Abstract: International Journal of Quantum Information, Volume 13, Issue 08, December 2015. Landsburg method of classifying mixed Nash equilibria for maximally entangled Eisert–Lewenstein–Wilkens (ELW) game is analyzed with special emphasis on symmetries inherent to the problem. Nash equilibria for the original ELW game are determined. Citation: International Journal of Quantum Information PubDate: 2016-03-07T09:11:51Z DOI: 10.1142/S0219749915500665

Abstract: International Journal of Quantum Information, Ahead of Print. By performing X-rays measurements in the underground laboratory of Gran Sasso, LNGS-INFN, we test a basic principle of quantum mechanics: the Pauli exclusion principle (PEP). In the future, we aim to use a similar experimental technique to search for X-rays as a signature of the spontaneous collapse of the wave function predicted by continuous spontaneous localization theories. We present the achieved results of the VIP experiment and the future plans to gain two orders of magnitude in testing PEP with the recently VIP2 setup installed at Gran Sasso. Citation: International Journal of Quantum Information PubDate: 2016-05-19T11:35:04Z DOI: 10.1142/S0219749916400177

Authors:Elena R. Loubenets Abstract: International Journal of Quantum Information, Ahead of Print. We specify the local quasi hidden variable (LqHV) model reproducing the probabilistic description of all N-partite joint von Neumann measurements on an N-qudit state. Via this local probability model, we derive a new upper bound on the maximal violation by an N-qudit state of Bell inequalities of any type (either on correlation functions or on joint probabilities) for S observables per site. This new upper bound not only improves for all [math] S and d the corresponding results available for general Bell inequalities in the literature but also, for the N-qubit case with two observables per site, reduces exactly to the attainable upper bound known for quantum violations of correlation [math] setting Bell inequalities in a dichotomic case. Citation: International Journal of Quantum Information PubDate: 2016-05-19T11:35:03Z DOI: 10.1142/S0219749916400104

Authors:Chao Wang, Shuang Wang, Wei Chen, Zhen-Qiang Yin, Zheng-Fu Han Abstract: International Journal of Quantum Information, Ahead of Print. Random numbers (RNs) have applications in many areas: lottery games, gambling, computer simulation, and, most importantly, cryptography [N. Gisin et al., Rev. Mod. Phys. 74 (2002) 145]. In cryptography theory, the theoretical security of the system calls for high quality RNs. Therefore, developing methods for producing unpredictable RNs with adequate speed is an attractive topic. Early on, despite the lack of theoretical support, pseudo RNs generated by algorithmic methods performed well and satisfied reasonable statistical requirements. However, as implemented, those pseudorandom sequences were completely determined by mathematical formulas and initial seeds, which cannot introduce extra entropy or information. In these cases, “random” bits are generated that are not at all random. Physical random number generators (RNGs), which, in contrast to algorithmic methods, are based on unpredictable physical random phenomena, have attracted considerable research interest. However, the way that we extract random bits from those physical entropy sources has a large influence on the efficiency and performance of the system. In this manuscript, we will review and discuss several randomness extraction schemes that are based on radiation or photon arrival times. We analyze the robustness, post-processing requirements and, in particular, the extraction efficiency of those methods to aid in the construction of efficient, compact and robust physical RNG systems. Citation: International Journal of Quantum Information PubDate: 2016-05-19T11:35:01Z DOI: 10.1142/S0219749916300011

