Complete Measurements of Quantum Observables

We define a complete measurement of a quantum observable (POVM) as a measurement of the maximally refined (rank-1) version of the POVM. Complete measurements give information on the multiplicities of the measurement outcomes and can be viewed as state preparation procedures. We show that any POVM can be measured completely by using sequential measurements or maximally refinable instruments. Moreover, the ancillary space of a complete measurement can be chosen to be minimal.     

Mueller matrix determination for one-dimensional rough surfaces: Four reduced measurement equivalent sets

There are several methods for the experimental determination of the Mueller matrix (MM) for a general scattering system. For the case of scattering in the plane-of-incidence, we apply the direct method of Mueller matrix ellipsometry to determine the MM associated to a one-dimensional scattering system. We show the MM for a 1-D surface can be determined with four different measurements from four equivalent sets consisting of four Stokes vector inputs and four analyzers. We show all the possible measurements can be reduced to a single set of four different intensity measurements.     

Weak measurements are universal

It is well known that any projective measurement can be decomposed into a sequence of weak measurements, which cause only small changes to the state. Similar constructions for generalized measurements, however, have relied on the use of an ancilla system. We show that any generalized measurement can be decomposed into a sequence of weak measurements without the use of an ancilla, and give an explicit construction for these weak measurements. The measurement procedure has the structure of a random walk along a curve in state space, with the measurement ending when one of the end points is reached. This shows that any measurement can be generated by weak measurements, and hence that weak measurements are universal. This may have important applications to the theory of entanglement.     

The hidden phase of Fock states; quantum non-local effects

We revisit the question of how a definite phase between Bose-Einstein condensates can spontaneously appear under the effect of measurements. We first consider a system that is the juxtaposition of two subsystems in Fock states with high populations, and assume that successive individual position measurements are performed. Initially, the relative phase is totally undefined, and no interference effect takes place in the first position measurement. But, while successive measurements are accumulated, the relative phase becomes better and better defined, and a clear interference pattern emerges. It turns out that all observed results can be interpreted in terms of a pre-existing, but totally unknown, relative phase, which remains exactly constant during the experiment. We then generalize the results to more condensates. We also consider other initial quantum states than pure Fock states, and distinguish between intrinsic phase of a quantum state and phase induced by measurements. Finally, we examine the case of multiple condensates of spin states. We discuss a curious quantum effect, where the measurement of the spin angular momentum of a small number of particles can induce a big angular momentum in a much larger assembly of particles, even at an arbitrary distance. This spin observable can be macroscopic, analogous to the pointer of a measurement apparatus, which illustrates the non-locality of standard quantum mechanics with particular clarity. The effect can be described as the teleportation at arbitrary distances of the continuous classical result of a local experiment. The EPR argument, transposed to this case, takes a particularly convincing form since it does not involve incompatible measurements and deals only with macroscopic variables.     

Method for improving the resolution and accuracy against birefringence dispersion in distributed polarization cross-talk measurements

We present a novel method for improving the spatial resolution and amplitude accuracy of distributed polarization cross-talk measurements in a polarization maintaining (PM) fiber against its birefringence dispersion. We show that the broadening of measured polarization cross-talk peaks caused by birefringence dispersion can be restored by simply multiplying the measurement data with a compensation function. The birefringence dispersion variable in the function can be obtained by finding the widths of measured cross-talk envelopes at known distances along the fiber. We demonstrate that this method can effectively improve spatial resolution and amplitude accuracy of the space-resolved polarization cross-talk measurements of long PM fibers.     

Atomic quantum zeno effect for ensembles and single systems

The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect, Itanoet al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations, we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss how far the experiment of Itanoet al. can be considered as a test of the quantum Zeno effect. We also analyze a new possible experiment on a single atom where stochastic light and dark periods can be interpreted as manifestation of the quantum Zeno effect. We show that the measurement point of view gives a quick and intuitive understanding of experiments of the above type, although a finer analysis has to take the corrections into account.     

Method for improving the resolution and accuracy against birefringence dispersion in distributed polarization cross-talk measurements

We present a novel method for improving the spatial resolution and amplitude accuracy of distributed polarization cross-talk measurements in a polarization maintaining (PM) fiber against its birefringence dispersion. We show that the broadening of measured polarization cross-talk peaks caused by birefringence dispersion can be restored by simply multiplying the measurement data with a compensation function. The birefringence dispersion variable in the function can be obtained by finding the widths of measured cross-talk envelopes at known distances along the fiber. We demonstrate that this method can effectively improve spatial resolution and amplitude accuracy of the space-resolved polarization cross-talk measurements of long PM fibers.     

Dynamical localization and repeated measurements in a quantum computation process

We study numerically the effects of measurements on dynamical localization in the kicked rotator model simulated on a quantum computer. Contrary to the previous studies, which showed that measurements induce a diffusive probability spreading, our results demonstrate that localization can be preserved for repeated single-qubit measurements. We detect a transition from a localized to a delocalized phase, depending on the system parameters and on the choice of the measured qubit.     

Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation

We present a normalized Born expansion that facilitates fluorescence reconstructions in turbid, tissuelike media. The algorithm can be particularly useful for tissue investigations of fluorochrome distributionin vivo, since it does not require absolute photon-field measurements or measurements before contrast-agent administration. This unique advantage can be achieved only in fluorescence mode. We used this algorithm to three-dimensionally image and quantify an indocyanine fluorochrome phantom, using a novel fluorescence tomographic imager developed for animals.     

