International Journal of Quantum Information

Some aspects of replacing C based physics by C_n based physics are discussed. Here C_n=R_n,I_n, where R_n (and I_n) is a set of length 2n string numbers in some basis. The discussion is limited to describing the experimental basis and choice for the numbers in R_n, and a few basic but interesting properties of R_n based space and time.

The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence α is identified with a quantum information quantity, represented by a density operator of a Hilbert space, whose dimension depends on the logical complexity of α. At the same time, the logical connectives of the language are interpreted as operations defined in terms of quantum logical gates. Standard quantum computational models can be described as special cases of Fock space models, where the meaning of any sentence is localized in a precise sector of a Fock space ℱ. From an intuitive point of view, the increasing number of particles described in the different sectors of ℱ can be interpreted as increasing information.

The "new orthodoxy" of quantum mechanics (QM) based on the decoherence approach requires many-worlds as an essential ingredient for logical consistency, and one may wonder what status to give to all these "other worlds." Here we advocate that it is possible to build a consistent approach to QM where no other worlds are needed, and where the quantum formalism appears as a consequence of requiring the enumerability of physical properties. Such a quantization hypothesis is closely related to indistinguishability, and is deeply inconsistent with classical physics.

Quantum search is a quantum mechanical technique for searching N possibilities in only steps. This has been proved to be the best possible algorithm for the exhaustive search problem in the sense that the number of queries it requires cannot be reduced. However, as this paper shows, the number of non-query operations can be reduced by a third without a single increase in the number of queries.

Quantum complexity theory is a powerful tool that provides deep insights into Quantum Information Processing (QIP) and aims to do that also for Quantum Mechanics (QM), in general. This paper is a short review of the main and new motivations, goals, tools, results and challenges of quantum complexity, oriented mainly for pedestrians.

In this survey paper we discuss the relation between the minimal output entropy and the χ-capacity for irreducibly covariant quantum channels implying equivalence of the additivity property for both quantities for such channels. The structure of the Weyl-covariant channels is described in detail.

If quantum computing is located somewhere between physics and theoretical computing, a basic question concerns which characteristic features are derived from the latter. From a logical point of view, the concept of computation provides a definition of the natural process of calculare. It rests on trust that a procedure of reason can be reproduced mechanically. Turing argues for the adequacy of the concept by introducing a requirement of "observability," which is expressed through finiteness and locality conditions. However, according to the uncertainty principle, no computational path can be observed. How does quantum computing contend with Turing's constraints? What observables are relevant to the computation? This is an attempt to sharpen such questions.

We review the problem of optimal estimation of multiple phases for systems with arbitrary finite dimension and derive the optimal estimation fidelity for equatorial states. We present optimal phase covariant cloning transformations for d-dimensional systems, relating these results to the optimal estimation procedure.

The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFTs). The key tool is provided by the fiber space structure underlying the model which exhibits combinatorial properties closely related to SU(2) state sum models, widely employed in discretizing TQFTs and quantum gravity in low spacetime dimensions.

Entanglement swapping is a fascinating generalization of quantum teleportation, where the entanglement between pairs is interchanged leading to entanglement between particles that never interacted. Extending the idea of Peres, we propose an experimental setup where the choice which quantum systems are finally entangled is made at a time after they have been registered and do not even exist anymore. Our proposed setup can be used in Third-Man Quantum Cryptography where a third party can control whether Alice and Bob are able to communicate secretly, but he does know their secret key.

We use fuzzy logic for the probabilistic interpretation of statistical ensemble and compare the result with the density matrix results for quantum entanglement.

Using spatial entanglement of two particles the rate of classical information gain has been increased by a logarithmic factor depending on the dimension of Hilbert space. To study Bell state measurement (BSM) of the two particles, at first, we have defined corresponding Bell bases in a typically general form. Then, the basic position gates are theoretically designed by side quantum channels and the usual CNOT gate. All the processes required in the BSM can be established based upon the introduced local and conditional basic gates.