Authors:Hooman Moradpour, Afshin Montakhab Abstract: International Journal of Quantum Information, Ahead of Print. Bell-like inequalities have been used in order to distinguish non-local quantum pure states by various authors. The behavior of such inequalities under Lorentz transformation (LT) has been a source of debate and controversies in the past. In this paper, we consider the two most commonly studied three-particle pure states, that of W and Greenberger–Horne–Zeilinger (GHZ) states which exhibit distinctly different types of entanglement. We discuss the various types of three-particle inequalities used in previous studies and point to their corresponding shortcomings and strengths. Our main result is that if one uses Czachor’s relativistic spin operator and Svetlichny’s inequality as the main measure of non-locality and uses the same angles in the rest frame (S) as well as the moving frame ([math]), then maximally violated inequality in S will decrease in the moving frame, and will eventually lead to lack of non-locality (i.e. satisfaction of inequality) in the [math] limit. This is shown for both the GHZ and W states and in two different configurations which are commonly studied (Cases 1 and 2). Our results are in line with a more familiar case of two particle case. We also show that the satisfaction of Svetlichny’s inequality in the [math] limit is independent of initial particles’ velocity. Our study shows that whenever we use Czachor’s relativistic spin operator, results draws a clear picture of three-particle non-locality making its general properties consistent with previous studies on two-particle systems regardless of the W state or the GHZ state is involved. Throughout the paper, we also address the results of using Pauli’s operator in investigating the behavior of [math] under LT for both of the GHZ and W states and two cases (Cases 1 and 2). Our investigation shows that the violation of [math] in moving frame depends on the particle’s energy in the lab frame, which is in agreement with some previous works on two and three-particle systems. Our work may also help us to classify the results of using Czachor’s and Pauli’s operators to describe the spin entanglement and thus the system spin in relativistic information theory. Citation: International Journal of Quantum Information PubDate: 2016-05-19T11:34:56Z DOI: 10.1142/S0219749916500088

Authors:Claire Levaillant Abstract: International Journal of Quantum Information, Ahead of Print. We present a way to physically realize a circulant 2-qubit entangling gate in the Kauffman–Jones version of SU(2) Chern–Simons theory at level 4. Our approach uses qubit and qutrit ancillas, braids, fusions and interferometric measurements. Our qubit is formed by four anyons of topological charges 1221. Among other 2-qubit entangling gates which we generate in the present work, we produce in particular the circulant gate CEG=14I+i34J−34J2+i34J3, where J denotes the permutation matrix associated with the cycle [math] and I denotes the identity matrix. Citation: International Journal of Quantum Information PubDate: 2016-05-19T11:34:54Z DOI: 10.1142/S0219749916500064

Authors:G. Adenier, D. Calonico, S. Micalizio, N. Samantaray, I. P. Degiovanni, I. Ruo Berchera Abstract: International Journal of Quantum Information, Ahead of Print. Four-wave mixing (4WM) is a known source of intense non-classical twin beams. It can be generated when an intense laser beam (the pump) and a weak laser beam (the seed) overlap in a [math] medium (here Cesium vapor), with frequencies close to resonance with atomic transitions. The twin beams generated by 4WM have frequencies naturally close to atomic transitions, and can be intense (gain [math]) even in the CW pump regime, which is not the case for PDC [math] phenomenon in nonlinear crystals. So, 4WM is well suited for atom-light interaction and atom-based quantum-protocols. Here, we present the first realization of a source of 4-wave mixing exploiting [math] line of Cesium atoms. Citation: International Journal of Quantum Information PubDate: 2016-05-19T03:27:06Z DOI: 10.1142/S0219749916400141

Abstract: International Journal of Quantum Information, Ahead of Print. We propose an adynamical interpretation of quantum theory called Relational Blockworld (RBW) where the fundamental ontological element is a 4D graphical amalgam of space, time and sources called a “spacetimesource element.” These are fundamental elements of space, time and sources, not source elements in space and time. The transition amplitude for a spacetimesource element is computed using a path integral with discrete graphical action. The action for a spacetimesource element is constructed from a difference matrix K and source vector J on the graph, as in lattice gauge theory. K is constructed from graphical field gradients so that it contains a non-trivial null space and J is then restricted to the row space of K, so that it is divergence-free and represents a conserved exchange of energy–momentum. This construct of K and J represents an adynamical global constraint between sources, the spacetime metric and the energy–momentum content of the spacetimesource element, rather than a dynamical law for time-evolved entities. To illustrate this interpretation, we explain the simple EPR-Bell and twin-slit experiments. This interpretation of quantum mechanics constitutes a realist, psi-epistemic model that might underwrite certain information-theoretic accounts of the quantum. Citation: International Journal of Quantum Information PubDate: 2016-05-13T06:45:32Z DOI: 10.1142/S0219749916400074

