Practical quantum bit commitment protocol

A quantum protocol for bit commitment the security of which is based on technological limitations on non demolition measurements and long-term quantum memory is presented.     

Simplified quantum bit commitment using single photon nonlocality

We simplified our previously proposed quantum bit commitment (QBC) protocol based on the Mach–Zehnder interferometer, by replacing symmetric beam splitters with asymmetric ones. It eliminates the need for random sending time of the photons; thus, the feasibility and efficiency are both improved. The protocol is immune to the cheating strategy in the Mayers-Lo-Chau no-go theorem of unconditionally secure QBC, because the density matrices of the committed states do not satisfy a crucial condition on which the no-go theorem holds.     

Cheat sensitive quantum bit commitment via pre- and post-selected quantum states

Cheat sensitive quantum bit commitment is a most important and realizable quantum bit commitment (QBC) protocol. By taking advantage of quantum mechanism, it can achieve higher security than classical bit commitment. In this paper, we propose a QBC schemes based on pre- and post-selected quantum states. The analysis indicates that both of the two participants’ cheat strategies will be detected with non-zero probability. And the protocol can be implemented with today’s technology as a long-term quantum memory is not needed.     

Informational correlation between two parties of a quantum system: spin-1/2 chains

We introduce the informational correlation \(E^{AB}\) between two interacting quantum subsystems \(A\) and \(B\) of a quantum system as the number of arbitrary parameters \(\varphi _i\) of a unitary transformation \(U^A\) (locally performed on the subsystem \(A\) ) which may be detected in the subsystem \(B\) by the local measurements. This quantity indicates whether the state of the subsystem \(B\) may be effected by means of the unitary transformation applied to the subsystem \(A\) . Emphasize that \(E^{AB}\ne E^{BA}\) in general. The informational correlations in systems with tensor product initial states are studied in more details. In particular, it is shown that the informational correlation may be changed by the local unitary transformations of the subsystem \(B\) . However, there is some non-reducible part of \(E^{AB}(t)\) which may not be decreased by any unitary transformation of the subsystem \(B\) at a fixed time instant \(t\) . Two examples of the informational correlations between two parties of the four-node spin-1/2 chain with mixed initial states are studied. The long chains with a single initially excited spin (the pure initial state) are considered as well.     

On the value of commitment

In game theory, it is well known that being able to commit to a strategy before other players move can be beneficial. In this paper, we analyze how much benefit a player can derive from commitment in various types of games, in a quantitative sense that is similar to concepts such as the value of mediation and the price of anarchy. Specifically, we introduce and study the value of pure commitment (the benefit of committing to a pure strategy), the value of mixed commitment (the benefit of committing to a mixed strategy), and the mixed versus pure commitment ratio (how much can be gained by committing to a mixed strategy rather than a pure one). In addition to theoretical results about how large these values are in the extreme case in various classes of games, we also give average-case results based on randomly drawn normal-form games.     

Minimum-error discrimination between two sets of similarity-transformed quantum states

Using the equality form of the necessary and sufficient conditions introduced in Jafarizadeh (Phys Rev A 84:012102 (9 pp), 2011), minimum error discrimination between states of the two sets of equiprobable similarity transformed quantum qudit states is investigated. In the case that the unitary operators describing the similarity transformations are generating sets of two irreducible representations and the states fulfill a certain constraint, the optimal set of measurements and the corresponding maximum success probability of discrimination are determined in closed form. In the cases that they are generating sets of reducible representations, there exist no closed-form formula in general, but the procedure can be applied properly in each case provided that the states obey some constraints. Finally, we give the maximum success probability of discrimination and optimal measurement operators for some important examples of mixed quantum states, such as generalized Bloch sphere m-qubit states, qubit states and their three special cases.     

On the relation between quantum walks and zeta functions

We present an explicit formula for the characteristic polynomial of the transition matrix of the discrete-time quantum walk on a graph via the second weighted zeta function. As applications, we obtain new proofs for the results on spectra of the transition matrix and its positive support.     

