Flip Operation Research Articles

Quantum interference in enhanced parametric interactions

Parametric interaction of a pair of cavity fields in a near-resonantly driven atomic system is described by a bilinear Hamiltonian that decouples from atomic flip operators and is proportional to the population difference between dressed states. For proper choice of parameters, the parametric interaction is enhanced by at least two orders compared to the dispersively dressed cases. Although spontaneous emission is fed into the cavity fields, destructive interference occurs in the fluctuations of a pair of collective modes. As a result of the two factors, perfect squeezing and Einstein–Podolsky–Rosen entanglement in the output occur when the cavity relaxation rates are much larger than in the dispersive case. The mechanism is applicable to a great variety of multilevel systems and has experimental advantages in the cavity QED generation of squeezed and entangled states of light.

Triangle-free triangulations

The flip operation on colored inner-triangle-free triangulations of a convex polygon is studied. It is shown that the affine Weyl group C ˜ n acts transitively on these triangulations by colored flips, and that the resulting colored flip graph is closely related to a lower interval in the weak order on C ˜ n . Lattice properties of this order are then applied to compute the diameter.

Coarse-to-fine surface reconstruction from silhouettes and range data using mesh deformation

We present a coarse-to-fine surface reconstruction method based on mesh deformation to build watertight surface models of complex objects from their silhouettes and range data. The deformable mesh, which initially represents the object visual hull, is iteratively displaced towards the triangulated range surface using the line-of-sight information. Each iteration of the deformation algorithm involves smoothing and restructuring operations to regularize the surface evolution process. We define a non-shrinking and easy-to-compute smoothing operator that fairs the surface separately along its tangential and normal directions. The mesh restructuring operator, which is based on edge split, collapse and flip operations, enables the deformable mesh to adapt its shape to the object geometry without suffering from any geometrical distortions. By imposing appropriate minimum and maximum edge length constraints, the deformable mesh, hence the object surface, can be represented at increasing levels of detail. This coarse-to-fine strategy, that allows high resolution reconstructions even with deficient and irregularly sampled range data, not only provides robustness, but also significantly improves the computational efficiency of the deformation process. We demonstrate the performance of the proposed method on several real objects.

ON STRUCTURAL AND GRAPH THEORETIC PROPERTIES OF HIGHER ORDER DELAUNAY GRAPHS

Given a set P of n points in the plane, the order-k Delaunay graph is a graph with vertex set P and an edge exists between two points p, q ∈ P when there is a circle through p and q with at most k other points of P in its interior. We provide upper and lower bounds on the number of edges in an order-k Delaunay graph. We study the combinatorial structure of the set of triangulations that can be constructed with edges of this graph. Furthermore, we show that the order-k Delaunay graph is connected under the flip operation when k ≤ 1 but not necessarily connected for other values of k. If P is in convex position then the order-k Delaunay graph is connected for all k ≥ 0. We show that the order-k Gabriel graph, a subgraph of the order-k Delaunay graph, is Hamiltonian for k ≥ 15. Finally, the order-k Delaunay graph can be used to efficiently solve a coloring problem with applications to frequency assignments in cellular networks.

κ-deformed oscillators, the choice of star product and free κ-deformed quantum fields