Modular-value-based metrology with spin coherent pointers

We discuss an optimal modular-value-based measurement with a spin coherent pointer: A quantum system is exposed to a field whose strength is to be estimated through its modular value. We evaluate the quantum Fisher information as a figure of merit. We found that the modular-value-based measurement can reach the same ultimate precision limit of the estimation as those of measurements without postselections. The quantum Fisher information can be increased when the dimension of the pointer state increases. We also consider the pointer under a phase-flip error. Our study should motivate researchers to apply the modular-value-based measurements for quantum metrology.     

Correcting movement errors in frequency-sweeping interferometry

Absolute distance measurements can be performed with an interferometric method that uses only a single tunable laser. This method has one major drawback, because a small target movement of the order of one wavelength during a measurement will be interpreted as a movement of one synthetic wavelength. This effect is usually mitigated by adding a second (nonscanning) laser. We show that absolute distance measurements can be performed with only one laser if the movements encountered are smooth, on the time scale of one measurement. In this case the movement errors can be compensated with a simple algorithm that combines several subsequent measurements. First experimental results show good agreement with theory.     

Separable measurement estimation of density matrices and its fidelity gap with collective protocols

We show that there exists a gap between the performance of separable and collective measurements in the qubit mixed-state estimation that persists in the large sample limit. We characterize the gap with sharp asymptotic bounds on mean fidelity. We present an adaptive protocol that attains the separable measurement bound. This protocol uses von Neumann measurements and can be easily implemented with current technology.     

Entanglement versus correlations in spin systems

We consider pure quantum states of N>1 spins or qubits and study the average entanglement that can be localized between two separated spins by performing local measurements on the other individual spins. We show that all classical correlation functions provide lower bounds to this localizable entanglement, which follows from the observation that classical correlations can always be increased by doing appropriate local measurements on the other qubits. We analyze the localizable entanglement in familiar spin systems and illustrate the results on the hand of the Ising spin model, in which we observe characteristic features for a quantum phase transition such as a diverging entanglement length.     

Consistency of ground state and spectroscopic measurements on flux qubits

We compare the results of ground state and spectroscopic measurements carried out on superconducting flux qubits which are effective two-level quantum systems. For a single qubit and for two coupled qubits we show excellent agreement between the parameters of the pseudospin Hamiltonian found using both methods. We argue that by making use of the ground state measurements the Hamiltonian of N coupled flux qubits can be reconstructed as well at temperatures smaller than the energy level separation. Such a reconstruction of a many-qubit Hamiltonian can be useful for future quantum information processing devices.     

Quarkonium polarization in pp and p-nucleus collisions

The existing measurements of quarkonium polarization in proton-antiproton and proton-nucleus collisions are puzzling. We highlight issues which are often underestimated in the experimental analyses: the importance of the choice of the experimental acceptance on the comparison between experimental measurements and theoretical calculations. New measurements must provide more detailed information, such that physical conclusions can be derived without relying on model-dependent assumptions. We also describe a frame-invariant formalism which minimizes the dependence of the measurements on the experimental acceptance, facilitates the comparison with theoretical calculations, and probes systematic effects due to experimental biases.     

Encoding of diffusion and T1 in the CPMG echo shape: single-shot D and T1 measurements in grossly inhomogeneous fields

We present a new approach of NMR measurements in the presence of grossly inhomogeneous fields where information is encoded in the echo shape of CPMG trains. The method is based on sequences that consist of an initial encoding sequence that generates echoes with contributions from at least two different coherence pathways that are then both refocused many times by a long string of closely spaced identical pulses. The generated echoes quickly assume an asymptotic shape that encodes the information of interest. High signal-to-noise ratios can be achieved by averaging the large number of echoes. We demonstrate this approach with different implementations of the measurements of longitudinal relaxation time, T(1), and diffusion coefficient, D. It is shown that the method can be used for novel single-shot measurements.     

Usefulness of multiqubit W-type states in quantum information processing

We analyze the efficiency of multiqubit W-type states as resources for quantum information. For this, we identify and generalize four-qubit W-type states. Our results show that these states can be used as resources for deterministic quantum information processing. The utility of results, however, is limited by the availability of experimental setups to perform and distinguish multiqubit measurements. We therefore emphasize protocols where two users want to establish an optimal bipartite entanglement using the partially entangled W-type states. We find that for such practical purposes, four-qubit W-type states can be a better resource in comparison to three-qubit W-type states. For a dense coding protocol, our states can be used deterministically to send two bits of classical message by locally manipulating a single qubit. In addition, we also propose a realistic experimental method to prepare the four-qubit W-type states using standard unitary operations and weak measurements.     

Quantitative determination of contributions to the thermoelectric power factor in Si nanostructures

We report thermoelectric measurements on a silicon nanoribbon in which an integrated gate provides strong carrier confinement and enables tunability of the carrier density over a wide range. We find a significantly enhanced thermoelectric power factor that can be understood by considering its behavior as a function of carrier density. We identify the underlying mechanisms for the power factor in the nanoribbon, which include quantum confinement, low scattering due to the absence of dopants, and, at low temperatures, a significant phonon-drag contribution. The measurements set a target for what may be achievable in ultrathin nanowires.     

Partial Measurements and the Realization of Quantum-Mechanical Counterfactuals

We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We first analyze the consequences of this rather unusual feature for the principle of superposition, for the complementarity principle, and for the issue of hidden variables. Then we move on to exploring non-local contexts, by reformulating the EPR paradox, the quantum teleportation experiment, and the entanglement-swapping protocol for the situation in which one uses partial measurements followed by their stochastic reversal. This leads to a number of counter-intuitive results, which are shown to be resolved if we give up the idea of attributing reality to the wavefunction of a single quantum system.