Authors:Satoshi Iriyama, Masanori Ohya Abstract: International Journal of Quantum Information, Ahead of Print. The adaptive dynamics is known as a new mathematics to treat with a complex phenomena, for example, chaos, quantum algorithm and psychological phenomena. In this paper, we briefly review the notion of the adaptive dynamics, and explain the definition of the generalized Turing machine (GTM) and recognition process represented by the Fock space. Moreover, we show that there exists the quantum channel which is described by the GKSL master equation to achieve the Chaos Amplifier used in [M. Ohya and I. V. Volovich, J. Opt. B 5(6) (2003) 639., M. Ohya and I. V. Volovich, Rep. Math. Phys. 52(1) (2003) 25.] Citation: International Journal of Quantum Information PubDate: 2016-05-13T06:45:28Z DOI: 10.1142/S0219749916400086

Authors:M. Kupczynski Abstract: International Journal of Quantum Information, Ahead of Print. Entangled physical systems are an important resource in quantum information. Many papers were published trying to grasp the meaning of entanglement. It was noticed that a Hilbert space of possible state vectors of compound physical system can be partitioned by introducing various tensor product structures induced by the experimentally accessible observables (interactions and measurements). In this sense, the entanglement is relative to a particular set of experimental capabilities. Inspired by these results some authors claim that in fact all quantum states are entangled. In this paper, we show that this claim is incorrect and we discuss in operational way differences existing between separable and entangled states. A sufficient condition for entanglement is the violation of Bell–CHSH-CH inequalities and/or steering inequalities. Since there exist experiments outside the domain of quantum physics violating these inequalities therefore in the operational approach one cannot say that the entanglement is an exclusive quantum phenomenon. We also explain that an unambiguous experimental certification of the entanglement is a difficult task because classical statistical significance tests may not be trusted if sample homogeneity cannot be tested or is not tested carefully enough. Citation: International Journal of Quantum Information PubDate: 2016-05-11T11:15:48Z DOI: 10.1142/S0219749916400037

Authors:Hans-Thomas Elze Abstract: International Journal of Quantum Information, Ahead of Print. Cellular automata (CA) can show well known features of quantum mechanics (QM), such as a linear updating rule that resembles a discretized form of the Schrödinger equation together with its conservation laws. Surprisingly, a whole class of “natural” Hamiltonian CA, which are based entirely on integer-valued variables and couplings and derived from an action principle, can be mapped reversibly to continuum models with the help of sampling theory. This results in “deformed” quantum mechanical models with a finite discreteness scale l, which for [math] reproduce the familiar continuum limit. Presently, we show, in particular, how such automata can form “multipartite” systems consistently with the tensor product structures of non-relativistic many-body QM, while maintaining the linearity of dynamics. Consequently, the superposition principle is fully operative already on the level of these primordial discrete deterministic automata, including the essential quantum effects of interference and entanglement. Citation: International Journal of Quantum Information PubDate: 2016-05-11T11:15:45Z DOI: 10.1142/S0219749916400013

Authors:Jiahua Wei, Hong-Yi Dai, Ming Zhang, Le Yang, Jingsong Kuang Abstract: International Journal of Quantum Information, Ahead of Print. In this paper, we put forward two novel schemes for probabilistic remote preparation of an arbitrary quantum state with the aid of appropriate local unitary operations when the sender and the receiver only have partial information of non-maximally entangled state, respectively. The concrete implementation procedures of the novel proposals are given in detail. Additionally, the physical realizations of our proposals are discussed based on the linear optics. Because of that neither the sender nor the receiver need to know fully the information of the partially entangled state, our schemes are useful to not only expand the application range of quantum entanglement, but also enlarge the research field of probabilistic remote state preparation (RSP). Citation: International Journal of Quantum Information PubDate: 2016-05-06T03:24:42Z DOI: 10.1142/S0219749916500039

Authors:Francesco De Martini, Enrico Santamato Abstract: International Journal of Quantum Information, Ahead of Print. The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle” but by the adoption of the complex standard relativistic quantum field theory. In a recent paper [E. Santamato and F. D. De Martini, Found. Phys. 45 (2015) 858] we presented a complete proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the “Conformal Quantum Geometrodynamics” (CQG). In this paper, by the same theory, the proof of the spin-statistics theorem (SST) is extended to the relativistic domain in the scenario of curved spacetime. No relativistic quantum field operators are used in the present proof and the particle exchange properties are drawn from rotational invariance rather than from Lorentz invariance. Our relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. As in the nonrelativistic case, we find once more that the “intrinsic helicity” of the elementary particles enters naturally into play. It is therefore this property, not considered in the standard quantum mechanics (SQM), which determines the correct spin-statistics connection observed in Nature. Citation: International Journal of Quantum Information PubDate: 2016-04-28T07:45:44Z DOI: 10.1142/S0219749916400116

