Showing papers in "International Journal of Quantum Information in 2008"
TL;DR: In this paper, the authors propose an approach which allows us to study general physical systems for which the above mentioned independence condition does not necessarily hold, based on an extension of various information-theoretical notions.
Abstract: Quantum Information Theory is an area of physics which studies both fundamental and applied issues in quantum mechanics from an information-theoretical viewpoint. The underlying techniques are, however, often restricted to the analysis of systems which satisfy a certain independence condition. For example, it is assumed that an experiment can be repeated independently many times or that a large physical system consists of many virtually independent parts. Unfortunately, such assumptions are not always justified. This is particularly the case for practical applications — e.g. in quantum cryptography — where parts of a system might have an arbitrary and unknown behavior. We propose an approach which allows us to study general physical systems for which the above mentioned independence condition does not necessarily hold. It is based on an extension of various information-theoretical notions. For example, we introduce new uncertainty measures, called smooth min- and max-entropy, which are generalizations of ...
1,059 citations
TL;DR: In this paper, the authors discuss several candidates that suggest themselves as generalizations P of for multi-path interferometers, and treat the case of three paths in considerable detail, in order to find those equal weight superpositions of the path amplitudes which maximize P for the emerging intensities.
Abstract: For two-path interferometers, the which-path predictability and the fringe visibility are familiar quantities that are much used to talk about wave-particle duality in a quantitative way. We discuss several candidates that suggest themselves as generalizations P of for multi-path interferometers, and treat the case of three paths in considerable detail. To each choice for the path knowledge P, the interference strength V — the corresponding generalization of — is found by a natural, operational procedure. In experimental terms, it amounts to finding those equal-weight superpositions of the path amplitudes which maximize P for the emerging intensities. Mathematically speaking, one needs to identify a certain optimum one among the Fourier transforms of the state of the interfering quantum object. Wave-particle duality is manifest, inasmuch as P = 1 implies V = 0 and V = 1 implies P = 0, whatever definition is chosen. The possible values of the pair (P,V) are restricted to an area with corners at (P,V) = (0,0), (P,V) = (1,0), and (P,V) = (0,1), with the shape of the border line from (1,0) to (0,1), depending on the particular choice for P and the induced definition of V.
100 citations
TL;DR: It is shown that half of Alice's and Bob's secret message is leaked through the classical channel, and it is seen that the quantum efficiency claimed in the quantum dialogue type of protocols is not achievable.
Abstract: Classical communications are used in the post-processing procedure of quantum key distribution. Since the security of quantum key distribution is based on the principles of quantum mechanics, intuitively, the secret key can only be derived from the quantum states. We find that classical communications are incorrectly used in the so-called quantum dialogue type protocols. In these protocols, public communications are used to transmit secret messages. Our calculations show that half of Alice's and Bob's secret message is leaked through the classical channel. By applying the Holevo bound, we can see that the quantum efficiency claimed in the quantum dialogue type of protocols is not achievable.
95 citations
TL;DR: A quantum key distribution (QKD) network is currently being implemented in Vienna by integrating seven QKD-link devices that connect five subsidiaries of Siemens Austria as mentioned in this paper.
Abstract: A quantum key distribution (QKD) network is currently being implemented in Vienna by integrating seven QKD-link devices that connect five subsidiaries of Siemens Austria. We give an architectural overview of the network and present the enabling QKD technologies, as well as the novel QKD network protocols.
91 citations
TL;DR: Using W state, which is much more robust than GHZ state, the efficient quantum circuit is constructed to implement the QSDC by means of primitive operations in quantum computation.
Abstract: Utilizing W state, which is much more robust than GHZ state, we propose a protocol for three-party controlled quantum secure direct communication (QSDC). The feature of this protocol is that the sender encodes the secret message directly on a sequence of particle states and faithfully transmits them to an arbitrary one of two receivers without revealing any information to a potential eavesdropper. On the other hand, we construct the efficient quantum circuit to implement the QSDC by means of primitive operations in quantum computation.
