ArXiv

Authors: Andrew M. Childs, David Gosset, Zak Webb

We show that multi-particle quantum walk is capable of universal quantum computation. A continuous-time multi-particle quantum walk is generated by a time-independent Hamiltonian with a term corresponding to a single-particle quantum walk for each particle, along with an interaction term. As in a previous single-particle construction, we use a discrete version of scattering theory to establish universality. However, we use a different encoding of quantum data and exploit interactions between particles to implement two-qubit gates. In our scheme, an n-qubit circuit with g gates can be simulated by the dynamics of O(n) particles evolving for time poly(n,g) on a planar graph of maximum degree 4 with poly(n,g) vertices. Thus our graphs are exponentially smaller (as a function of n) than those used in the single-particle construction, offering the potential for efficient implementation by a system with a physical degree of freedom for each vertex of the graph. Our results apply to a broad class of multi-particle quantum walk Hamiltonians, including the Bose-Hubbard model and models with nearest-neighbor interactions for fermions and distinguishable particles.

Authors: Horace P. Yuen

It is pointed out that treatments of the error correcting code in current quantum key distribution protocols of the BB84 type are not correct under joint attack, and the general interpretation of the trace distance security criterion is also incorrect. With correct interpretation of the criterion as well as a correct treatment of the error correcting code and privacy amplification code, it is shown that even for an ideal system under just collective attack, the maximum tolerable quantum bit error rate is about 1.5% and a net key cannot actually be generated with practical error correcting codes even at such low rates, contrary to claims in the literature.

Authors: Howard Barnum, Alexander Wilce

This paper offers a brief introduction to the framework of "general probabilistic theories", otherwise known as the "convex-operational" approach the foundations of quantum mechanics. Broadly speaking, the goal of research in this vein is to locate quantum mechanics within a very much more general, but conceptually very straightforward, generalization of classical probability theory. The hope is that, by viewing quantum mechanics "from the outside", we may be able better to understand it. We illustrate several respects in which this has proved to be the case, reviewing work on cloning and broadcasting, teleportation and entanglement swapping, key distribution, and ensemble steering in this general framework. We also discuss a recent derivation of the Jordan-algebraic structure of finite-dimensional quantum theory from operationally reasonable postulates.

Authors: T. V. Gevorgyan, G. Yu. Kryuchkyan

We consider preparation of nonclassical oscillatory states in a degenerate parametric oscillator combined with phase modulation. In this scheme intracavity oscillatory mode is excited by train of Gaussian laser pulses through degenerate down-conversion process and phase modulation element inserted in a cavity leads to anharmonicity of oscillatory mode. We demonstrate production of nonclassical oscillatory states with two-fold symmetry in phase-space including the superposition of Fock states and quantum localized states on the level of few excitation numbers and in over-transient dissipative regime.

Authors: Oded Zilberberg, Alessandro Romito, David J. Starling, Gregory A. Howland, John C. Howell, Yuval Gefen

We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol is comprised of a projective measurement performed on the system with small probability (a.k.a. weak partial-collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with straightforward strong measurement) when discerning between the two quantum states.

Authors: T. V. Gevorgyan, G. Yu. Kryuchkyan

Generating multi-photon entangled states is a primary task for applications of quantum information processing. We investigate production of photon-triplet in a regime of light amplification in second-order nonlinear media under action of a pulsed laser beam. For this goal the process of cascaded three-photon splitting in an optical cavity driven by a sequence of laser pulses with Gaussian time-dependent envelopes is investigated. Considering production of photon-triplet for short-time regime and in the cascaded three-wave collinear configuration Generating multi-photon entangled states is a primary task for applications of quantum information processing. We investigate production of photon-triplet in a regime of light amplification in second-order nonlinear media under action of a pulsed laser beam. For this goal the process of cascaded three-photon splitting in an optical cavity driven by a sequence of laser pulses with Gaussian time-dependent envelopes is investigated. Considering production of photon-triplet for short-time regime and in the cascaded three-wave collinear configuration we shortly analyze preparation of polarization-non-product states looking further applications of these results in the cascaded optical parametric oscillator. It is also demonststed the nonclassical characteritics of the photon-triplet in phase-space on the base of the Wigner function. Calculating the normalized third-order correlation functions below-and at the generation threshold of cascaded optical parametric oscillator, we demonstrate that in the pulsed regime, depending on the duration of pulses and the time-interval separations between them, the degree of three-photon-number correlation essentially exceed the analogous one for the case of continuous pumping.

