Abstract: We investigate a space-inhomogeneous discrete-time quantum walk in one dimension. We show that the walk exhibits localization by a path counting method.

Abstract: A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results and present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling correlations. This includes an alternative simpler proof of the Toner-Verstraete monogamy inequality for quantum correlations, as well as a strengthening thereof. Further, the relationship between sharing non-local quantum correlations and sharing mixed entangled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial. Also, a recently proposed new interpretation of Bell's theorem by Schumacher in terms of shareability of correlations is critically assessed. Finally, the relevance of monogamy of non-local correlations for secure quantum key distribution is pointed out, and in this regard it is stressed that not all non-local correlations are monogamous.

Abstract: Quantum computing offers new concepts for the simulation of complex physical systems A quantum computing algorithm for electromagnetic field simulation is presented here The electromagnetic field simulation is performed on the basis of the Transmission Line Matrix (TLM) method The Hilbert space formulation of TLM allows us to obtain a time evolution operator for the TLM method, which can then be interpreted as the time evolution operator of a quantum system, thus yielding a quantum computing algorithm Further, the quantum simulation is done within the framework of the quantum circuit model of computation Our aim has been to address the design problem in electromagnetics--given an initial condition and a final field distribution, find the structures which satisfy these Quantum computing offers us the possibility to solve this problem from first principles Using quantum parallelism we simulate a large number of electromagnetic structures in parallel in time and then try to filter out the ones which have the required field distribution

Abstract: The utility of a five-qubit entangled state for quantum teleportation, quantum state sharing and superdense coding is investigated. The state can be utilized for perfect teleportation and quantum state sharing of an arbitrary single- and two-qubit state. The capacity of superdense coding of the state reaches the "Holevo bound", which means that five classical bits can be transmitted by sending three qubits. The preparation of the five-qubit state and detection of the multipartite states in cavity QED are discussed. The distinct advantage of the feasible cavity QED technology that we use is insensitive to the thermal field and the cavity decay.

Abstract: The crucial issue of quantum communication protocol is its security. In this paper, the security of a secure direct communication based on ping-pong protocol [Chamoli A, Bhandari CM, Quantum Inf Process 8, 347 (2009)] is analyzed. It is shown that in this protocol any dishonest party can obtain all the other one's secret message with zero risk of being detected by using a special type of attack, i.e., using fake entangled particles (FEP attack). Finally, a simple improvement to resist this attack is proposed.

Abstract: We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and they are not restricted to possess the Calderbank---Shor---Steane structure as in previous work. We provide two significant advances for quantum convolutional coding theory. We first show how to "expand" a given set of quantum convolutional generators. This expansion step acts as a preprocessor for a polynomial symplectic Gram---Schmidt orthogonalization procedure that simplifies the commutation relations of the expanded generators to be the same as those of entangled Bell states (ebits) and ancilla qubits. The above two steps produce a set of generators with equivalent error-correcting properties to those of the original generators. We then demonstrate how to perform online encoding and decoding for a stream of information qubits, halves of ebits, and ancilla qubits. The upshot of our theory is that the quantum code designer can engineer quantum convolutional codes with desirable error-correcting properties without having to worry about the commutation relations of these generators.

Abstract: We show how to convert an arbitrary stabilizer code into a bipartite quantum code. A bipartite quantum code is one that involves two senders and one receiver. The two senders exploit both nonlocal and local quantum resources to encode quantum information with local encoding circuits. They transmit their encoded quantum data to a single receiver who then decodes the transmitted quantum information. The nonlocal resources in a bipartite code are ebits and nonlocal information qubits, and the local resources are ancillas and local information qubits. The technique of bipartite quantum error correction is useful in both the quantum communication scenario described above and in fault-tolerant quantum computation. It has application in fault-tolerant quantum computation because we can prepare nonlocal resources offline and exploit local encoding circuits. In particular, we derive an encoding circuit for a bipartite version of the Steane code that is local and additionally requires only nearest-neighbor interactions. We have simulated this encoding in the CNOT extended rectangle with a publicly available fault-tolerant simulation software. The result is that there is an improvement in the "pseudothreshold" with respect to the baseline Steane code, under the assumption that quantum memory errors occur less frequently than quantum gate errors.

