Off-diagonal geometric phase for mixed states

We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase [Phys. Rev. Lett. {\bf 85}, 2845 (2000)]. Extension to higher dimensional Hilbert spaces is delineated. A physical scenario for the off-diagonal mixed state geometric phase in polarization-entangled two-photon interferometry is proposed.Comment: small corrections; journal reference adde

Practical learning method for multi-scale entangled states

We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires single particle measurements and the total number of measurements is polynomial in the number of particles. Data post-processing for state reconstruction uses standard tools, namely matrix diagonalisation and conjugate gradient method, and scales polynomially with the number of particles. Our method prevents the build-up of errors from both numerical and experimental imperfections

Testing the bounds on quantum probabilities

Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as criteria for the validity of quantum mechanics.Comment: 9 pages, Revte

Characterization and tomography of a hidden qubit

In circuit-based quantum computing, the available gate set typically consists of single-qubit gates acting on each individual qubit and at least one entangling gate between pairs of qubits. In certain physical architectures, however, some qubits may be 'hidden' and lacking direct addressability through dedicated control and readout lines, for instance because of limited on-chip routing capabilities, or because the number of control lines becomes a limiting factor for many-qubit systems. In this case, no single-qubit operations can be applied to the hidden qubits and their state cannot be measured directly. Instead, they may be controlled and read out only via single-qubit operations on connected 'control' qubits and a suitable set of two-qubit gates. We first discuss the impact of such restricted control capabilities on the quantum volume of specific qubit coupling networks. We then experimentally demonstrate full control and measurement capabilities in a superconducting two-qubit device with local single-qubit control and iSWAP and controlled-phase two-qubit interactions enabled by a tunable coupler. We further introduce an iterative tune-up process required to completely characterize the gate set used for quantum process tomography and evaluate the resulting gate fidelities

Visual Processing in Rapid-Chase Systems: Image Processing, Attention, and Awareness

Visual stimuli can be classified so rapidly that their analysis may be based on a single sweep of feedforward processing through the visuomotor system. Behavioral criteria for feedforward processing can be evaluated in response priming tasks where speeded pointing or keypress responses are performed toward target stimuli which are preceded by prime stimuli. We apply this method to several classes of complex stimuli. (1) When participants classify natural images into animals or non-animals, the time course of their pointing responses indicates that prime and target signals remain strictly sequential throughout all processing stages, meeting stringent behavioral criteria for feedforward processing (rapid-chase criteria). (2) Such priming effects are boosted by selective visual attention for positions, shapes, and colors, in a way consistent with bottom-up enhancement of visuomotor processing, even when primes cannot be consciously identified. (3) Speeded processing of phobic images is observed in participants specifically fearful of spiders or snakes, suggesting enhancement of feedforward processing by long-term perceptual learning. (4) When the perceived brightness of primes in complex displays is altered by means of illumination or transparency illusions, priming effects in speeded keypress responses can systematically contradict subjective brightness judgments, such that one prime appears brighter than the other but activates motor responses as if it was darker. We propose that response priming captures the output of the first feedforward pass of visual signals through the visuomotor system, and that this output lacks some characteristic features of more elaborate, recurrent processing. This way, visuomotor measures may become dissociated from several aspects of conscious vision. We argue that “fast” visuomotor measures predominantly driven by feedforward processing should supplement “slow” psychophysical measures predominantly based on visual awareness

New Aspects of Geometric Phases in Experiments with polarized Neutrons

Geometric phase phenomena in single neutrons have been observed in polarimeter and interferometer experiments. Interacting with static and time dependent magnetic fields, the state vectors acquire a geometric phase tied to the evolution within spin subspace. In a polarimeter experiment the non-additivity of quantum phases for mixed spin input states is observed. In a Si perfect-crystal interferometer experiment appearance of geometric phases, induced by interaction with an oscillating magnetic field, is verified. The total system is characterized by an entangled state, consisting of neutron and radiation fields, governed by a Jaynes-Cummings Hamiltonian. In addition, the influence of the geometric phase on a Bell measurement, expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, is studied. It is demonstrated that the effect of geometric phase can be balanced by an appropriate change of Bell angles.Comment: 17 pages, 9 figure

Generalizing Tsirelson's bound on Bell inequalities using a min-max principle

Bounds on the norm of quantum operators associated with classical Bell-type inequalities can be derived from their maximal eigenvalues. This quantitative method enables detailed predictions of the maximal violations of Bell-type inequalities.Comment: 4 pages, 2 figures, RevTeX4, replaced with published versio

Geometric Phase in Entangled Systems: A Single-Neutron Interferometer Experiment

The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. in [Phys. Rev. A 69, 032112 (2004)], and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time dependent interaction with two radio-frequency (rf) fields. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme, yields a sinusoidal oscillation of the correlation function S, dependent on the geometric phase, such that it varies in the range between 2 and 2\sqrt{2} and, therefore, always exceeds the boundary value 2 between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like-CHSH inequality, where S remains 2\sqrt2 for all settings of the geometric phase.Comment: 10 pages 9 figure

Optical tomography of Fock state superpositions

We consider optical tomography of photon Fock state superpositions in connection with recent experimental achievements. The emphasis is put on the fact that it suffices to represent the measured tomogram as a main result of the experiment. We suggest a test for checking the correctness of experimental data. Explicit expressions for optical tomograms of Fock state superpositions are given in terms of Hermite polynomials. Particular cases of vacuum and low photon-number state superposition are considered as well as influence of thermal noise on state purity is studied.Comment: 5 pages, 2 figure