Maximum confidence quantum measurements

We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result. For linearly dependent sets an analogous measurement is one which allows us to be as confident as possible that when a given state is identified on the basis of the measurement result, it is indeed the correct state.     

Experimental realization of maximum confidence quantum state discrimination for the extraction of quantum information

We present the first experimental demonstration of the maximum confidence measurement strategy for quantum state discrimination. Applying this strategy to an arbitrary set of states assigns to each input state a measurement outcome which, when realized, gives the highest possible confidence that the state was indeed present. The theoretically optimal measurement for discriminating between three equiprobable symmetric qubit states is implemented in a polarization-based free-space interferometer. The maximum confidence in the measurement result is 2/3. This is the first explicit demonstration that an improvement in the confidence over the optimal minimum error measurement is possible for linearly dependent states.     

Entangling capabilities of symmetric two-qubit gates

Our work addresses the problem ofgenerating maximally entangled two spin-1/2 (qubit) symmetric states using NMR, NQR, Lipkin–Meshkov–Glick Hamiltonians. Time evolution of such Hamiltonians provides various logic gates which can be used for quantum processing tasks. Pairs of spin-1/2s have modelled a wide range of problems in physics. Here, we are interested in two spin-1/2 symmetric states which belong to a subspace spanned by the angular momentum basis {|j = 1, μ〉; μ = + 1, 0, ?1}. Our technique relies on the decomposition of a Hamiltonian in terms of SU(3) basis matrices. In this context, we define a set of linearly independent, traceless, Hermitian operators which provides an alternate set of SU(n) generators. These matrices are constructed out of angular momentum operators J _x , J _y , J _z . We construct and study the properties of perfect entanglers acting on a symmetric subspace, i.e., spin-1 operators that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power.     

Rotationally Symmetric Massless Modes in Closed Robertson-Walker Universe

The aim of the present paper is to investigate the minimally coupled rotationally symmetric scalar field configurations in spatially closed Friedman-Robertson-Walker Universe with incoherent dust. We have got the closed form solution of the Klein-Gordon equation in terms of two real-valued linearly independent hypergeometric functions. The orthonormal set of positive-frequency-like parity modes thereafter derived points out that each parity given state is conformally built up of three Einsteinian particle states and also leads to the explicit coordinate-representation of the field propagator.     

Quantum Superimposing Multiple Anti-Cloning Machine

We prove that the nonorthogonal states randomly selected from a set can evolve into a linear superposition of multiple copies of anti-cloned state (an orthogonal state along with the original) with failure branch if and only if the input states are linearly independent. We derive a bound on the success probabilities of our machine. We show that probabilistic anti-cloning and multiple anti-cloning machines are special cases of our machine. The results for a single input state are also generalized into the case of several input copies of a state.     

Remote Minimum-Error Discrimination of <Emphasis Type="Italic">N</Emphasis> Nonorthogonal Symmetric Qudit States

We present a scheme for implementing a remote minimum-error discrimination (MD) among N linearly independent nonorthogonal symmetric qudit states. The probability of correct guesses is in agreement with the optimal probability for local MD among the N nonorthogonal states. The procedure we use is a remote probability operator measure (POM). We show that this remote POM can be performed as a remote von Neumann measurement by remote basis transformation. We construct a quantum network for realizing the remote MD using local operations, classical communications and shared entanglement (LOCCSE), and thus provide a feasible physical means to realize the remote MD.     

Invariant Amplitudes for Coherent Electromagnetic Pseudoscalar Production from a Spin-One Target, II: Crossing, Multipoles, and Observables

 The formal properties of the recently derived set of linearly independent invariant amplitudes for the electromagnetic production of a pseudoscalar particle from a spin-one particle have been further exploited. The crossing properties are discussed in detail. Since not all of the amplitudes have simple crossing behaviour, we introduce an alternative set of basic amplitudes which are either symmetric or antisymmetric under crossing. The multipole decomposition is given, and the representation of the multipoles as integrals over the invariant functions weighted with Legendre polynomials is derived. Furthermore, differential cross section and polarization observables are expressed in terms of the corresponding invariant functions. Received July 5, 1999; accepted for publication September 19, 1999     

Distinguishability and indistinguishability by local operations and classical communication

It is well known that orthogonal quantum states can be distinguished perfectly. However, if we assume that these orthogonal quantum states are shared by spatially separated parties, the distinguishability of these shared quantum states may be completely different. We show that a set of linearly independent quantum states [formula: see text] where U(m,n) are generalized Pauli matrices, cannot be discriminated deterministically or probabilistically by local operations and classical communication. On the other hand, any l maximally entangled states from this set are locally distinguishable if l(l-1)< or =2d. The explicit projecting measurements are obtained to locally discriminate these states. As an example, we show that four Werner states are locally indistinguishable.     

Maximum confidence measurements via probabilistic quantum cloning

Probabilistic quantum cloning(PQC) cannot copy a set of linearly dependent quantum states.In this paper,we show that if incorrect copies are allowed to be produced,linearly dependent quantum states may also be cloned by the PQC.By exploiting this kind of PQC to clone a special set of three linearly dependent quantum states,we derive the upper bound of the maximum confidence measure of a set.An explicit transformation of the maximum confidence measure is presented.     