The aim of this paper is to study in D = 4 the general framework providing various κ-deformations of field oscillators and consider the commutator function of the corresponding κ-deformed free fields. In order to obtain free κ-deformed quantum fields (with c-number commutators) we proposed earlier a particular model of a κ-deformed oscillator algebra (Daszkiewicz M, Lukierski J and Woronowicz M 2008 Mod. Phys. Lett. A 23 9 (arXiv:hep-th/0703200)) and the modification of κ-star product (Daszkiewicz M, Lukierski J, Woronowicz M 2008 Phys. Rev. D 77 105007 (arXiv:0708.1561 [hep-th])), implementing in the product of two quantum fields the change of standard κ-deformed mass-shell conditions. We recall here that other different models of κ-deformed oscillators recently introduced in Arzano M and Marciano A (2007 Phys. Rev. D 76 125005 (arXiv:0707.1329 [hep-th])), Young C A S and Zegers R (2008 Nucl. Phys. B 797 537 (arXiv: 0711.2206 [hep-th])), Young C A S and Zegers R (2008 arXiv: 0803.2659 [hep-th]) are defined on a standard κ-deformed mass shell. In this paper, we consider the most general κ-deformed field oscillators, parametrized by a set of arbitrary functions in 3-momentum space. First, we study the fields with the κ-deformed oscillators defined on the standard κ-deformed mass shell, and argue that for any such choice of a κ-deformed field oscillators algebra we do not obtain the free quantum κ-deformed fields with the c-number commutators. Further, we study κ-deformed quantum fields with the modified κ-star product and derive a large class of κ-oscillators defined on a suitably modified κ-deformed mass shell. We obtain a large class of κ-deformed statistics depending on six arbitrary functions which all provide the c-number field commutator functions. This general class of κ-oscillators can be described by the composition of suitably defined κ-multiplications and the κ-deformation of the flip operator.

κ-deformed oscillators: Deformed multiplication versus deformed flip operator and multiparticle clusters

We transform the oscillator algebra with kappa-deformed multiplication rule, proposed in [1],[2], into the oscillator algebra with kappa-deformed flip operator and standard multiplication. We recall that the kappa-multiplication of the kappa-oscillators puts them off-shell. We study the explicit forms of modified mass-shell conditions in both formulations: with kappa-multiplication and with kappa-flip operation. On the example of kappa-deformed 2-particle states we study the clustered nonfactorizable form of the kappa-deformed multiparticle states. We argue that the kappa-deformed star product of two free fields leads in similar way to a nonfactorizable kappa-deformed bilocal field. We conclude with general remarks concerning the kappa-deformed n-particle clusters and kappa-deformed star product of n fields.

Deformed oscillator algebras and QFT inκ-Minkowski spacetime

In this paper, we study the deformed statistics and oscillator algebras of quantum fields defined in $\ensuremath{\kappa}$-Minkowski spacetime. The twisted flip operator obtained from the twist associated with the star product requires an enlargement of the Poincar\'e algebra to include the dilatation generators. Here we propose a novel notion of a fully covariant flip operator and show that to the first order in the deformation parameter it can be expressed completely in terms of the Poincar\'e generators alone. The $R$ matrices corresponding to the twisted and the covariant flip operators are compared up to first order in the deformation parameter and they are shown to be different. We also construct the deformed algebra of the creation and annihilation operators that arise in the mode expansion of a scalar field in $\ensuremath{\kappa}$-Minkowski spacetime. We obtain a large class of such new deformed algebras which, for certain choice of realizations, reduce to results known in the literature.

Experimental demonstration of a teleportation-based programmable quantum gate

We experimentally demonstrate a programmable quantum gate that applies a sign flip operation to data qubit in an arbitrary basis fully specified by the quantum state of a two-qubit program register. Our linear-optical implementation is inspired by teleportation-based schemes for quantum computing and relies on multiphoton interference and coincidence detection. We confirm the programmability of the gate and its high-fidelity performance by carrying out full quantum process tomography of the resulting operation on data qubit for several different programs.

An electron's spin---Part I

In Part I of this article, we introduced the notion of encoding binary bit information in the spin polarization of a single electron confined in a quantum dot and placed in a magnetic field. The spin polarization becomes bistable in a magnetic field and the spin can point either parallel to the field or antiparallel to it. These two polarizations encode the classical binary bits 0 and 1. We showed that since the bits can be switched by simply flipping the electron's spin without physically moving the electron in space and causing a current, the energy dissipated during the bit flip operation could be made very small. In Part II we discuss the notion of using a single electron's spin as a quantum bit (or qubit) that represents information in quantum computers. Just as spin is superior to charge as a vehicle to host classical bit information in classical computers it turns out that spin is superior to charge to host quantum information as well. That is why spin-based quantum information processing is gradually becoming the staple of scalable solid state versions of quantum computers.