Authors:Noboru Watanabe Abstract: International Journal of Quantum Information, Ahead of Print. We review some notions for quantum dynamical entropies. The dynamical entropy of quantum systems is discussed and a numerical computation of the dynamical entropy is carried for the open system dynamics. Citation: International Journal of Quantum Information PubDate: 2016-04-28T07:45:36Z DOI: 10.1142/S0219749916400050

Authors:Ye-Feng He, Wen-Ping Ma Abstract: International Journal of Quantum Information, Ahead of Print. Based on four-particle GHZ states, the double CNOT operation and the delayed measurement technique, a two-party quantum key agreement (QKA) protocols is proposed. The double CNOT operation makes each four-particle GHZ state collapse into two independent quantum states without any entanglement. Furthermore, one party can directly know the two quantum states and the other party can be aware of the two quantum states by using the corresponding measurement. According to the initial states of the two quantum states, two parties can extract the secret keys of each other by using the publicly announced value or by performing the delayed measurement, respectively. Then the protocol achieves the fair establishment of a shared key. The security analysis shows that the new protocol can resist against participant attacks, the Trojan horse attacks and other outsider attacks. Furthermore, the new protocol also has no information leakage problem and has high qubit efficiency. Citation: International Journal of Quantum Information PubDate: 2016-04-28T07:45:34Z DOI: 10.1142/S0219749916500076

Authors:Anmer Daskin Abstract: International Journal of Quantum Information, Ahead of Print. Quantum phase estimation algorithm (PEA) has been successfully adapted as a sub frame of many other algorithms applied to a wide variety of applications in different fields. However, the requirement of a good approximate eigenvector given as an input to the algorithm hinders the application of the algorithm to the problems where we do not have any prior knowledge about the eigenvector. In this paper, we show that the principal eigenvalue of an irreducible non-negative operator can be determined by using an equal superposition initial state in the PEA. This removes the necessity of the existence of an initial good approximate eigenvector. Moreover, we show that the success probability of the algorithm is related to the closeness of the operator to a stochastic matrix. Therefore, we draw an estimate for the success probability by using the variance of the column sums of the operator. This provides a priori information which can be used to know the success probability of the algorithm beforehand for the non-negative matrices and apply the algorithm only in cases when the estimated probability is reasonably high. Finally, we discuss the possible applications and show the results for random symmetric matrices and 3-local Hamiltonians with non-negative off-diagonal elements. Citation: International Journal of Quantum Information PubDate: 2016-04-28T07:45:32Z DOI: 10.1142/S0219749916500052

Authors:Abdullah Dertli, Yasemin Cengellenmis, Senol Eren Abstract: International Journal of Quantum Information, Ahead of Print. In this paper, we study the structure of cyclic, quasi-cyclic codes and their skew codes over the finite ring [math], [math] for [math]. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic codes over [math] are obtained. A necessary and sufficient condition for cyclic code over [math] that contains its dual has been given. The parameters of quantum error correcting codes are obtained from cyclic codes over [math]. Citation: International Journal of Quantum Information PubDate: 2016-04-28T05:52:44Z DOI: 10.1142/S021974991650012X

Authors:Yinzhu Wang, Danxia Wang, Li Huang Abstract: International Journal of Quantum Information, Ahead of Print. In this paper, an extended negativity entanglement measure for multipartite k-nonseparable states with respect to k-partition was proposed. We show that this measure is well-defined, i.e. it satisfies some basic properties as an entanglement measure. In addition, we give a relation between this measure and k-ME concurrence, and obtain a lower bound of this measure. Citation: International Journal of Quantum Information PubDate: 2016-04-18T09:13:56Z DOI: 10.1142/S0219749916500015