Quasi-solid states of micropolar elastic bodies

The states of a linearly elastic micropolar body in which there are pure couple stresses are studied, while the force stresses are zero. The plane and spherically symmetric problems are investigated for a micropolar body under conditions of quasi-solid states. The obtained solutions can be useful for experimental determination of the moment constants of micropolar media.     

Quantum key distribution with time coding on linearly dependent states

A quantum key distribution protocol with information coding by the time of photon arrival based on four linearly dependent single-photon states is proposed and the resistance of the protocol to a realistic intercept-resend attack is analyzed. The protocol on four linearly independent states is shown to be sensitive to an attack with unambiguous discrimination of all states when the level of losses in the quantum channel is higher than 7.2 dB.     

Exact confined eigenstates in one-dimensional finite periodic systems with arbitrary symmetric basis

A set of eigenenergy equations for complete confinement of N periodic one-dimensional system with arbitrary symmetric potential in each cell is presented. Exact eigenenergies and their eigenfunctions are solved analytically. We find different solutions on the band edge states comparing early results solved by conventional methods. Our results show that higher band edge state of each bandgap is dependent on the confined length, but lower band edge state is independent of the length. Moreover, wavefunctions for lower band edge states are Bloch waves but those for other eigenstates, including higher band edge states, do not obey Bloch waves.     

Optimal unambiguous discrimination of pure quantum states using SDP method

In the present paper, an exact analytic solution for the optimal unambiguous state discrimination(OPUSD) problem involving an arbitrary number of pure linearly independent quantum states with real and complex inner product is presented. Using semidefinite programming and Karush-Kuhn-Tucker convex optimization method, we derive an analytical formula which shows the relation between optimal solution of unambiguous state discrimination problem and an arbitrary number of pure linearly independent quantum states.     

De Finetti Theorem on the CAR Algebra

The symmetric states on a quasi local C*–algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend the De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki–Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self–containing interest.     

Trapped states and transitions between them in double-well pseudopotentials

We analyze a model of a double-well pseudopotential (DWPP), based in the 1D Gross-Pitaevskii equation with a spatially modulated self-attractive nonlinearity. In the limit case when the DWPP structure reduces to the local nonlinearity coefficient represented by a set of two delta-functions, analytical solutions are obtained for symmetric, antisymmetric and asymmetric states. In this case, the transition from symmetric to asymmetric states, i.e., a spontaneous-symmetry-breaking (SSB) bifurcation, is subcritical. Numerical analysis demonstrates that the symmetric states are stable up to the SSB point, while emerging asymmetric states (together with all antisymmetric solutions) are unstable in the delta-function model. In a general model, which features a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the bifurcation into the supercritical type. Antisymmetric solutions may also enjoy stabilization in the finite-width DWPP structure, demonstrating a bistability involving the asymmetric states. The symmetric states require a finite norm for their existence. A full diagram for the existence and stability of the trapped states is produced for the general model.     

Reconstruction of Superoperators from Incomplete Measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[ρ_j] that originate from a set of four linearly independent “test” states ρ_j (j = 1,2,3,4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator ρ = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.We have originally dedicated this paper to Asher Peres on the occasion of his 70th birthday. Unfortunately, since the submission of the paper for publication Asher Peres passed away so we dedicate this paper to his memory.     

Effects of Ellipticity Angle on Modulation Instabilities in Birefringent Optical Fibers

Previous studies on modulation instabilities(MIs) in birefringent optical fibers focus on the ordinary linearly and circularly ones. This paper reports an analysis of MIs in the general elliptically birefringent fibers with the emphasis on investigating the effects of ellipticity angle(0? ≤θ≤ 90?). Both symmetric and antisymmetric CW states are considered. In the anomalous dispersion regime, for the symmetric(antisymmetric) CW states, we show that MI gain increases dramatically(reduces first and then enhances greatly) as the increment of θ. In the normal dispersion regime, for the both CW states, the distinctive feature is that the gain of the MI bands reduces first, vanishes at θ = 45?,reappears across this ellipticity angle, and quickly increases after then.     

Resonant invisibility with finite range interacting fermions

We study the eigenstates of two opposite spin fermions on a one-dimensional lattice with finite range interaction. The eigenstates are projected onto the set of Fock eigenstates of the noninteracting case. We find antiresonances for symmetric eigenstates, which eliminate the interaction between two symmetric Fock states when satisfying a corresponding selection rule.     

Gauge invariance structure of quantum chromodynamics

Perturbative QCD may be subdivided into separately gauge-invariant sectors according to the projection of non-abelian color weights onto linearly independent basis elements. We exploit the general Lie group structure of the theory to give an algorithm for finding these gauge-invariant sets and present several examples of its use. The planar sector and the systematics of the non-planar corrections are defined for any gauge theory. Our gauge set classification has implications for QCD bound states, finite order perturbative QCD calculations, the study of QCD infrared singularities and for the question of convergence of the perturbation series.     

Coherence stability in three-level systems

We study the decoherence rate for estimating the time at which the coherence instability of a quantum pure state is onset. We analyze the coherence stability of pure states of a three-level quantum system under the effect of a bosonic reservoir and driven by two Raman classical fields. By assuming the boson systems to be in thermal states we find for a symmetric V-system a set of three states free from decoherence and, for a symmetric cascade-system, a two-dimensional subspace whose states are stable against the considered decoherence mechanism.