Abstract: We introduce finite-level concatenation threshold regions for quantum fault tolerance. These volume thresholds are regions in an error probability manifold that allow for the implemented system dynamics to satisfy a prescribed implementation inaccuracy bound at a given level of quantum error correction concatenation. Satisfying this condition constitutes our fundamental definition of fault tolerance. The prescribed bound provides a halting condition identifying the attainment of fault tolerance that allows for the determination of the optimum choice of quantum error correction code(s) and number of concatenation levels. Our method is constructed to apply to finite levels of concatenation, does not require that error proabilities consistently decrease from one concatenation level to the next, and allows for analysis, without approximations, of physical systems characterized by non-equiprobable distributions of qubit error probabilities. We demonstrate the utility of this method via a general error model.

Abstract: We study the effect of quantum memory in magic squares game when played in quantum domain. We consider different noisy quantum channels and analyze their influence on the magic squares quantum pseudo-telepathy game. We show that the probability of success can be used to distinguish the quantum channels. It is seen that the mean success probability decreases with increase of quantum noise. Where as the mean success probability increases with increase of quantum memory. It is also seen that the behaviour of amplitude damping and phase damping channels is similar. On the other hand, the behaviour of depolarizing channel is similar to the flipping channels. Therefore, the probability of success of the game can be used to distinguish the quantum channels.

Abstract: NMR quantum information processing studies rely on the reconstruction of the density matrix representing the so-called pseudo-pure states (PPS). An initially pure part of a PPS state undergoes unitary and non-unitary (relaxation) transformations during a computation process, causing a “loss of purity” until the equilibrium is reached. Besides, upon relaxation, the nuclear polarization varies in time, a fact which must be taken into account when comparing density matrices at different instants. Attempting to use time-fixed normalization procedures when relaxation is present, leads to various anomalies on matrices populations. On this paper we propose a method which takes into account the time-dependence of the normalization factor. From a generic form for the deviation density matrix an expression for the relaxing initial pure state is deduced. The method is exemplified with an experiment of relaxation of the concurrence of a pseudo-entangled state, which exhibits the phenomenon of sudden death, and the relaxation of the Wigner function of a pseudo-cat state.

Abstract: Binary superposed decision diagrams (BSQDDs) are a new type of quantum decision diagram that can be used for representing arbitrary quantum superpositions. One major advantage of BSQDDs is that they are dependent on the types of gates used in synthesis and a BSQDD can be used to efficiently generate a quantum array that will initialize the quantum superposition that the BSQDD represents. Transformation rules for BSQDDs allow BSQDDs to be reduced into simpler BSQDDs that represent the same quantum superposition. Canonical forms exist for a broad class of BSQDDs. This allows BSQDDs to be used for synthesizing quantum arrays that are capable of initializing arbitrary quantum superpositions.

Abstract: The score operators of a quantum system are the symmetric logarithmic derivatives of the system's parametrically defined quantum state. Score operators are central to the calculation of the quantum Fisher information (QFI) associated with the state of the system, and the QFI determines the maximum precision with which the state parameters can be estimated. We give a simple, explicit expression for score operators of a qubit and apply this expression in a series of settings. We treat in detail the task of identifying a quantum Pauli channel from the state of its qubit output, and we show that a "balanced" probe state is highly robust for this purpose. The QFI for this task is a matrix, and we study its determinant, for which we establish a Cramer-Rao inequality.

Abstract: The quantum information transfer between a single photon and a two-level atom is considered as a part of a quantum channel. The channel is a degradable channel even when there are decays of the atomic excited state and the single photon state, as far as the total excitation of the combined initial state does not exceed one. The single letter formula for quantum capacity is obtained.

Abstract: Generalisation of the quantum weakest precondition result of D'Hondt and Panangaden is presented. In particular the most general notion of quantum predicate as positive operator valued measure (termed POVM) is introduced. The previously known quantum weakest precondition result has been extended to cover the case of POVM playing the role of a quantum predicate. Additionally, our result is valid in infinite dimension case and also holds for a quantum programs defined as a positive but not necessary completely positive transformations of a quantum states.

Abstract: Motivated by the fast Pauli block transforms (or matrices) over the finite field GF(q) for an arbitrary number q, we suggest how to construct the simplified quantum code on the basis of quadratic residues. The present quantum code, which is the stabilizer quantum code, can be fast generated from an Abelian group with commutative quantum operators being selected from a suitable Pauli block matrix. This construction does not require the dual-containing or self-orthogonal constraint for the standard quantum error-correction code, thus allowing us to construct a quantum code with much efficiency.