Signal processing techniques will lean on blind methods in the near future, where no redundant, resource allocating information will be transmitted through the channel. To achieve a proper decision, however, it is essential to know at least the probability density function (PDF), which to estimate is classically a time consumpting and/or less accurate hard task that may make decisions to fail. This paper describes the design of a quantum assisted PDF estimation method also by way of an example, which promises to achieve the exact PDF by proper setting of parameters in a very rapid way.

The nature of quantum entropies, and its use in Quantum Information Theory in the form of (i) total entropy, (ii) relative entropy and (iii) conditional entropy is revisited. In this ordering, we first show the correlations existing between the total q-entropy and entanglement, quantified in the form of entanglement of formation. Then, we revisit the use of the quantum relative entropy as a measure of entanglement, and we finally discuss some features of the quantum conditional q-entropies, which are used in turn as a separability criterion.

We consider the logical assertions of a hypothetical observer who is inside a quantum computer and performs a reversible quantum measurement, obtaining a symmetric couple of new axioms, valid only inside the quantum computer. The result is that, in this logical framework, symmetry and paraconsistency hold.

The super-resolution effects obtained by monochromatic evanescent waves are related to many photon momentum cooperative effects reducing the propagation wavelength inversely proportional to the photon momentum number and increasing the resolution far beyond the Rayleigh criterion. The quantization of such monochromatic waves is made in momentum space using a special dispersion relation.

In this paper, we describe how it is possible to verify the quantum statistics of identical particles prepared in distinguishable internal states without ever bringing these particles to the same internal state. Examples are given for two, three and four identical particles prepared in two, three or four distinct states, respectively. We show that the identical nature of the particles can be probed through entanglement and their specific statistics can be probed by discriminating between types of entangled states.

In quantum communication, feedback may be defined in a number of distinct ways. An analysis of the effect feedback has on the rate information may be communicated is given, and a number of results and conjectures are stated.

A possible link between holography and information theory is presented. Using the relation between the Shannon and Boltzmann formulas, holography can be seen as the best encoding scheme.

We define a new kind of quantum channel capacity by extending the concept of zero-error capacity for a noisy quantum channel. The necessary requirement for which a quantum channel has zero-error capacity greater than zero is given. Finally, we point out some directions on how to calculate the zero-error capacity of such channels.

We present the architecture and recent experimental results for a quantum key distribution system realized at Elsag spa Quantum Optics Laboratory with a key distribution rate suitable for practical industrial applications. The current system can reliably distribute secure cryptographic keys at a rate of 1,500 bit per second and higher at a few hundred meters, with a quantum bit error rate lower than 1%.

By using the "subtracting projectors" method in proving the separability of PPT states on multiple quantum spaces, we derive a canonical form of PPT states in composite quantum systems with rank N, from which a sufficient separability condition for these states is presented.

The entropy at the output of a Bosonic channel is analyzed when coherent fields are randomly added to the signal. Coherent-state inputs are conjectured to provide the minimum output entropy. Supporting physical and mathematical evidence is provided.

In this paper we briefly define distance vector routing algorithms, their advantages and possible drawbacks. On these possible drawbacks, currently widely used methods split horizon and poisoned reverse are defined and compared. The count to infinity problem is specified and classified to be a halting problem, and a proposition stating that entangled states used in quantum computation can be used to handle this problem is examined. Several solutions to this problem by using entangled states are proposed and a very brief introduction to entangled states is presented.

Recent suggestions to supply quantum mechanics (QM) with realistic foundations by reformulating it in light of quantum information theory (QIT) are examined and are found wanting by pointing to a basic conceptual problem that QIT itself ignores, namely, the measurement problem. Since one cannot ignore the measurement problem and at the same time pretend to be a realist, as they stand, the suggestions to reformulate QM in light of QIT are nothing but instrumentalism in disguise.

Finding the extreme value of a database or a function plays an important role in computing and communication applications. Unfortunately, classical solutions suffer from computational complexity if the database is unsorted or, equivalently, the function has many local minimum/maximum points. Proposed quantum computing based solutions can guarantee success only in terms of the expected value of the database queries. In this paper we introduce a new technique exploiting the parallel processing capabilities of quantum computing in a different way. We derive quantum existence testing which allows adapting the classical logarithmic search algorithm suitable for structured databases to unstructured ones while maintaining its efficiency.