84 citations
TL;DR: A novel controlled quantum secure direct communication (QSDC) with quantum encryption under the supervision and help of the third side, the sender and the receiver can securely share the private quantum entanglement keys used to encrypt and decrypt the secret message.
Abstract: Utilizing a partially entangled GHZ state, we propose a novel controlled quantum secure direct communication (QSDC) with quantum encryption. Under the supervision and help of the third side, the sender and the receiver can securely share the private quantum entanglement keys used to encrypt and decrypt the secret message. According to the results of checking the eavesdropping on decoy photons, communicators can decide whether the quantum keys are reused in the next round. Not only will eavesdropping inevitably disturb the states of the decoy photons and be detected, but arbitrary transmission errors can also be corrected.
73 citations
TL;DR: This paper presents a QKD protocol with classical Alice and proves that this protocol is completely robust against any eavesdropping attack and presents the amount of tolerable noise against Eve's individual attack.
Abstract: It seems that quantum key distribution (QKD) may be completely insecure when the message sender Alice always encodes her key bits in a fixed basis. In this paper, we present a QKD protocol with classical Alice, i.e. Alice always encodes her key bit in the {|0>, |1>} basis (we call it classical {0,1} basis) and the eavesdropper Eve knows this fact. We prove that our protocol is completely robust against any eavesdropping attack and present the amount of tolerable noise against Eve's individual attack. Next, we present a QKD protocol to demonstrate that secure key bits can be distributed even if neither Alice nor Bob has quantum capacities, and extend this idea to a QKD network protocol with numerous parties who have only classical capacities. Finally, we discuss that quantum is necessary in QKD for security reasons, but both Alice and Bob may be classical.
70 citations
TL;DR: In this paper, Barenco, Bennett, Cleve, Di Vincenzo, Margolus and Shor extended their calculation and gave two analytic expressions for the construction of general n-qubit controlled unitary gates in terms of one qubit and two qubit CNOT gates.
Abstract: General n-qubit controlled unitary gates are frequently used in quantum information processing tasks. Barenco, Bennett, Cleve, Di Vincenzo, Margolus and Shor [Phys. Rev. A52 (1995) 3457] have given the general construction methods, and explicit results for up-to-four-qubits controlled unitary gates. We extended their calculation and gave two analytic expressions for the construction of general n-qubit controlled unitary gates in terms of one-qubit and two-qubit CNOT gates. There are two expressions – one is exponential in the qubit number which is efficient for up to ten qubits, and the other is polynomial in the qubit number, which is efficient for more than ten qubits.
65 citations
TL;DR: The quantum adiabatic algorithm is a Hamiltonian-based quantum algorithm designed to find the minimum of a classical cost function whose domain has size N as mentioned in this paper, and it is shown that poor choices for the Hamiltonian can guarantee that the algorithm will not reach the minimum if the run time grows more slowly than.
Abstract: The quantum adiabatic algorithm is a Hamiltonian based quantum algorithm designed to find the minimum of a classical cost function whose domain has size N. We show that poor choices for the Hamiltonian can guarantee that the algorithm will not find the minimum if the run time grows more slowly than . These poor choices are nonlocal and wash out any structure in the cost function to be minimized, and the best that can be hoped for is Grover speedup. These failures tell us what not to do when designing quantum adiabatic algorithms.
64 citations
TL;DR: In this article, the entanglement of superposition of multi-state states is investigated in three cases when the states in the superposition are mutually biorthogonal, mutually orthogonal and non-orthogonal.
Abstract: In this letter, we investigate the entanglement of superposition of multi-states. Three cases are considered when the states in the superposition are mutually biorthogonal, mutually orthogonal and nonorthogonal. The relations between the entanglement of superposition and the entanglements of the superposed states are explored.
61 citations
TL;DR: It is shown that any M ≥ 2 distant parties who independently share the complete classical knowledge of a secret qubit state can collectively prepare the state at another remote location.