Abstract: We design an adiabatic quantum algorithm for the counting problem, i.e., approximating the proportion, ?, of the marked items in a given database. As the quantum system undergoes a designed cyclic adiabatic evolution, it acquires a Berry phase 2??. By estimating the Berry phase, we can approximate ?, and solve the problem. For an error bound $${\epsilon}$$ , the algorithm can solve the problem with cost of order $${(\frac{1}{\epsilon})^{3/2}}$$ , which is not as good as the optimal algorithm in the quantum circuit model, but better than the classical random algorithm. Moreover, since the Berry phase is a purely geometric feature, the result may be robust to decoherence and resilient to certain noise.

Abstract: `Correlations without correlata' is an influential way of thinking of quantum entanglement as a form primitive correlation which nonetheless maintains locality of quantum theory. A number of arguments have sought to suggest that such a view leads either to internal inconsistency or to conflict with the empirical predictions of quantum mechanics. Here we explicate and provide a partial defence of the notion, arguing that these objections import unwarranted conceptions of correlation properties as hidden variables. A more plausible account sees the properties in terms of Everettian relative states. The ontological robustness of entanglement is also defended from recent objections.

Abstract: We calculate the zeros of an exponential polynomial of some variables by a classical algorithm and quantum algorithms which are based on the method of van Dam and Shparlinski, they treated the case of two variables, and compare with the time complexity of those cases. Further we consider the ratio (classical/quantum) of the exponent in the time complexity. Then we can observe the ratio is virtually 2 when the number of the variables is sufficiently large.

Abstract: Prior versions of the article published on non-commercial pre-print servers like arXiv.org can remain on these servers and/or can be updated with the authors accepted version. The final published version (in PDF or HTML/XML format) cannot be used for this purpose. Acknowledgement needs to be given to the final publication and a link should be inserted to the published article on Springers website, accompanied by the text The final publication is available at www.springerlink.com. This book promotes information as the core concept underlying a proper appreciation of quantum theory. Given this, it is ironic that the authors’ perpetuate, on page 2, one of the great myths in information transmission: that Paul Revere cried, on his midnight ride of 18th April 1775, “the British are coming!” This historical slip aside, choosing such a dramatic illustration of the nature of information — a message (that the Regulars were staying put in Boston, that they were marching down the Neck, or that they were crossing the harbour by boat) that can be encoded into a signal (zero, one, or two lamps hung in a Boston church steeple), and that it can be transformed (into the thoughts and actions of Revere and others that night) – is an inspired start to an inspiring book. Schumacher and Westmoreland are both eminent researchers in quantum information theory. The former has the distinction of having coined the term qubit [2] (only 15 years ago!) in the same paper that introduced quantum data compression. This book however is not a research monograph in quantum information. Rather it is, as the authors say, “designed to be both an undergraduate textbook on quantum mechanics H. M. Wiseman Centre for Quantum Computer Technology Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111 Australia E-mail: h.wiseman@griffith.edu.au 1 The American colonists at this time still considered themselves to be British. According to eyewitness accounts of the ride and Revere’s own descriptions, his cry was “The Regulars are coming out.” [1]

Abstract: We consider classical and entanglement-assisted versions of a distributed computation scheme that computes nonlinear Boolean functions of a set of input bits supplied by separated parties. Communication between the parties is restricted to take place through a specific apparatus which enforces the constraints that all nonlinear, nonlocal classical logic is performed by a single receiver, and that all communication occurs through a limited number of one-bit channels. In the entanglement-assisted version, the number of channels required to compute a Boolean function of fixed nonlinearity can become exponentially smaller than in the classical version. We demonstrate this exponential enhancement for the problem of distributed integer addition.

Abstract: The canonical decomposition for two-qubit operators has proven very useful for applications in quantum computing. This decomposition generates equivalence classes up to local quantum gates. We provide a variety of complete, explicit decompositions of given two-qubit operators in terms of single, double, and triple controlled-NOT (CNOT) gates. By analytically addressing the needed pre- and post-tensor product factors, we demonstrate that exact results are possible, even when a parameter is included. The examples given are of interest to superconducting qubit, spin-based, dipolar molecule, and other quantum information processing systems.