We give an update on a quantum adiabatic algorithm for the Turing noncomputable Hilbert's tenth problem, and briefly go over some relevant issues and misleading objections to the algorithm.

Correlated equilibria are sometimes more efficient than the Nash equilibria of a game without signals. We investigate whether the availability of quantum signals in the context of a classical strategic game may allow the players to achieve even greater efficiency than in any correlated equilibrium with classical signals, and find the answer to be positive.

We present a scheme for secure deterministic quantum communication without using entanglement, in a plug-and-play fashion. The protocol is completely deterministic, both in the encoding procedure and in the control one, thus doubling the communication rate with respect to other setups; moreover, the deterministic nature of transmission, apart from rendering unnecessary bases revelation on the public channel, allows the realization of protocols like 'direct communication' and 'quantum dialogue.' The encoding exploits the phase degree of freedom of a photon, thus paving the way for an optical fiber implementation, feasible with present-day technology.

We describe the package of functions useful for simulations of quantum algorithms and protocols. The presented package allows one to perform simulations with mixed states. We present numerical implementation of important quantum mechanical operations — partial trace and partial transpose. Those operations are used as building blocks of algorithms for analysis of entanglement and quantum error correction codes. A simulation of Shor's algorithm is presented as an example of package capabilities.

Particle statistics is a fundamental part of quantum physics, and yet its role and use in the context of quantum information have been poorly explored so far. After briefly introducing particle statistics and the Symmetrization Postulate, we argue that this fundamental aspect of nature can be seen as a resource for quantum information processing and present examples showing how it is possible to do useful and efficient quantum information processing using only the effects of particle statistics.

The effects of quantum error correction (QEC) on the dynamics of entanglement between logical qubits in the presence of a dephasing interaction with a correlated environment is investigated. Such a correlated reservoir introduces entanglement between physical qubits which, for short times, is interpreted as error and suppressed by the QEC routine. However for longer times, although QEC is no longer able to correct errors, it enhances the rate of entanglement production due to the interaction with the environment.

Entanglement transfer processes from a continuous-variable (CV) to a qubit system have primary importance in quantum information processing due to some practical implications in the realization of a quantum network. A CV system can propagate entanglement while a qubit system is easy to manipulate. We study conditions to entangle two atomic qubits with a two-mode squeezed field driving two cavities containing the atoms.

Quantum measurement is universal for quantum computation. The model of quantum computation introduced by Nielsen and further developed by Leung relies on a generalized form of teleportation. In order to simulate any n-qubit unitary transformation with this model, four auxiliary qubits are required. Moreover Leung exhibited a universal family of observables composed of one one-qubit measurement and four two-qubit measurements. We introduce a model of quantum computation via measurements only, relying on state transfer: state transfer only retains the part of teleportation which is necessary for computation. In order to simulate any n-qubit unitary transformation with this new model, only one auxiliary qubit is required. Moreover we exhibit a universal family of observables composed of three one-qubit measurements and only one two-qubit measurement. This model improves those of Nielsen and Leung in terms of both the number of auxiliary qubits and the number of two-qubit measurements required for quantum universality. In both cases, the minimal amounts of necessary resources are now reached: one auxiliary qubit (because measurement is destructive) and one two-qubit measurement (for creating entanglement).

In this work we review the security vulnerability of quantum cryptography with respect to "man-in-the-middle attacks" and the standard authentication methods applied to counteract these attacks. We further propose a modified authentication algorithm which features higher efficiency with respect to consumption of mutual secret bits.

Providing quantum theory, and thus quantum information, with some meaning, can only be the result of adopting a well-defined approach to the notion of probability. From a subjectivistic Bayesian approach to the latter, it follows that not only quantum states, but also quantum operations, are structural elements of a subjective nature. Furthermore, we provide a representation of any quantum operation as a stochastic matrix.