Photon-arrival detector with a controlled phase flip operation between a photon and a V-type atomic system

We propose a photon-arrival detector (PAD), which detects the arrival of a signal photon and simultaneously projects the signal input state to a single-photon state, with an atom-cavity system. In this proposal, use of a V-type system as the intracavity atom is discussed for implementing the PAD since V-type systems have been widely studied in the field of solid state, enabling us to miniaturize and integrate that implementation. The performance of the proposed PAD is evaluated for a specific method of the detection process. The proposed PAD is capable of repeating the procedure for detecting the arrival of input photons and it has improved the detection probability so that it has a higher quantum efficiency than those of conventional photodetectors.

Multipartite entanglement measure for all discrete systems

Via a multidimensional complementarity relation we derive an operational entanglement measure for any discrete quantum system, i.e., for any multidimensional and multipartite system. This measure admits a separation into different classes of entanglement obtained by using a flip operator $2,3,\dots{},n$ times, defining a $m$-flip concurrence. This operator sum has the practical feature to allow one to calculate for mixed states bounds on this $m$-flip concurrence. Moreover, the information content of an $n$-partite multidimensional system admits a simple and intuitive interpretation in terms of single particle obtainable information, entanglement, and information due to lack of classical knowledge of the quantum state under investigation. Explicitly, the three qubit system is analyzed and, e.g., the physical difference in entanglement of the W state, the Greenberger-Horne-Zeilinger (GHZ) state, or a biseparable state is revealed.

Erratum: Bit storage and bit flip operations in an electromechanical oscillator

Nature Nanotechnology 3, 275–279 (2008) There were two errors in thirteenth paragraph of this letter. The relation from which the power consumption can be extracted should read CV2fs, and the actual expression for the power consumed should read mω3x2/2πQ. These errors have also been corrected in thesupplementary information.

Twisted statistics inκ-Minkowski spacetime

We consider the issue of statistics for identical particles or fields in $\ensuremath{\kappa}$-deformed spaces, where the system admits a symmetry group $G$. We obtain the twisted flip operator compatible with the action of the symmetry group, which is relevant for describing particle statistics in the presence of the noncommutativity. It is shown that for a special class of realizations, the twisted flip operator is independent of the ordering prescription.

Bit storage and bit flip operations in an electromechanical oscillator

The Parametron was first proposed as a logic-processing system almost 50 years ago. In this approach the two stable phases of an excited harmonic oscillator provide the basis for logic operations. Computer architectures based on LC oscillators were developed for this approach, but high power consumption and difficulties with integration meant that the Parametron was rendered obsolete by the transistor. Here we propose an approach to mechanical logic based on nanoelectromechanical systems that is a variation on the Parametron architecture and, as a first step towards a possible nanomechanical computer, we demonstrate both bit storage and bit flip operations.

All triangulations are reachable via sequences of edge-flips: an elementary proof

A simple proof is provided for the fact that the set of all possible triangulations of a planar point set in a polygonal domain is closed under the basic diagonal flip operation.

Deterministic six states protocol for quantum communication

We consider a two-way deterministic protocol for quantum communication using six mutually unbiased states in the Poincaré sphere. The logical information is encoded by flip or not-flip operations on the states. Despite the nonexistence of a universal flip gate the protocol saturates the bound of a unitary efficiency. Three eavesdropping strategies are analyzed suggesting better probabilities of detecting an unauthorized adversary.

