QIC Abstracts

 Vol.7 No.1&2 January 1, 2007

An introduction to entanglement measures (pp001-051) PDF
          M.B. Plenio and S. Virmani
We review the theory of entanglement measures, concentrating mostly on the finite dimensional two-party case. Topics covered include: single-copy and asymptotic entanglement manipulation; the entanglement of formation; the entanglement cost; the distillable entanglement; the relative entropic measures; the squashed entanglement; log-negativity; the robustness monotones; the greatest cross-norm; uniqueness and extremality theorems. Infinite dimensional systems and multi-party settings will be discussed briefly.

Research Articles: 
Modeling ion trap thermal noise decoherence (pp052-072) PDF
          D. Leibrandt, B. Yurke, and R. Slusher 
We present a detailed analysis of ion heating caused by thermal fluctuation noise in ion traps. The results of the analysis are used to estimate thermal noise ion heating rates for a variety of trap electrode configurations and materials, including recent scalable multiplexed planar ion trap proposals based on silicon VLSI technology. We find that minimizing thermal noise ion heating places severe constraints on the design and materials used for ion traps.

Time-shift attack in practical quantum cryptosystems (pp073-082) PDF
           B. Qi, C.-H. F. Fung, H.-K. Lo, and F.-X. Ma       
Recently, a new type of attack, which exploits the efficiency mismatch of two single photon detectors (SPD) in a quantum key distribution (QKD) system, has been proposed. In this paper, we propose another ``time-shift'' attack that exploits the same imperfection. In our attack, Eve shifts the arrival time of either the signal pulse or the synchronization pulse or both between Alice and Bob. In particular, in a QKD system where Bob employs time-multiplexing technique to detect both bit "0'' and bit "1'' with the same SPD, Eve, in some circumstances, could acquire full information on the final key without introducing any error. In addition, we prove that if Alice and Bob are unaware of our attack, the final key they share is insecure. We emphasize that our attack is simple and feasible with current technology. Finally, we discuss some counter measures against our and earlier attacks.

Hidden symmetry detection on a quantum computer (pp083-092) PDF
          R. Schutzhold and W.G. Unruh     
The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved efficiently by quantum computers, it will be demonstrated by means of a simple example, that the detection of more general hidden (two-point) symmetries {$V\{f(x),f(U[x])\}=0$} by a quantum algorithm can also admit an exponential speed-up. E.g., one member of this class of symmetries {$V\{f(x),f(U[x])\}=0$} is discrete self-similarity (or discrete scale invariance).

Quantum walks on directed graphs (pp093-102) PDF
           A. Montanaro      
We consider the definition of quantum walks on directed graphs. Call a directed graph reversible if, for each pair of vertices $(v_i, v_j)$, if $v_i$ is connected to $v_j$ then there is a path from $v_j$ to $v_i$. We show that reversibility is a necessary and sufficient condition for a directed graph to allow the notion of a discrete-time quantum walk, and discuss some implications of this condition. We present a method for defining a "partially quantum'' walk on directed graphs that are not reversible.

Invertible quantum operations and perfect encryption of quantum states (pp103-110) PDF
           A. Nayak and P. Sen 
In this note, we characterize the form of an invertible quantum operation, i.e., a completely positive trace preserving linear transformation (a CPTP map) whose inverse is also a CPTP map. The precise form of such maps becomes important in contexts such as self-testing and encryption. We show that these maps correspond to applying a unitary transformation to the state along with an ancilla initialized to a fixed state, which may be mixed. The characterization of invertible quantum operations implies that one-way schemes for encrypting quantum states using a classical key may be slightly more general than the "private quantum channels'' studied by Ambainis, Mosca, Tapp and de Wolf {AmbainisMTW00}. Nonetheless, we show that their results, most notably a lower bound of 2n bits of key to encrypt n quantum bits, extend in a straightforward manner to the general case.

Multiplayer quantum minority game with decoherence (pp111-126) PDF
           A.P. Flitney and L.L.C. Hollenberg 
A quantum version of the Minority game for an arbitrary number of agents is considered. It is known that when the number of agents is odd, quantizing the game produces no advantage to the players, but for an even number of agents new Nash equilibria appear that have no classical analogue and have improved payoffs. We study the effect on the Nash equilibrium payoff of various forms of decoherence. As the number of players increases the multipartite GHZ state becomes increasingly fragile, as indicated by the smaller error probability required to reduce the Nash equilibrium payoff to the classical level.

Feedback control for communication with non-orthogonal states (pp127-138) PDF
            K. Jacobs      
Communicating classical information with a quantum system involves the receiver making a measurement on the system so as to distinguish as well as possible the alphabet of states used by the sender. We consider the situation in which this measurement takes an appreciable time. In this case the measurement must be described by a continuous measurement process. We consider a continuous implementation of the optimal measurement for distinguishing between two non-orthogonal states, and show that feedback control can be used during this measurement to increase the rate at which the information regarding the initial preparation is obtained. We show that while the maximum obtainable increase is modest, the effect is purely quantum mechanical in the sense that the enhancement is only possible when the initial states are non-orthogonal. We find further that the enhancement in the rate of information gain is achieved at the expense of reducing the total information which the measurement can extract in the long-time limit.

Fault-tolerant quantum computation for local leakage faults (pp139-156) PDF
            P. Aliferis and B.M. Terhal 
We provide a rigorous analysis of fault-tolerant quantum computation in the presence of local leakage faults. We show that one can systematically deal with leakage by using appropriate leakage-reduction units such as quantum teleportation. The leakage noise is described microscopically, by Hamiltonian couplings, and the noise is treated coherently, similar to general non-Markovian noise analyzed in Refs. \cite{Terhal04} and \cite{Aliferis05b}. We describe ways to limit the use of leakage-reduction units while keeping the quantum circuits fault-tolerant and we also discuss how leakage reduction by teleportation is naturally achieved in measurement-based computation.

An anomaly of non-locality (pp157-170) PDF
           A.A. Methot and V. Scarani
Ever since the work of Bell, it has been known that entangled quantum states can produce non-local correlations between the outcomes of separate measurements. However, for almost forty years, it has been assumed that the most non-local states would be the maximally entangled ones. Surprisingly it is not the case: non-maximally entangled states are generally more non-local than maximally entangled states for all the measures of non-locality proposed to date: Bell inequalities, the Kullback-Leibler distance, entanglement simulation with communication or with non-local boxes, the detection loophole and efficiency of cryptography. In fact, one can even find simple examples in low dimensions, confirming that it is not an artefact of a specifically constructed Hilbert space or topology. This anomaly shows that entanglement and non-locality are not only different concepts, but also truly different resources. We review the present knowledge on this anomaly, point out that Hardy's theorem has the same feature, and discuss the perspectives opened by these discoveries.

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