Generating multi-photon W-like states for perfect quantum teleportation and superdense coding

An interesting aspect of multipartite entanglement is that for perfect teleportation and superdense coding, not the maximally entangled W states but a special class of non-maximally entangled W-like states are required. Therefore, efficient preparation of such W-like states is of great importance in quantum communications, which has not been studied as much as the preparation of W states. In this paper, we propose a simple optical scheme for efficient preparation of large-scale polarization-based entangled W-like states by fusing two W-like states or expanding a W-like state with an ancilla photon. Our scheme can also generate large-scale W states by fusing or expanding W or even W-like states. The cost analysis shows that in generating large-scale W states, the fusion mechanism achieves a higher efficiency with non-maximally entangled W-like states than maximally entangled W states. Our scheme can also start fusion or expansion with Bell states, and it is composed of a polarization-dependent beam splitter, two polarizing beam splitters and photon detectors. Requiring no ancilla photon or controlled gate to operate, our scheme can be realized with the current photonics technology and we believe it enable advances in quantum teleportation and superdense coding in multipartite settings.     

Controlled quantum dialogue using cluster states

This paper presents a new controlled quantum dialogue (CQD) protocol based on the cluster entangled states. The security analyses indicate that the proposed scheme is secure under not only various well-known attacks but also the collusive attack, where the participants may collude to communicate without the controller’s permission. Compared to a previous CQD scheme, which is also robust against the conspiracy attack, the proposed protocol is more efficient in both the qubit efficiency and the hardware requirement.     

QDENSITY—A Mathematica quantum computer simulation

This Mathematica 6.0 package is a simulation of a Quantum Computer. The program provides a modular, instructive approach for generating the basic elements that make up a quantum circuit. The main emphasis is on using the density matrix, although an approach using state vectors is also implemented in the package. The package commands are defined in Qdensity.m which contains the tools needed in quantum circuits, e.g., multiqubit kets, projectors, gates, etc.

New version program summary

Program title: QDENSITY 2.0Catalogue identifier: ADXH_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXH_v2_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 26 055No. of bytes in distributed program, including test data, etc.: 227 540Distribution format: tar.gzProgramming language: Mathematica 6.0Operating system: Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and Linux FC4Catalogue identifier of previous version: ADXH_v1_0Journal reference of previous version: Comput. Phys. Comm. 174 (2006) 914Classification: 4.15Does the new version supersede the previous version?: Offers an alternative, more up to date, implementationNature of problem: Analysis and design of quantum circuits, quantum algorithms and quantum clusters.Solution method: A Mathematica package is provided which contains commands to create and analyze quantum circuits. Several Mathematica notebooks containing relevant examples: Teleportation, Shor's Algorithm and Grover's search are explained in detail. A tutorial, Tutorial.nb is also enclosed.Reasons for new version: The package has been updated to make it fully compatible with Mathematica 6.0Summary of revisions: The package has been updated to make it fully compatible with Mathematica 6.0Running time: Most examples included in the package, e.g., the tutorial, Shor's examples, Teleportation examples and Grover's search, run in less than a minute on a Pentium 4 processor (2.6 GHz). The running time for a quantum computation depends crucially on the number of qubits employed.     

Public key encryption without random oracle made truly practical

In this paper, we report our success in identifying an efficient public key encryption scheme whose formal security proof does not require a random oracle. Specifically, we focus our attention on a universal hash based public key encryption scheme proposed by Zheng and Seberry at Crypto’92. Although Zheng and Seberry’s encryption scheme is very simple and efficient, its reductionist security proof has not been provided. We show how to tweak the Zheng-Seberry scheme so that the resultant scheme not only preserves the efficiency of the original scheme but also admits provable security against adaptive chosen ciphertext attack without random oracle. For the security proof, our first attempt is based on a strong assumption called the oracle Diffie-Hellman⁺ assumption. This is followed by a more challenging proof that employs a weaker assumption called the adaptive decisional Diffie-Hellman assumption, which is in alignment with adaptively secure assumptions advocated by Pandey, Pass and Vaikuntanathan.     

Relativistic entanglement in single-particle quantum states using non-linear entanglement witnesses

In this study, the spin-momentum correlation of one massive spin- ${\frac{1}{2}}$ and spin-1 particle states, which are made based on the projection of a relativistic spin operator into timelike direction is investigated. It is shown that by using Non-Linear entanglement witnesses (NLEWs), the effect of Lorentz transformation would decrease both the amount and the region of entanglement.     

Generating random connected planar graphs

Connected planar graphs are of interest to a variety of scholars. Being able to simulate a database of such graphs with selected properties would support specific types of inference for spatial analysis and other network-based disciplines. This paper presents a simple, efficient, and flexible connected planar graph generator for this purpose. It also summarizes a comparison between an empirical set of specimen graphs and their simulated counterpart set, and establishes evidence for positing a conjecture about the principal eigenvalue of connected planar graphs. Finally, it summarizes a probability assessment of the algorithm’s outcomes as well as a comparison between the new algorithm and selected existing planar graph generators.     