Entanglement and quantum state transfer between two atoms trapped in two indirectly coupled cavities

Quantum Information Processing - We propose a one-step scheme for implementing entanglement generation and the quantum state transfer between two atomic qubits trapped in two different cavities...     

Mathematical models of the battle between parties for electorate or between companies for markets

A model of optimization of strategies for any number of political parties (companies) in election (advertising) campaigns is proposed. We formulated the problem of choosing an optimal strategy for allocating scarce resources among regions (markets) in which political parties (companies) have different influences. The optimization model is analyzed and the existence of a unique solution is proved for different functions of dependencies between investments and winning. An analytical solution to the model is found for the case of two parties (companies). A direction for further development is the study of the sensitivity of an optimal solution to model parameters and formation of a stochastic model.     

On the impossibility of bringing a flat membrane to rest with boundary forces

We consider exact control problems for the oscillations of two-dimensional membranes with boundary forces. We say that a system can be brought to the state of rest of for any initial conditions there exists a control such that the corresponding solution becomes zero in finite time and remains zero in the future. We prove that under certain restrictions on the controlling influence some systems with distributed parameters cannot be brought to the state of rest in finite time.     

On the flow between two rotating shrouded discs

Numerical solutions to the full Navier Stokes equations for the flow enclosed between two rotating discs and a sidewall are presented. The sidewall remains fixed throughout, while we consider examples in which: (i) the bottom disc is rotating and the top disc is fixed; (ii) the two discs rotate in the same sense; (iii) the two discs rotate in opposite senses. We present solutions up to a Reynolds number of 1200, using second order central finite differencing.     

On the power of synchronization between two adjacent processes

We study the power of local computations on labelled edges (which allow two adjacent vertices to synchronize and to modify their states simultaneaously in function of their previous states) through the classical election problem. We characterize the graphs for which this problem has a solution. As corollaries we characterize graphs which admit an election algorithm for two seminal models: Angluin’s model and asynchronous systems where processes communicate with synchronous message passing (i.e., there is a synchronization between the process sending the message and the one receiving it).     

Dynamical behavior of quantum correlations between two qubits coupled to an external environment

We investigate the dynamics of quantum correlations of a two-qubit system coupled to an external environment. We have considered both cases: a spin environment and a bosonic environment. In all cases, we have chosen the Bell-diagonal state as the initial state and computed the evolution of quantum correlations in terms of entanglement, quantum discord and trace distance geometric quantum discord. Special attention is paid to the singular quantum phenomena, such as entanglement sudden death, sudden transition and double sudden transitions from classical to quantum decoherence, which all depend on the initial state and the parameters related to the system and the environment. We find the trace distance geometric quantum discord has a good robustness in resisting the spin and bosonic environmental noise.     

量子位Bloch坐标的量子人工蜂群优化算法

为了改善人工蜂群(ABC)算法在解决多变量优化问题时存在的收敛速度较慢、容易陷入局部最优的不足,结合量子理论和人工蜂群算法提出一种新的量子优化算法。算法首先采用量子位Bloch坐标对蜂群算法中食物源进行编码,扩展了全局最优解的数量,提高了蜂群算法获得全局最优解的概率;然后用量子旋转门实现搜索过程中的食物源更新。对于量子旋转门的转角关系的确定,提出了一种新的方法。从理论上证明了蜂群算法在Bloch球面每次以等面积搜索时,量子旋转门的两个旋转相位大小近似于反比例关系,避免了固定相位旋转的不均等性,使得搜索呈现规律性。在典型函数优化问题的实验中,所提算法在搜索能力和优化效率两个方面优于普通量子人工蜂群(QABC)算法和单一人工蜂群算法。     

On the use of one bit quantizers in networked control

This paper addresses the following problem in networked control: “If a control law is implemented over a channel that supports a certain fixed bit rate what is the best choice for the control update rate and, consequently, the number of bits carried in each sample?” A restricted architecture in which linear filters are used for the encoder/decoder is considered and a quantizer with linear feedback is deployed. Subject to these restrictions, a procedure for designing the controller and associated filters is presented. These filters are then deployed to choose the best number of bits per control update. It is shown, subject to the above restrictions, that it is generally best to use one bit per sample, in which case, the control update rate is equal to the bit rate. Our analysis has two points of departure from contemporary literature in this area. Firstly, we focus on bits per unit time, as opposed to bits per sample. Secondly we use a fixed number of bits in every time period as opposed to an average bit rate.     