Perfect pattern formation of neutral atoms in an addressable optical lattice

We propose a physical scheme for formation of an arbitrary pattern of neutral atoms in an addressable optical lattice. We focus specifically on the generation of a perfect optical lattice of simple orthorhombic structure with unit occupancy, as required for initialization of a neutral atom quantum computer. The scheme employs a compacting process that is accomplished by sequential application of two types of operations: a flip operator that changes the internal state of the atoms, and a shift operator that selectively moves the atoms in one internal state along the lattice principal axis. Realizations of these elementary operations and their physical limitations are analyzed. The complexity of the compacting scheme is analyzed and we show that this scales linearly with the number of lattice sites per row of the lattice. Neutral atoms trapped in an optical lattice constitute an attractive system for implementation of scalable quantum computation f1-3g, simulation of many-body systems f4g, and implementation of topological quantum computing f5-9g. In standard optical lattices, small lattice constants present a serious obstacle to implementing quantum compu- tation, since it is difficult to address individual qubits with an external field. An optical lattice with a large lattice constant is in principle addressable, and can allow for the quantum state manipulation of individual atoms by an optical field. High addressability and controllability and low decoherence make addressable lattices promising candidates for large- scale quantum computer implementation. The present work focuses on preparation of the initializa- tion of an addressable optical lattice for the purposes of quantum computing. The objective is a perfectly filled, regu- lar optical lattice, with each site occupied by a single atom in its motional ground state and in a specific internal state. We consider one-dimensional s1Dd, orthorhombic two- dimensional s2Dd, and three-dimensional s3Dd lattices. After loading and laser-cooling atoms in the optical lattice, half the sites have a single atom and half are vacant. In order to use this system for scalable quantum computation, a perfect lat- tice with each site occupied by a single atom is required. We propose here an efficient, feasible scheme forcompacting the optical lattice, i.e., for removing vacant sites to the edge of the lattice, thus creating a smaller lattice, but one more suit- able for quantum computation. The scheme presented here can as well be used to make arbitrary patterns of neutral atoms in an addressable optical lattice. These include lattices with fractional occupation, a specific translational and rotational lattice symmetry, a bro- ken symmetry, and heteroatomic patterns. Another important property of the scheme is that it can be applied recursively to reach any desired accuracy of the pattern formation. After a large number of elementary operations, the lattice can be cooled and imaged again. The remaining defects can be eliminated by repeating the compacting scheme. This recur- sion increases the total pattern formation time by the total duration of additional cooling and imaging cycles, but does not result in any increase in the scaling of the pattern forma- tion, i.e., the algorithmic complexity of the scheme is un- changed. The possibility of preparing any homoatomic or heteroatomic pattern of neutral atoms to an arbitrarily high degree of perfection makes this scheme attractive for initial- ization of quantum simulations of condensed phase systems, in addition to initialization of quantum computation.

Form factor decomposition of generalized parton distributions at leading twist

We extend the counting of generalized form factors presented in [Phys. Rev. D 63 (2001) 076005] by Ji and Lebed to the axial vector and the tensor operator at twist-2 level. Following this, a parameterization of all higher moments in x of the tensor (helicity flip) operator is given in terms of generalized form factors.

Transformations and invariances in equally tempered scales

In this work the invariance of the number of accidentals in equally tempered scales (ETSs) under various transformations are proven analytically. ETSs with N semitones, M notes and interval structures n={n1,n2,...,nM}, where ni is the number of semitones between adjacent notes, form multiplets of N scales. Member scales of a multiplet are ordered and indexed by scale labels ck=kM reduced modulo (N), where k=0,1,...,N−1. Ordered members of the multiplets having the interval structures {Cjn} and {CℓMIn} (where C is a cyclical permutation, j,ℓ=0,1,...,M−1, and MI is a mirror image or flip operation on n) are shown to have the same number of sharps and the same number of flats, Nσ(ck,Cjn)=Nσ(ck,CℓMIn) (where σ=♯ or ♭, for all j, ℓ and for any scale label ck). Complementary scales nC related to n by a note ↔ no-note transformation (e.g., major ↔ pentatonic), however, have scale labels with opposite signs, and the number of sharps and flats are interchanged N♯(ck,n)=N♭(−ck,nC). This explains the degeneracy of the complexity parameter defined as the sum of the number of sharps and flats, proposed as a measure for ETS, explored numerically and reported earlier.

Pseudotriangulations from Surfaces and a Novel Type of Edge Flip

We prove that planar pseudotriangulations have realizations as polyhedral surfaces in three-space. Two main implications are presented. The spatial embedding leads to a novel flip operation that allows for a drastic reduction of flip distances, especially between (full) triangulations. Moreover, several key results for triangulations, like flipping to optimality, (constrained) Delaunayhood, and a convex polytope representation, are extended to pseudotriangulations in a natural way.