SusyMath: A Mathematica package for quantum superfield calculations

SusyMath is a Mathematica package for quantum superfield calculations. It defines a standard form to translate the correction to the effective action corresponding to a given supergraph into a Mathematica expression, which is then evaluated and simplified. Several functions for manipulations of these expressions are provided, and the package also has the ability to save the outcomes of its calculations in form.

Program summary

Title of program: SusyMathCatalogue identifier:ADYQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYQ_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland, also at http://fma.if.usp.br/~alysson/SusyMathLicensing provisions: LGPL, CPC non-profit use licenseProgramming language: MathematicaPlatform: Any platform supporting Mathematica 4.0 or higherComputer tested on: PC (Athlon64 X2 +3800); 1 GB RAMOperating system under which the program has been tested: Linux (Debian 4.0); XOrg 7.0.22; Mathematica 5.2No. of lines in distributed program, including test data, etc.:42 472No. of bytes in distributed program, including test data, etc.:471 596Distribution format:tar.gzNature of the problem: Evaluate quantum corrections to the effective action of supersymmetric field theories, formulated in the superfield formalism, both in three- and four-spacetime dimensions.Solution method: A set of procedures for integration by parts, application of the algebra of covariant derivatives and Grassman integration, along with several auxiliary functions, is introduced.Restrictions: At the moment, the background field method is not implemented, but the system is designed to be further generalized.Running time: Depends on the complexity of the problem. From seconds for simpler one-loop diagrams to several hours for simple two-loop graphs.     

Generalized Elias schemes for efficient harvesting of truly random bits

The problem of generating a sequence of true random bits (suitable for cryptographic applications) from random discrete or analog sources is considered. A generalized version, including vector quantization, of the classical approach by Elias for the generation of truly random bits is introduced, and its performance is analyzed, both in the finite case and asymptotically. The theory allows us to provide an alternative proof of the optimality of the original Elias’ scheme. We also consider the problem of deriving random bits from measurements of a Poisson process and from vectors of iid Gaussian variables. The comparison with the scheme of Elias, applied to geometric-like non-binary vectors, originally based on the iso-probability property of permutations of iid variables, confirms the potential of the generalized scheme proposed in our work.     

Generating correlated matrix exponential random variables

In this paper, we focus on inter-arrival time autocorrelation and its impact on model performance. We present a technique to generate matrix exponential random variables that match first-order statistics (moments) and second-order statistics (autocorrelation) from an empirical distribution. We briefly explain the matrix exponential distribution and show that we can represent any empirical distribution arbitrarily closely as matrix exponential. We then show how we can incorporate an autocorrelation structure into our matrix exponential random variables using the autoregressive to anything technique. We present examples showing how we match first and second-order statistics from empirical distributions and finally we show that our autocorrelation matrix exponential random variables produce more accurate performance metrics from simulation models than traditional techniques.     

Semi-quantum protocol for deterministic secure quantum communication using Bell states

Based on Bell states, this paper proposes a semi-quantum protocol enabling the limited semi-quantum or “classical” user Bob to transmit the secret message to a fully quantum Alice directly. A classical user is restricted to measure, prepare, reorder and send quantum states only in the classical basis \( \{ \left| 0 \right\rangle ,\left| 1 \right\rangle \} \). The protocol must rely on the quantum Alice to produce Bell states, perform Bell basis measurement and store qubits, but the classical party Bob does not require quantum memory. Security and efficiency of the proposed schemes have been discussed. The analysis results show that the protocol is secure against some eavesdropping attacks and the qubit efficiency of the protocol is higher than the other related semi-quantum protocols.     

Efficient deterministic secure quantum communication protocols using multipartite entangled states

We propose two deterministic secure quantum communication protocols employing three-qubit GHZ-like states and five-qubit Brown states as quantum channels for secure transmission of information in units of two bits and three bits using multipartite teleportation schemes developed here. In these schemes, the sender’s capability in selecting quantum channels and the measuring bases leads to improved qubit efficiency of the protocols.     

Quantum random walk polynomial and quantum random walk measure

In the paper, we introduce a quantum random walk polynomial (QRWP) that can be defined as a polynomial $\{P_{n}(x)\}$ , which is orthogonal with respect to a quantum random walk measure (QRWM) on $[-1, 1]$ , such that the parameters $\alpha _{n},\omega _{n}$ are in the recurrence relations $$\begin{aligned} P_{n+1}(x)= (x - \alpha _{n})P_{n}(x) - \omega _{n}P_{n-1}(x) \end{aligned}$$ and satisfy $\alpha _{n}\in \mathfrak {R},\omega _{n}> 0$ . We firstly obtain some results of QRWP and QRWM, in which case the correspondence between measures and orthogonal polynomial sequences is one-to-one. It shows that any measure with respect to which a quantum random walk polynomial sequence is orthogonal is a quantum random walk measure. We next collect some properties of QRWM; moreover, we extend Karlin and McGregor’s representation formula for the transition probabilities of a quantum random walk (QRW) in the interacting Fock space, which is a parallel result with the CGMV method. Using these findings, we finally obtain some applications for QRWM, which are of interest in the study of quantum random walk, highlighting the role played by QRWP and QRWM.     