Abstract: We show that any M ≥ 2 distant parties who independently share the complete classical knowledge of a secret qubit state can collectively prepare the state at another remote location. Two distinct schemes for such a task are proposed: one via a single (M + 1)-partite GHZ-type state and the other via M EPR-type pairs. Analytical expressions of the total success probability are derived explicitly for both the schemes. Of interest is the M-dependence of both the success probability and the receiver's action. We also construct simple quantum circuits for the two-qubit operators whose execution is necessary to accomplish the schemes.
TL;DR: It is shown that it is possible to achieve unity fidelity remote preparation of the polarization state using optical elements and this protocol may be used for converging the split information at one point.
Abstract: We present a linear optical protocol for multiparty remote state preparation (MRSP) in terms of optical elements. MRPS is a procedure for multiparty collaboration with each other to remote preparation of a known quantum state to a distant party. We show that it is possible to achieve unity fidelity remote preparation of the polarization state using optical elements. This protocol may be used for converging the split information at one point.
TL;DR: In this paper, it was shown that whether the behavior of a particle is quantum or classical depends on three factors: the initial qubit, the number of coins M, d = [t/M], where t is time step.
Abstract: We obtain some rigorous results on limit theorems for quantum walks driven by many coins introduced by Brun et al. in the long time limit. The results imply that whether the behavior of a particle is quantum or classical depends on the three factors: the initial qubit, the number of coins M, d = [t/M], where t is time step. Our main theorem shows that we can see a transition from classical behavior to quantum one for a class of three factors.
TL;DR: A sound and complete axiomatization of QCTL is given and the standard CTL model-checking algorithm with the dEQPL model- checking algorithm is combined to obtain a model- Checking algorithm for QCTl.
Abstract: Logics for reasoning about quantum states and their evolution have been given in the literature In this paper, we consider quantum computation tree logic (QCTL), which adds temporal modalities to exogenous quantum propositional logic We give a sound and complete axiomatization of QCTL and combine the standard CTL model-checking algorithm with the dEQPL model-checking algorithm to obtain a model-checking algorithm for QCTL Finally, we illustrate the use of the logic by reasoning about the BB84 key distribution protocol
TL;DR: In this paper, the authors presented a scheme of remote preparation of the two-particle state by using two Einstein-Podolsky-Rosen pairs or two partially entangled twoparticle states as the quantum channel.
Abstract: We present a scheme of remote preparation of the two-particle state by using two Einstein–Podolsky–Rosen pairs or two partially entangled two-particle states as the quantum channel. The probability of the successful remote state preparation is obtained.
TL;DR: It is shown that the probability of success can be used to determine characteristics of quantum channels and the game deserves more careful study aiming at its implementation.
Abstract: In the article we analyse how noisiness of quantum channels can influence the magic squares quantum pseudo-telepathy game. We show that the probability of success can be used to determine characteristics of quantum channels. Therefore the game deserves more careful study aiming at its implementation.
TL;DR: In this article, D'Alessandro et al. introduced the first mathematician-written textbook on the subject of quantum control, focusing on the applications of Lie algebra and Lie group theory in quantum control.
Abstract: With the importance of quantum information science being widely recognized, introductory textbooks on quantum control will be required by many students from diversified backgrounds. Intended for undergraduate and beginning graduate students in mathematics, engineering, and physics, this book by Dr. D'Alessandro is the first mathematician-written textbook on the subject of quantum control. Representative quantum control problems from various contexts are introduced with clarity and strictness. Emphasis is placed on the applications of Lie algebra and Lie group theory in quantum control.
TL;DR: Jafarizadeh and Salimi as discussed by the authors studied the continuous-time quantum walk on Cayley graphs and showed that the quantum walk can be reduced to a subspace that is considerably smaller than the original one.
Abstract: In the present paper, we study the continuous-time quantum walk on quotient graphs. On such graphs, there is a straightforward reduction of the problem to a subspace that can be considerably smaller than the original one. Along the lines of reductions, by using the idea of calculation of the probability amplitudes for continuous-time quantum walk in terms of the spectral distribution associated with the adjacency matrix of graphs [Jafarizadeh and Salimi (Ann. Phys.322 (2007))], we show that the continuous-time quantum walk on original graph Γ induces a continuous-time quantum walk on quotient graph ΓH. Finally, for example, we investigate the continuous-time quantum walk on some quotient Cayley graphs.