We investigate a game where a sender (Alice) teleports coherent states to two receivers (Bob and Charlie) through a tripartite Gaussian state. The aim of the receivers is to optimize their teleportation fidelities by means of local operations and classical communications. We show that a non-cooperative strategy corresponding to the standard telecloning protocol can be outperformed by a cooperative strategy which gives rise to a novel (cooperative) telecloning protocol.

Large optical nonlinearities occurring in a coherently prepared atomic system are shown to produce phase shifts of order π. Such an effect may be observed in ultracold rubidium atoms where it could be feasibly exploited toward the realization of a polarization phase gate.

This special issue gives us the chance to focus on meaningful interaction fields, which are not only possible, but also often necessary. Our aim is to point out many relevant similarities in our disciplines, in spite of the relative different languages and theories we use. Moreover, we would like to find the areas where new instruments and technologies are necessary, to give a new energy to a quite immobile research. Even if this research seems quite far from quantum information, we will try to show you that your questions are closer to what we are studying. Thanks to an extremely specific approach, special issue points out relevant themes, also for humanities faculties. We will consider the relation between communication models and learning/teaching ones; both in communication and in learning, the transmissive model has changed into the interactive model. The methods and technologies we have are not always satisfactory. That is why this special issue seems so interesting to us.

We revise the 'no-signaling' condition for the supraluminal communication between two spatially separated finite quantum systems of arbitrary dimensions, thus generalizing a similar preceding approach for two-qubits: non-linear evolution does not necessarily imply the possibility of supraluminal communication between any sort of finite quantum systems.

In the proposed non-Aristotelian finitary logic (NAFL), truths for formal propositions can exist only with respect to axiomatic theories, essentially as temporary axiomatic declarations in the human mind. An undecidable proposition P in a consistent NAFL theory T is true/false with respect to T if and only if it has been axiomatically declared as true/false by virtue of its provability/refutability in an interpretation T* of T. In the absence of any such axiomatic declarations, P is in a superposed state of 'neither true nor false' and the consistency of T requires the existence of a non-classical model for T in which P&¬P is the case. Here T* is an axiomatic NAFL theory that, like T, resides in the human mind and acts as the 'truth-maker' for (a model of) T. Quantum superposition is justified by identifying 'axiomatic declarations' for the truth/falsity of P (by virtue of its provability/refutability in T*) with 'measurement' in the real world. NAFL also explains and de-mystifies the phenomenon of entanglement. NAFL severely restricts classical infinitary reasoning, but possibly provides sufficient machinery for a consistent axiomatization of quantum mechanics.

We introduce and discuss the recent Agrawal–Kayal–Saxena deterministic algorithm solving primality in polynomial time.

We show how collective vibrational modes of two distant mirrors of an optical Fabry–Perot cavity can be entangled by the light bouncing between them. Such an entanglement can be demonstrated even at the macroscopic level of vibrational modes with an effective mass of the order of milligrams.

Algorithmic cooling is a method that uses novel data compression techniques and simple quantum computing devices to improve NMR spectroscopy, and to offer scalable NMR quantum computers. The algorithm recursively employs two steps. A reversible entropy compression of computation quantum-bits (qubits) of the system and an irreversible heat transfer from the system to the environment through a set of reset qubits that reach thermal relaxation rapidly. Is it possible to experimentally demonstrate algorithmic cooling using existing technology? To allow experimental algorithmic cooling, the thermalization time of the reset qubits must be much shorter than the thermalization time of the computation qubits. However, such high thermalization-times ratios have yet to be reported. We investigate here the effect of a paramagnetic salt on the thermalization-times ratio of computation qubits (carbons) and a reset qubit (hydrogen). We show that the thermalization-times ratio is improved by approximately three-fold. Based on this result, an experimental demonstration of algorithmic cooling by thermalization and magnetic ions has been performed by the authors and collaborators.

We consider the quantum computational process as viewed by an insider observer: this is equivalent to an isomorphism between the quantum computer and a quantum space, namely the fuzzy sphere. The result is the formulation of a reversible quantum measurement scheme, with no hidden information.