Protocols of quantum key agreement solely using Bell states and Bell measurement

Two protocols of quantum key agreement (QKA) that solely use Bell state and Bell measurement are proposed. The first protocol of QKA proposed here is designed for two-party QKA, whereas the second protocol is designed for multi-party QKA. The proposed protocols are also generalized to implement QKA using a set of multi-partite entangled states (e.g., 4-qubit cluster state and \(\Omega \) state). Security of these protocols arises from the monogamy of entanglement. This is in contrast to the existing protocols of QKA where security arises from the use of non-orthogonal state (non-commutativity principle). Further, it is shown that all the quantum systems that are useful for implementation of quantum dialogue and most of the protocols of secure direct quantum communication can be modified to implement protocols of QKA.     

Efficient quantum dialogue using entangled states and entanglement swapping without information leakage

We propose a novel quantum dialogue protocol by using the generalized Bell states and entanglement swapping. In the protocol, a sequence of ordered two-qutrit entangled states acts as quantum information channel for exchanging secret messages directly and simultaneously. Besides, a secret key string is shared between the communicants to overcome information leakage. Different from those previous information leakage-resistant quantum dialogue protocols, the particles, composed of one of each pair of entangled states, are transmitted only one time in the proposed protocol. Security analysis shows that our protocol can overcome information leakage and resist several well-known attacks. Moreover, the efficiency of our scheme is acceptable.     

Generalized Choi states and 2-distillability of quantum states

We investigate the distillability of bipartite quantum states in terms of positive and completely positive maps. We construct the so-called generalized Choi states and show that it is distillable when it has negative partial transpose. We convert the distillability problem of 2-copy \(n\times n\) Werner states into the determination of the positivity of an Hermitian matrix. We obtain several sufficient conditions by which the positivity holds. Further, we investigate the case \(n=3\) by the classification of \(2\times 3\times 3\) pure states.     

Generating random networks from a given distribution

Several variations are given for an algorithm that generates random networks approximately respecting the probabilities given by any likelihood function, such as from a p^∗ social network model. A novel use of the genetic algorithm is incorporated in these methods, which improves its applicability to the degenerate distributions that can arise with p^∗ models. Our approach includes a convenient way to find the high-probability items of an arbitrary network distribution function.     

Generating labeled planar graphs uniformly at random

We present a deterministic polynomial time algorithm to sample a labeled planar graph uniformly at random. Our approach uses recursive formulae for the exact number of labeled planar graphs with n$n$ vertices and m$m$ edges, based on a decomposition into 1-, 2-, and 3-connected components. We can then use known sampling algorithms and counting formulae for 3-connected planar graphs.     

Generating inverse Gaussian random variates by approximation

The inverse Gaussian distribution is a useful distribution with important applications. But there is less discussion in the literature on sampling of this distribution. The method given in [Atkinson, A.C., 1982. The simulation of generalized inverse Gaussian and hyperbolic random variables. SIAM Journal on Scientific and Statistical Computing 3(4), 502-515] is based on rejection method where some (uniform) random numbers from the sample are discarded. This feature makes it difficult to take advantage of the low discrepancy sequences which have important applications. In [Michael, J., Schucany, W., Haas, R., 1976. Generating random variates using transformations with multiple roots. The American Statistician 30(2), 88-90], Michael et al. give a method to generate random variables with inverse Gaussian distribution. In their method, two pseudorandom numbers uniformly distributed on (0, 1) are needed in order to generate one inverse Gaussian random variable. In this short paper, we present a new method, based on direct approximate inversion, to generate the inverse Gaussian random variables. In this method, only one pseudorandom number is needed in generating one inverse Gaussian random variate. This method enables us to make use of the better convergence of low discrepancy sequence than the pseudorandom sequence. Numerical results show the superiority of low discrepancy sequence than the pseudorandom sequence in simulating the mean of the inverse Gaussian distribution by using our sampling method. Further application of this method in exotic option pricing under the normal inverse Gaussian model is under investigation.     

Fault tolerant deterministic quantum communications using GHZ states over collective-noise channels

This study proposes two new coding functions for a GHZ state and a GHZ-like state, respectively. Based on these coding functions, two fault tolerant deterministic quantum communication (DQC) protocols are proposed. Each of the new DQC’s is robust under one kind of collective noises: collective-dephasing noise and collective-rotation noise, respectively. The sender can use the proposed coding functions to encode his/her message, and the receiver can perform the Bell measurement to obtain the sender’s message. In comparison to the existing fault tolerant DQC protocols over collective-noise channels, the proposed protocols provide the best qubit efficiency. Moreover, the proposed protocols are also free from the ordinary eavesdropping and the information leakage.