TL;DR: A scheme for splitting a two-qubit quantum information by using two asymmetric W states as quantum channel that finds that for some states the SSP can reach 0.5 or even unity after consuming a little additional classical resource.
Abstract: We propose a scheme for splitting a two-qubit quantum information by using two asymmetric W states as quantum channel In this scheme the split state is assumed to be completely known by the sender Because of this, during the splitting process, the sender only needs to perform a two-qubit projective measurement Once the sender announces the measurement result in terms of the prior agreement, then using this message the two receivers can recover the quantum information via their mutual assistance We calculate the success probability and classical communication cost of the scheme In general, the splitting success probability (SSP) is 1/4 and the average classical communication cost is 025 bit However, we find that for some states the SSP can reach 05 or even unity after consuming a little additional classical resource
TL;DR: In this article, the role played by entanglement in the dynamical evolution of composite fermionic systems is explored, and two different applications of free spin fermions in a four site cluster are studied.
Abstract: The time that a given initial quantum state requires to evolve to an orthogonal state is used to explore the role played by entanglement in the dynamical evolution of composite fermionic systems. We study two different applications of free spin fermions in a four site cluster. It is shown that through selection of the hopping matrix elements, the relationship between entanglement and speed of quantum evolution can be controlled. Consequently, the result recently pointed out [J. Batle et al., Phys. Rev. A72 (2005) 032337] represents only a particular choice of the energy spectrum of the system.
TL;DR: In this article, the authors calculate the geometric phase of spin-boson and spin-spin models in the non-unitary regime and propose a model with slow decoherence rate.
Abstract: We calculate the geometric phase for different open systems (spin-boson and spin-spin models). We study not only how they are corrected by the presence of the different type of environments but also discuss the appearence of decoherence effects. These should be taken into account when planning experimental setups to study the geometric phase in the nonunitary regime. We propose a model with slow decoherence rate in which the geometric phase is still modified and might be measured.
TL;DR: In this article, the quantum Jensen Shannon divergence (QJSD) between quantum states is used as a geometrical measure of entanglement and applied to different families of states.
Abstract: The notion of distance in Hilbert space is relevant in many scenarios. In particular, "distances" between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon divergence (QJSD) between quantum states. Here we study this distance as a geometrical measure of entanglement and apply it to different families of states.
TL;DR: The first protocol of multiparty quantum secret sharing of secure direct communication is generalized to the high-dimensional case via quantum superdense coding and has the advantages of higher capacity and better security.
Abstract: The first protocol of multiparty quantum secret sharing of secure direct communication [Phys. Lett. A342 (2005) 60] is generalized to the high-dimensional case via quantum superdense coding. The generalized protocol has the advantages of higher capacity and better security.
TL;DR: In this article, the authors considered the effect of decoherence on teleportation fidelity and showed that the minimum assured fidelity (MAF) is still nonzero for any arbitrary information, except for the case when the information is in even coherent state.
Abstract: We consider the scheme proposed by Wang [Phys. Rev. A64 (2001) 022302] for teleporting bipartite entangled states, which is a superposition of coherent states |α,α〉 and |-α,-α〉, with our suggested modification [Phys. Rev. A75 (2007) 044305] and discuss the effect of decoherence on teleportation fidelity. We find that if no photons are counted in both final outputs, the minimum assured fidelity (MAF), which is the minimum of the fidelity for any arbitrary information), is still nonzero except for the case when there is no decoherence and the information is in even coherent state. For non-zero photon counts, MAF decreases with increase in |α|2 for low noise but in the case of high noise, it increases, attains a maximum value and then decreases with |α|2. We discuss the variation of average fidelity with |α|2 and show that it depends appreciably on the information for low values of |α|2 only.