Authors:Brian R. La Cour, Corey I. Ostrove, Granville E. Ott, Michael J. Starkey, Gary R. Wilson Abstract: International Journal of Quantum Information, Ahead of Print. This paper describes a novel approach to emulate a universal quantum computer with a wholly classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any modality (e.g. acoustic, electromagnetic, etc.) but this paper will focus on electronic signals. Individual qubits are represented by in-phase and quadrature sinusoidal signals, while unitary gate operations are performed using simple analog electronic circuit devices. In this manner, the Hilbert space structure of a multi-qubit quantum state, as well as a universal set of gate operations, may be fully emulated classically. Results from a programmable prototype system are presented and discussed. Citation: International Journal of Quantum Information PubDate: 2016-04-07T08:50:53Z DOI: 10.1142/S0219749916400049

Abstract: International Journal of Quantum Information, Ahead of Print. We discuss the recently observed “loophole free” violation of Bell’s inequalities in the framework of a physically realist view of quantum mechanics (QM), which requires that physical properties are attributed jointly to a system, and to the context in which it is embedded. This approach is clearly different from classical realism, but it does define a meaningful “quantum realism” from a general philosophical point of view. Consistently with Bell test experiments, this quantum realism embeds some form of non-locality, but does not contain any action at a distance, in agreement with QM. Citation: International Journal of Quantum Information PubDate: 2016-04-07T08:50:52Z DOI: 10.1142/S0219749916400025

Authors:S. A. Rashkovskiy Abstract: International Journal of Quantum Information, Ahead of Print. It is shown that the Schrödinger equation can be written in the form of the diffusion equation for classical particles moving in a continuous space. A class of classical random processes described by the Schrödinger equation is considered. It is shown that such classical random processes can be used as a tool for the numerical solution of the Schrödinger equation. Citation: International Journal of Quantum Information PubDate: 2016-04-07T08:50:50Z DOI: 10.1142/S0219749916400062

Authors:Song Lin, Hui Wang, Gong-De Guo, Guo-Hua Ye, Hong-Zhen Du, Xiao-Fen Liu Abstract: International Journal of Quantum Information, Ahead of Print. Quantum key distribution (QKD) has been growing rapidly in recent years and becomes one of the hottest issues in quantum information science. During the implementation of QKD on a network, identity authentication has been one main problem. In this paper, an efficient authenticated multi-user quantum key distribution (MQKD) protocol with single particles is proposed. In this protocol, any two users on a quantum network can perform mutual authentication and share a secure session key with the assistance of a semi-honest center. Meanwhile, the particles, which are used as quantum information carriers, are not required to be stored, therefore the proposed protocol is feasible with current technology. Finally, security analysis shows that this protocol is secure in theory. Citation: International Journal of Quantum Information PubDate: 2016-03-29T07:03:48Z DOI: 10.1142/S0219749916500027

Abstract: International Journal of Quantum Information, Ahead of Print. In order to assess the susceptibility of the quantum key distribution (QKD) systems to the hacking attack including simultaneous and frequent system self-decalibrations, we analyze the stability of the QKD transmission organized in two commercially available systems. The first one employs non-entangled photons as flying qubits in the dark quantum channel for communication whereas the second one utilizes the entangled photon pairs to secretly share the cryptographic key. Applying standard methods of the statistical data analysis to the characteristic indicators of the quality of the QKD communication (the raw key exchange rate [RKER] and the quantum bit error rate [QBER]), we have estimated the pace of the self-decalibration of both systems and the repeatability rate in the case of controlled worsening of the dark channel quality. Citation: International Journal of Quantum Information PubDate: 2016-02-23T03:18:37Z DOI: 10.1142/S0219749915500641

Authors:Won Sang Chung Abstract: International Journal of Quantum Information, Ahead of Print. In this paper, we consider the generalized Schrödinger cat states. Using these states, we obtain the corresponding quasi-Bell states and the reduced density operator. For these quasi-Bell states, we investigate the non-classical effects such as oscillatory photon statistics, sub-Poissonian property and violation of the Cauchy–Schwarz inequality. Citation: International Journal of Quantum Information PubDate: 2016-02-23T03:18:36Z DOI: 10.1142/S0219749915500653

Authors:Jian Gao Abstract: International Journal of Quantum Information, Ahead of Print. We give a construction of quantum codes over [math] from cyclic codes over a finite non-chain ring [math], where [math], p is a prime, [math] and [math]. Citation: International Journal of Quantum Information PubDate: 2016-02-23T03:18:33Z DOI: 10.1142/S021974991550063X