IrisCode decompression based on the dependence between its bit pairs

IrisCode is an iris recognition algorithm developed in 1993 and continuously improved by Daugman. Understanding IrisCode's properties is extremely important because over 60 million people have been mathematically enrolled by the algorithm. In this paper, IrisCode is proved to be a compression algorithm, which is to say its templates are compressed iris images. In our experiments, the compression ratio of these images is 1:655. An algorithm is designed to perform this decompression by exploiting a graph composed of the bit pairs in IrisCode, prior knowledge from iris image databases, and the theoretical results. To remove artifacts, two postprocessing techniques that carry out optimization in the Fourier domain are developed. Decompressed iris images obtained from two public iris image databases are evaluated by visual comparison, two objective image quality assessment metrics, and eight iris recognition methods. The experimental results show that the decompressed iris images retain iris texture that their quality is roughly equivalent to a JPEG quality factor of 10 and that the iris recognition methods can match the original images with the decompressed images. This paper also discusses the impacts of these theoretical and experimental findings on privacy and security.     

Mediating and inducing quantum correlation between two separated qubits by one-dimensional plasmonic waveguide

We investigate the dynamics of quantum correlation between two separated qubits trapped in one-dimensional plasmonic waveguide. It is found that for a class of initial states, the quantum discord shows a sudden change phenomenon during the dynamical evolution. Furthermore, we demonstrate that the quantum discord can be enhanced if a proper product of the plasmon wave number and two qubits distance is chosen. Finally, we find that the non-zero quantum discord between two qubits can be created for the states without initial quantum discord during the time evolution of the system.     

On bit reduction of chain coded line drawings

A bit reduction scheme is proposed for storing the chain code of line drawings. The chain code sequence is broken into digital straight line segements, which are encoded using a table lookup. For the case of high accuracy using a small grid size a significant reduction is achieved over conventional coding.     

Evolution of quantum correlations in the open quantum systems consisting of two coupled oscillators

The open quantum systems consisting of coupled and uncoupled asymmetric oscillators are considered with an initial quantum-dot trapped-ion coherent state. The quantum correlations between spatial modes of this trapped ion are examined to find their dependence on the temperature, asymmetric parameter, dissipation coefficient and the magnetic field. It is observed that the discord of the initial state is an increasing function of the asymmetric parameter and the magnetic field. Moreover, in the case of two uncoupled modes, entanglement and discord are decreasing functions of temperature and the dissipation coefficient. However, as the temperature and dissipation coefficient increase, the discord fades out faster. In the case of two coupled modes, as the temperature and dissipation coefficient increase, the sudden death of the entanglement and fade out of the discord happen sooner; moreover, as the magnetic field increases, the entanglement sudden death and the discord fade out time occur sooner. Also, with the increase in the asymmetric parameter, the entanglement sudden death is postponed. In addition, in the asymmetric system, appreciable discord can be created in the temperature range 0–10 K, while appreciable entanglement can be created in the temperature range 0–5 mK. Finally, it is observed that non-monotonic evolution of quantum correlations is due to coupling of modes.     

The gap in circumventing the impossibility of consensus

The impossibility of reaching deterministic consensus in an asynchronous and crash prone system was established for a weak variant of the problem, usually called weak consensus, where a set of processes need to decide on a common value in {0,1}, so that both 0 and 1 are possible decision values. On the other hand, approaches to circumventing the impossibility focused on a stronger variant of the problem, called consensus, where the processes need to decide on one of the values they initially propose (0 or 1). This paper studies the computational gap between the two problems. We show that any set of deterministic object types that, combined with registers, implements weak consensus, also implements consensus. Then we exhibit a non-deterministic type that implements weak consensus, among any number of processes, but, combined with registers, cannot implement consensus even among two processes. In modern terminology, this type has consensus power 1 and weak consensus power ∞.