Authors: Spiridon Dumitru

Discussions on uncertainty relations (UR) and quantum measurements (QMS) persisted until nowadays in publications about quantum mechanics (QM). They originate mainly from the conventional interpretation of UR (CIUR). In the most of the QM literarure, it is underestimated the fact that, over the years, a lot of deficiencies regarding CIUR were signaled. As a rule the alluded deficiencies were remarked disparately and discussed as punctual and non-essential questions. Here we approach an investigation of the mentioned deficiencies collected in a conclusive ensemble. Subsequently we expose a reconsideration of the major problems referring to UR and QMS. We reveal that all the basic presumption of CIUR are troubled by insurmountable deficiencies which require the indubitable failure of CIUR and its necessary abandonment. Therefore the UR must be deprived of their statute of crucial pieces for physics. So, the aboriginal versions of UR appear as being in postures of either (i) thought-experimental fictions or (ii) simple QM formulae and, any other versions of them, have no connection with the QMS. Then the QMS must be viewed as an additional subject comparatively with the usual questions of QM. For a theoretical description of QMS we propose an information-transmission model, in which the quantum observables are considered as random variables. Our approach directs to natural solutions and simplifications for many problems regarding UR and QMS.

Authors: Altug Arda, Ramazan Sever

We intend to realize the step-up and step-down operators of the potential $V(x)=V_{1}e^{2\beta x}+V_{2}e^{\beta x}$. It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the eigenvalues of the potential by using the Laplace transform approach to study the Lie algebra satisfied the ladder operators of the potential under consideration. Our results are similar to the ones obtained for the Morse potential ($\beta \rightarrow -\beta$).

Authors: Xiao-song Ma, Thomas Herbst, Thomas Scheidl, Daqing Wang, Sebastian Kropatschek, William Naylor, Alexandra Mech, Bernhard Wittmann, Johannes Kofler, Elena Anisimova, Vadim Makarov, Thomas Jennewein, Rupert Ursin, Anton Zeilinger

Quantum teleportation [1] is a quintessential prerequisite of many quantum information processing protocols [2-4]. By using quantum teleportation, one can circumvent the no-cloning theorem [5] and faithfully transfer unknown quantum states to a party whose location is even unknown over arbitrary distances. Ever since the first experimental demonstrations of quantum teleportation of independent qubits [6] and of squeezed states [7], researchers have progressively extended the communication distance in teleportation, usually without active feed-forward of the classical Bell-state measurement result which is an essential ingredient in future applications such as communication between quantum computers. Here we report the first long-distance quantum teleportation experiment with active feed-forward in real time. The experiment employed two optical links, quantum and classical, over 143 km free space between the two Canary Islands of La Palma and Tenerife. To achieve this, the experiment had to employ novel techniques such as a frequency-uncorrelated polarization-entangled photon pair source, ultra-low-noise single-photon detectors, and entanglement-assisted clock synchronization. The average teleported state fidelity was well beyond the classical limit of 2/3. Furthermore, we confirmed the quality of the quantum teleportation procedure (without feed-forward) by complete quantum process tomography. Our experiment confirms the maturity and applicability of the involved technologies in real-world scenarios, and is a milestone towards future satellite-based quantum teleportation.

Authors: Margarida Hinarejos, A. Pérez, Mari-Carmen Bañuls

We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase space construction, propose a meaningful definition of the Wigner function in this case, and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states, and to their superpositions.

Authors: Sonya Berg

We construct an efficient quantum algorithm to compute the quantum Schur-Weyl transform for any value of the quantum parameter $q \in [0,\infty]$. Our algorithm is a $q$-deformation of the Bacon-Chuang-Harrow algorithm, in the sense that it has the same structure and is identically equal when $q=1$. When $q=0$, our algorithm is the unitary realization of the Robinson-Schensted-Knuth (or RSK) algorithm, while when $q=\infty$ it is the dual RSK algorithm together with phase signs. Thus, we interpret a well-motivated quantum algorithm as a generalization of a well-known classical algorithm.

Authors: A. Gonzalez-Tudela, P. A. Huidobro, L. Martin-Moreno, C. Tejedor, F.J. Garcia-Vidal

Here we present the theoretical foundation of the strong coupling phenomenon between quantum emitters and propagating surface plasmons observed in two-dimensional metal surfaces. For that purpose, we develop an ab-initio quantum framework that accounts for the coherent coupling be- tween emitters and surface plasmons and incorporates the presence of dissipation and dephasing. For both a single emitter and a disordered ensemble of emitters, our formalism is able to reveal the key physical mechanisms that explain the reported phenomenology and also to determine the physical parameters that optimize the strong coupling.

Authors: Bart Jacobs

Traditionally in categorical logic predicates on an object/type X are represented as subobjects of X. Here we break with that tradition and use maps of the form p : X --> X + X with [id, id] o p = id as predicates. This new view gives a more dynamic, measurement-oriented view on predicates, that works well especially in a quantitative setting. In classical logic (in the category of sets) these new predicates coincide with the traditional ones (subsets, or characteristic maps X --> {0,1}); in probabilistic logic (in the category of sets and Markov chains), the new predicates correspond to fuzzy predicates X --> [0,1]; and in quantum logic (in Hilbert spaces) they correspond to effects (positive endomaps below the identity), which may be understood as fuzzy predicates on a changed basis.

