems it is easy to distinguish proper Bloch vectors from improper ones, i.e. the ones corresponding to quantum states from the other ones. I propose an alternative approach to the problem in which more than one vector is used. In particular, I show that a state of the qutrit can be described by the three qubit-like Bloch vectors.

Finite-key analysis for quantum key distribution with decoy states (pp0374-0389)
          
Ting-Ting Song, Jie Zhang, Su-Juan Qin, Fei Gao, and Qiao-Yan Wen
We analyze the security of finite-resource quantum key distribution with decoy states, and present the security bound for the practical implementations by introducing the deviations of the probability of sending a $k$-photon pulse and the error rate of the quantum state. The bound is simulated under reasonable values of the observed parameters. Compared with the previous works, the security bound is more stringent.

Evolution of entanglement (pp0390-0419)
          
M. Merkli, G.P. Berman, F. Borgonovi, and K. Gebresellasie
We analyze the dynamics of entanglement between two qubits which interact through collective and local environments. Our approach is based on a resonance theory which assumes a small interaction between qubits and environments and which gives rigorous perturbation theory results, valid for all times. We obtain expressions for (i) characteristic time-scales for decoherence, relaxation, disentanglement, and for (ii) the evolution of observables, valid uniformly in time $t\geq 0$. We introduce a classification of decoherence times based on clustering of the reduced density matrix elements, persisting on all time-scales. We examine characteristic dynamical properties such as creation, death and revival of entanglement. We discuss possible applications of our results for superconducting quantum computation and quantum measurement technologies.

Coherence preservation in 3-level atom (pp0420-0433)
          
Fei Yang and Shuang Cong
Coherence preservation of a multilevel system subject to Markovian decoherence is studied. A Lambda-type three-level atom is selected as the system model. Coherence preservation between a ground state and the excited state of such a system is defined as the control object. A control field is designed by means of constraining the constant coherence condition. For the singularities of the control field, we qualitatively analyze the breakdown time, i.e. the time of control diverging. We obtain the region in which the state stays to maintain coherence forever in the case that the three-level system is reduced to a two-level one. For other cases, we investigate how different parameters affect the breakdown time qualitatively. Numerical experiments are implemented on a three-level quantum system and the experimental results are analyzed.

Security of a kind of quantum secret sharing with single photons (pp0434-0443)
          
Tian-Yin Wang and Qiao-Yan Wen
The security of a kind of quantum secret sharing with single photons was analyzed recently, and it was shown that almost all the present schemes in this kind were not secure in the sense that an unauthorized set of participants can gain access to the dealer's secret without introducing any error. In this paper, we give a general model for this kind of quantum secret sharing. Then we analyze the conditions that make it immune to all the present attacks. Finally, we give a feasible way to design secure quantum secret sharing schemes in the model.

HQC with the AC setup associated with topological defects (pp0444-0455)
          
Knut Bakke and ClŠudio Furtado
In this work, we propose a new formulation allowing to realize the holonomic quantum computation with neutral particles with a permanent magnetic dipole moments interacting with an external electric field in the presence of a topological defect. We show that both the interaction of the electric field with the magnetic dipole moment and the presence of topological defect generate independent contributions to the geometric quantum phases which can be used to describe any arbitrary rotation on the magnetic dipole moment without using the adiabatic approximation.

Quantum memory for light with a quantum dot system coupled to a nanomechanical resonator (pp0456-0465)
          
Jin-Jin Li and Ka-Di Zhu

The specific features including high factor and long vibration lifetime of nanomechanical resonator (NR) in nano-optomechanical systems have stimulated research to realize some optical devices. In this work, we demonstrate theoretically that it is possible to achieve quantum memory for light on demand via a quantum dot system coupled to a nanomechanical resonator. This quantum memory for light is based on mechanically induced exciton polaritons, which makes the dark-state polariton reaccelerated and converted back into a photon pulse. Our presented device could open the door to all-optical routers for light memory devices and quantum information processing.

Depolarizing behavior of quantum channels in higher dimensions (pp0466-0484)
          
Easwar Magesan

The paper analyzes the behavior of quantum channels, particularly in large dimensions, by proving various properties of the quantum gate fidelity. Many of these properties are of independent interest in the theory of distance measures on quantum operations. A non-uniqueness result for the gate fidelity is proven, a consequence of which is the existence of non-depolarizing channels that produce a constant gate fidelity on pure states. Asymptotically, the gate fidelity associated with any quantum channel is shown to converge to that of a depolarizing channel. Methods for estimating the minimum of the gate fidelity are also presented.

Localization of quantum walks via the CGMV method (pp0485-0495)
          
Norio Konno and Etsuo Segawa
We study discrete-time quantum walks on a half line by means of spectral analysis. Cantero et al.  showed that the CMV matrix, which gives a recurrence relation for the orthogonal Laurent polynomials on the unit circle, expresses the dynamics of the quantum walk. Using the CGMV method introduced by them, the name is taken from their initials, we obtain the spectral measure for the quantum walk. As a corollary, we give another proof for localization of the quantum walk on homogeneous trees shown by Chisaki et al.

Assisted entanglement distillation (pp0496-0520)
          
Nicolas Dutil and Patrick Hayden
Motivated by the problem of designing quantum repeaters, we study entanglement distillation between two parties, Alice and Bob, starting from a mixed state and with the help of ``repeater'' stations. To treat the case of a single repeater, we extend the notion of entanglement of assistance to arbitrary mixed tripartite states and exhibit a protocol, based on a random coding strategy, for extracting pure entanglement. The rates achievable by this protocol formally resemble those achievable if the repeater station could merge its state to one of Alice and Bob even when such merging is impossible. This rate is provably better than the hashing bound for sufficiently pure tripartite states. We also compare our assisted distillation protocol to a hierarchical strategy consisting of entanglement distillation followed by entanglement swapping. We demonstrate by the use of a simple example that our random measurement strategy outperforms hierarchical distillation strategies when the individual helper stations' states fail to individually factorize into portions associated specifically with Alice and Bob. Finally, we use these results to find achievable rates for the more general scenario, where many spatially separated repeaters help two recipients distill entanglement.

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