No Arabic abstract
In this letter we present the first implementation of a quantum coin tossing protocol. This protocol belongs to a class of ``two-party cryptographic problems, where the communication partners distrust each other. As with a number of such two-party protocols, the best implementation of the quantum coin tossing requires qutrits. In this way, we have also performed the first complete quantum communication protocol with qutrits. In our experiment the two partners succeeded to remotely toss a row of coins using photons entangled in the orbital angular momentum. We also show the experimental bounds of a possible cheater and the ways of detecting him.
The security of quantum communication using a weak coherent source requires an accurate knowledge of the sources mean photon number. Finite calibration precision or an active manipulation by an attacker may cause the actual emitted photon number to deviate from the known value. We model effects of this deviation on the security of three quantum communication protocols: the Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol without decoy states, Scarani-Acin-Ribordy-Gisin 2004 (SARG04) QKD protocol, and a coin-tossing protocol. For QKD, we model both a strong attack using technology possible in principle, and a realistic attack bounded by todays technology. To maintain the mean photon number in two-way systems, such as plug-and-play and relativistic quantum cryptography schemes, bright pulse energy incoming from the communication channel must be monitored. Implementation of a monitoring detector has largely been ignored so far, except for ID Quantiques commercial QKD system Clavis2. We scrutinize this implementation for security problems, and show that designing a hack-proof pulse-energy-measuring detector is far from trivial. Indeed the first implementation has three serious flaws confirmed experimentally, each of which may be exploited in a cleverly constructed Trojan-horse attack. We discuss requirements for a loophole-free implementation of the monitoring detector.
Given a sequence of numbers ${p_n}$ in $[0,1]$, consider the following experiment. First, we flip a fair coin and then, at step $n$, we turn the coin over to the other side with probability $p_n$, $nge 2$. What can we say about the distribution of the empirical frequency of heads as $ntoinfty$? We show that a number of phase transitions take place as the turning gets slower (i.e. $p_n$ is getting smaller), leading first to the breakdown of the Central Limit Theorem and then to that of the Law of Large Numbers. It turns out that the critical regime is $p_n=text{const}/n$. Among the scaling limits, we obtain Uniform, Gaussian, Semicircle and Arcsine laws.
The control of quantum walk is made particularly transparent when the initial state is expressed in terms of the eigenstates of the coin operator. We show that the group-velocity density acquires a much simpler form when expressed in this basis. This allows us to obtain a much deeper understanding of the role of the initial coin state on the dynamics of quantum walks and control it. We find that the eigenvectors of the coin result in an extremal regime of a quantum walk. The approach is illustrated on two examples of quantum walks on a line.
A quantum board game is a multi-round protocol between a single quantum player against the quantum board. Molina and Watrous discovered quantum hedging. They gave an example for perfect quantum hedging: a board game with winning probability < 1, such that the player can win with certainty at least 1-out-of-2 quantum board games played in parallel. Here we show that perfect quantum hedging occurs in a cryptographic protocol - quantum coin flipping. For this reason, when cryptographic protocols are composed, hedging may introduce serious challenges into their analysis. We also show that hedging cannot occur when playing two-outcome board games in sequence. This is done by showing a formula for the value of sequential two-outcome board games, which depends only on the optimal value of a single board game; this formula applies in a more general setting, in which hedging is only a special case.
We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. {[}Phys. Rev. Lett. textbf{93}, 180601(2004){]} which exhibits interesting dynamical localization and quasiperiodic dynamics. Our proposal allows for a much easier implementation of this particular rich dynamics than the original one. Moreover, it allows for an additional control on the walk, which can be used to compensate for phases appearing due to external interactions. To illustrate its feasibility, we discuss an example using an optical cavity. We also derive an approximated solution in the continuous limit (long--wavelength approximation) which provides physical insight about the process.