Abstract: Quantum error-correction code (QECC), an important issue in quantum information processing as well as in quantum communication, has demonstrated a formal possibility of storing and manipulating quantum data in the presence of noise [1]. Recently, several types ofQECCshave been developed and investigated [2–8].As these codes are mostly based on the stabilizer formalism, awell-designed structure should be involved. Usually, this code is called the stabilizer quantum code because of the stabilizer’s involvement. However, the fixed structure of the stabilizer is usually inconvenient when considering constructions of long-length quantum codes with fast algorithms.

Abstract: As quantum parallelism allows the effective co-representation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose eigenvalues are different from one.

Abstract: In this paper we define a family of hermitian operators by which to extract what we call quantum-relative-phase properties of a pure or mixed multipartite quantum state, and we relate these properties to known measures of entanglement, namely the m-tangle and the invariant $${S_{(m)}^2}$$ of the multi-local Lorentz-group $${SL(2, \mathbb{C})^{\otimes m}}$$ . Our construction is based on the orthogonal complement of a positive operator valued measure on quantum phase.

Abstract: Although it has been mainly during the last 15years that the number of scientific investigationsrelatingtoquantuminformationhasbecomegreatenoughthatQuantum Information Science (QIS) could be identified as a distinct field of research encompassing quantum computing and cryptography, its roots can be seen as extending back to the early decades of quantum theory itself. That is, QIS can be viewed as resulting from the on-going study of fundamental questions in quantum mechanics, now often referred to as simply Quantum Foundations. It relates mechanics and information in the microscopic realm, offering new insights by connecting the concepts and constraints of communications theory to information theory in a way that provides new methods for probing the elements of fundamental mechanics. It is to such probing of the implications of quantum correlations, measurements, and information theory that this Special Issue of Quantum Information Processing is devoted, focusing on foundational ones. Despite a tremendous increase in activity surrounding the technological aspects of quantum information and entanglement, which is to say surrounding applications of the qubit and the e-bit in communication and information processing, foundational issues relating to quantum correlation, measurement, and information theory remain in need of further clarification and development (cf., e.g. [1]). This is evident here, for example, in the contribution of Mauro D’Ariano and Alessandro Tosini, who consider tests of postulates of the “fair operational framework” in which quantum mechanics is understood as a set of rules allowing experimenters to predict the results of future measurement events that can be used toyieldinformation on thebasis of suitabletests,

Abstract: Zero-knowledge proof system is an important protocol that can be used as a basic block for construction of other more complex cryptographic protocols. An intrinsic characteristic of a zero-knowledge systems is the assumption that is impossible for the verifier to show to a third party that he has interacted with the prover. However, it has been shown that using quantum correlations the impossibility of transferring proofs can be successfully attacked. In this work we show two new protocols for proof transference, being the first one based on teleportation and the second one without using entangled states. In this last case, we assume that the third party can communicate in advance with both verifier and prover. Following, we present a quantum zero-knowledge protocol based on quantum bit commitment that can be implemented with today technology.

Abstract: New quantum distance is introduced as a half-sum of several singular values of difference between two density operators. This is, up to factor, the metric induced by so-called Ky Fan norm. The partitioned trace distances enjoy similar properties to the standard trace distance, including the unitary invariance, the strong convexity and the close relations to the classical distances. The partitioned distances cannot increase under quantum operations of certain kind including bistochastic maps. All the basic properties are re-formulated as majorization relations. Possible applications to quantum information processing are briefly discussed.

Abstract: We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical transport processes on graphs, and calculate the spacetime transition probabilities between two vertices of the lattice. Then we analytically show that there are two power law decays ~ t ?3 and ~ t ?1.5 at the beginning of the transport for transition probability in the continuous-time quantum and classical random walk, respectively. This results illustrate the decay of quantum mechanical transport processes is quicker than that of the classical one. Due to the result, the characteristic time t c , which is the time when the first maximum of the probabilities occur on an infinite graph, for the quantum walk is shorter than that of the classical walk. Therefore, we can interpret that the quantum transport speed on spidernet is faster than that of the classical one. In the end, we investigate the results by numerical analysis for two examples.

Abstract: Two quantum events, represented by positive operators (effects), are coexistent if they can occur as possible outcomes in a single measurement scheme. Equivalently, the corresponding effects are coexistent if and only if they are contained in the ranges of a single (joint) observable. Here we give several equivalent characterizations of coexistent pairs of qubit effects. We also establish the equivalence between our results and those obtained independently by other authors. Our approach makes explicit use of the Minkowski space geometry inherent in the four-dimensional real vector space of selfadjoint operators in a two-dimensional complex Hilbert space.