It is shown that, under certain conditions about coproducts +, predicates p : X --> X + X form effect algebras and carry a scalar multiplication (with probabilities). Suitable substitution functors give rise to indexed/fibred categories. In the quantum case the famous Born rule - describing the probability of observation outcomes - follows directly from the form of these substitution functors: probability calculation becomes substitution in predicate logic. Moreover, the characteristic maps associated with predicates provide tests in a dynamic logic, and turn out to capture measurement in a form that uniformly covers the classical, probabilistic and quantum case. The probabilities incorporated in predicates (as eigenvalues) serves as weights for the possible measurement outcomes.

Authors: Cleverson Filgueiras, D. Cogollo, E. O. Silva

In this work we investigate which radial field configuration yields bound states for neutral particles showing non-zero magnetic and electric dipole moments. The main result is that, in contrast with previous works, the Landau analog levels only exist if these radial magnetic and electric external fields are proportional to the third power of distance, not proportional to the distance. We derive the wave functions and the energy levels in the context of commutative and non-commutative quantum mechanics. We also show that, in the case of non-commutative phase space, these harmonic oscillator like spectrum do exist even if there is no external radial magnetic and electric fields. They are only consequence of the non-commutativity in the momenta.

Authors: Soojoon Lee

Using the negativity as an entanglement measure, we investigate the possible amount of remotely prepared entanglement. For two identical isotropic states on two-qudit systems 12 and 34, we calculate the average amount of entanglement remotely distributed on the system 13 by joint measurement on the system 24, and show that the remote preparation of entanglement by the generalized Bell-measurement is optimal among rank-one measurements if the isotropic states have a certain fidelity with a maximally entangled state in higher dimensional quantum systems, or if the fidelity of the isotropic states is greater than a certain value depending on the dimension. In addition, we construct a measurement better than the generalized Bell-measurement with respect to the remote preparation of entanglement when the isotropic states have small fidelity.

Authors: Emerson Sadurní

The propagator of the discrete Schr\"odinger equation is computed and its properties are revealed through a Feynman path summation in discrete space. Initial data problems such as diffraction in discrete space and continuous time are studied analytically by the application of the new propagator. In the second part of this paper, the analogy between time propagation and 2D scattering by 1D obstacles is explored. New results are given in the context of diffraction by edges within a periodic medium. A connection with tight-binding arrays and photonic crystals is indicated.

Authors: João N. C. Especial

Bell inequalities applicable to non-ideal EPRB experiments are critical to the interpretation of experimental Bell tests. In this article it is shown that previous treatments of this subject are incorrect due to an implicit assumption and new inequalities are derived under general conditions. Published experimental evidence is reinterpreted under these results and found to be entirely compatible with local-realism, both, when experiments involve inefficient detection, if fair-sampling detection is assumed, as well as when experiments have nearly ideal detection and measurement crosstalk is taken into account.

Authors: Jianxin Chen, Zhengfeng Ji, Mary Beth Ruskai, Bei Zeng, Duanlu Zhou

The structure of the ground spaces of quantum systems consisting of local interactions is of fundamental importance to different areas of physics. In this Letter, we present a necessary and sufficient condition for a subspace to be the ground space of a k-local Hamiltonian. Our analysis are motivated by the concept of irreducible correlations studied by [Linden et al., PRL 89, 277906] and [Zhou, PRL 101, 180505], which is in turn based on the principle of maximum entropy. It establishes a better understanding of the ground spaces of local Hamiltonians and builds an intimate link of ground spaces to the correlations of quantum states.

Authors: Xie Chen, Zheng-Xin Liu, Xiao-Gang Wen

Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry protected topological orders exist. In this paper, we present a model in a 2D interacting spin system with nontrivial on-site $Z_2$ symmetry protected topological order. The order is nontrivial because we can prove that the 1D system on the boundary must be gapless if the symmetry is not broken, which generalizes the gaplessness of Wess-Zumino-Witten model for Lie symmetry groups to any discrete symmetry groups. The construction of this model is related to a nontrivial 3-cocycle of the $Z_2$ group and can be generalized to any symmetry group. It potentially leads to a complete classification of symmetry protected topological orders in interacting boson and fermion systems of any dimension. Specifically, this exactly solvable model has a unique gapped ground state on any closed manifold and gapless excitations on the boundary if $Z_2$ symmetry is not broken. We prove the latter by developing the tool of matrix product unitary operator to study the nonlocal symmetry transformation on the boundary and revealing the nontrivial 3-cocycle structure of this transformation. Similar ideas are used to construct a 2D fermionic model with on-site $Z_2$ symmetry protected topological order.

Authors: Francesco Buscemi

Departing from the usual paradigm of local operations and classical communication adopted in entanglement theory, here we study the interconversion of quantum states by means of local operations and shared randomness. A set of necessary and sufficient conditions for the existence of such a transformation between two given quantum states is given in terms of the payoff they yield in a suitable class of nonlocal games. It is shown that, as a consequence of our result, such a class of nonlocal games is able to witness quantum entanglement, however weak, and reveal nonlocality in any entangled quantum state. An example illustrating this fact is provided.