TL;DR: It is shown that Bob can obtain the unknown state with probability 1/4 for maximally entangled state, however, for four kinds of special states, the success probability of preparation can be enhanced to unity.
Abstract: By means of the method of the positive operator-valued measure, two schemes to remotely prepare an arbitrary two-particle entangled state were presented. The first scheme uses a one-dimensional four-particle non-maximally entangled cluster state while the second one uses two partially entangled two-particle states as the quantum channel. For both schemes, if Alice performs two-particle projective measurements and Bob adopts positive operator-valued measure, the remote state preparation can be successfully realized with certain probability. The success probability of the remote state preparation and classical communication cost are calculated. It is shown that Bob can obtain the unknown state with probability 1/4 for maximally entangled state. However, for four kinds of special states, the success probability of preparation can be enhanced to unity.
TL;DR: An explicit scheme for probabilistically teleporting an arbitrary two-qu bit state is proposed by using a one-dimensional four-qubit cluster-class state as the quantum channel.
Abstract: An explicit scheme for probabilistically teleporting an arbitrary two-qubit state is proposed by using a one-dimensional four-qubit cluster-class state as the quantum channel. In the scheme, the sender first performs two Bell state measurements (BSMs). Then with the sender's help, the receiver can reconstruct the original state probabilistically by introducing an auxiliary qubit and making appropriate unitary operations. Moreover, the total success probability and classical communication cost of the present scheme are also calculated.
TL;DR: A new quantum algorithm for solving the minimum searching problem that has the same order of time and space complexities as the algorithm proposed by Durr and Hoyer, but it provides a quadratic reduction in the number of measurements.
Abstract: In this paper, we propose a new quantum algorithm for solving the minimum searching problem. This algorithm has the same order of time and space complexities as the algorithm proposed by Durr and Hoyer, but it provides a quadratic reduction in the number of measurements. In addition to the correctness and complexity analysis of the algorithm, we present simulation results considering an NP-hard problem.
TL;DR: The only known family of graphs whose quantum walk instantaneously mixes to uniform is the Hamming graphs with small arities as discussed by the authors, which is the class of graphs H(n,q) is not uniform mixing if and only if q ≥ 5.
Abstract: We study continuous-time quantum walks on graphs which generalize the hypercube. The only known family of graphs whose quantum walk instantaneously mixes to uniform is the Hamming graphs with small arities. We show that quantum uniform mixing on the hypercube is robust under the addition of perfect matchings but not much else. Our specific results include: • The graph obtained by augmenting the hypercube with an additive matching x ↦ x ⊕ η is instantaneous uniform mixing whenever |η| is even, but with a slower mixing time. This strictly includes the result of Moore and Russell1 on the hypercube. • The class of Hamming graphs H(n,q) is not uniform mixing if and only if q ≥ 5. This is a tight characterization of quantum uniform mixing on Hamming graphs; previously, only the status of H(n,q) with q < 5 was known. • The bunkbed graph whose adjacency matrix is I ⊗ Qn + X ⊗ Af, where Af is a -circulant matrix defined by a Boolean function f, is not uniform mixing if the Fourier transform of f has support of size smaller than 2n-1. This explains why the hypercube is uniform mixing and why the join of two hypercubes is not. Our work exploits the rich spectral structure of the generalized hypercubes and relies heavily on Fourier analysis of group-circulants.
TL;DR: In this paper, the channel capacity of the 4-qubit 4-term cluster state (i.e. (|0000〉 + |0011〉+ |1100〉 - |1111〉)/2) for bipartite quantum information splitting was investigated.
Abstract: In this paper, we explore the channel capacity of the 4-qubit 4-term cluster state (i.e. (|0000〉 + |0011〉 + |1100〉 - |1111〉)/2) for splitting arbitrary two-qubit quantum information. After our extensive investigations, we found that 4 out of 12 possible distributions of the 4 qubits can be utilized to realize bipartite splitting. In terms of each distribution, the corresponding splitting scheme is presented and LOCCs (local operation and classical communication) are explicitly given.