Abstract: International Journal of Quantum Information, Ahead of Print. We present a study of extremal entanglement witnesses on a bipartite composite quantum system. We define the cone of witnesses as the dual of the set of separable density matrices, thus [math] when [math] is a witness and [math] is a pure product state, [math] with [math]. The set of witnesses of unit trace is a compact convex set, uniquely defined by its extremal points. The expectation value [math] as a function of vectors [math] and [math] is a positive semidefinite biquadratic form. Every zero of [math] imposes strong real-linear constraints on f and [math]. The real and symmetric Hessian matrix at the zero must be positive semidefinite. Its eigenvectors with zero eigenvalue, if such exist, we call Hessian zeros. A zero of [math] is quadratic if it has no Hessian zeros, otherwise it is quartic. We call a witness quadratic if it has only quadratic zeros, and quartic if it has at least one quartic zero. A main result we prove is that a witness is extremal if and only if no other witness has the same, or a larger, set of zeros and Hessian zeros. A quadratic extremal witness has a minimum number of isolated zeros depending on dimensions. If a witness is not extremal, then the constraints defined by its zeros and Hessian zeros determine all directions in which we may search for witnesses having more zeros or Hessian zeros. A finite number of iterated searches in random directions, by numerical methods, leads to an extremal witness which is nearly always quadratic and has the minimum number of zeros. We discuss briefly some topics related to extremal witnesses, in particular the relation between the facial structures of the dual sets of witnesses and separable states. We discuss the relation between extremality and optimality of witnesses, and a conjecture of separability of the so-called structural physical approximation (SPA) of an optimal witness. Finally, we discuss how to treat the entanglement witnesses on a complex Hilbert space as a subset of the witnesses on a real Hilbert space. Citation: International Journal of Quantum Information PubDate: 2016-02-23T03:16:12Z DOI: 10.1142/S0219749915500604

Authors:Zhen Wang, Zhi-Xi Wang Abstract: International Journal of Quantum Information, Ahead of Print. It is strictly proved that a two-qubit [math]-invariant state reaches its relative entropy of entanglement (REE) by the separable state having the same matrix structure. We also formulate three quadratic equations for the corresponding closest separable state (CSS) of [math]-invariant states by their symmetric property. Thus, the CSS of [math]-invariant state can be provided. Furthermore, to illustrate our result we consider two concrete examples. Citation: International Journal of Quantum Information PubDate: 2016-01-27T01:35:41Z DOI: 10.1142/S0219749915500586

Authors:Y. Ben-Aryeh, A. Mann Abstract: International Journal of Quantum Information, Ahead of Print. Explicitly separable density matrices are constructed for all separable two-qubits states based on Hilbert–Schmidt (HS) decompositions. For density matrices which include only two-qubits correlations the number of HS parameters is reduced to 3 by using local rotations, and for two-qubits states which include single qubit measurements, the number of parameters is reduced to 4 by local Lorentz transformations. For both cases, we related the absolute values of the HS parameters to probabilities, and the outer products of various Pauli matrices were transformed to pure state density matrices products. We discuss related problems for three-qubits. For n-qubits correlation systems ([math]) the sufficient condition for separability may be improved by local transformations, related to high order singular value decompositions (SVDs). Citation: International Journal of Quantum Information PubDate: 2016-01-27T01:35:38Z DOI: 10.1142/S0219749915500616

Authors:Constantin V. Usenko Abstract: International Journal of Quantum Information, Ahead of Print. In the direct communication quantum channels, the authorized recipient (Bob) and the non-authorized recipient (Eve) have different abilities for verification of received information. Bob can apply the feedback to commit the sender (Alice) to perform verification. Eve has to use for verification an indirect method based on the measurement of a set of incompatible observables enough for determination of the coding basis used by Alice. In the protocol of direct communication, regular modification of coding basis and masking it with an equilibrium in average information carrier density matrix prevents reconstruction of coding basis by the results of Eve’s measurements of an arbitrary set of observables. This provides unconditional security of the channel. Citation: International Journal of Quantum Information PubDate: 2016-01-27T01:35:35Z DOI: 10.1142/S0219749915500628