Path-sum solution of the Weyl quantum walk in 3 + 1 dimensions.

We consider the Weyl quantum walk in 3+1 dimensions, that is a discrete-time walk describing a particle with two internal degrees of freedom moving on a Cayley graph of the group [Formula: see text], which in an appropriate regime evolves according to Weyl's equation. The Weyl quantum walk was recently derived as the unique unitary evolution on a Cayley graph of [Formula: see text] that is homogeneous and isotropic. The general solution of the quantum walk evolution is provided here in the position representation, by the analytical expression of the propagator, i.e. transition amplitude from a node of the graph to another node in a finite number of steps. The quantum nature of the walk manifests itself in the interference of the paths on the graph joining the given nodes. The solution is based on the binary encoding of the admissible paths on the graph and on the semigroup structure of the walk transition matrices.This article is part of the themed issue 'Second quantum revolution: foundational questions'.

Optimal quantum tomography of States, measurements, and transformations.

We present the first complete optimization of quantum tomography, for states, positive operator value measures, and various classes of transformations, for arbitrary prior ensemble and arbitrary representation, giving corresponding feasible experimental schemes in terms of random Bell measurements.

Quantum circuit architecture.

We present a method for optimizing quantum circuits architecture, based on the notion of a quantum comb, which describes a circuit board where one can insert variable subcircuits. Unexplored quantum processing tasks, such as cloning and storing or retrieving of gates, can be optimized, along with setups for tomography and discrimination or estimation of quantum circuits.

Erasable and unerasable correlations.

We address the problem of removing correlation from sets of states while preserving as much local quantum information as possible. We prove that states obtained from universal cloning can only be decorrelated at the expense of complete erasure of local information (i.e., information about the copied state). We solve analytically the problem of decorrelation for two qubits and two qumodes (harmonic oscillators in Gaussian states), and provide sets of decorrelable states and the minimum amount of noise to be added for decorrelation.

Optimal data processing for quantum measurements.

We consider the general measurement scenario in which the ensemble average of an operator is determined via suitable data processing of the outcomes of a quantum measurement described by a positive operator-valued measure. We determine the optimal processing that minimizes the statistical error of the estimation.

Optimal quantum circuits for general phase estimation.

We address the problem of estimating the phase phi given N copies of the phase-rotation gate uphi. We consider, for the first time, the optimization of the general case where the circuit consists of an arbitrary input state, followed by any arrangement of the N phase rotations interspersed with arbitrary quantum operations, and ending with a general measurement. Using the polynomial method, we show that, in all cases where the measure of quality of the estimate phi for phi depends only on the difference phi-phi, the optimal scheme has a very simple fixed form. This implies that an optimal general phase estimation procedure can be found by just optimizing the amplitudes of the initial state.

Distributed quantum dense coding.

We introduce the notion of distributed quantum dense coding, i.e., the generalization of quantum dense coding to more than one sender and more than one receiver. We show that global operations (as compared to local operations) of the senders do not increase the information transfer capacity, in the case of a single receiver. For the case of two receivers, using local operations and classical communication, a nontrivial upper bound for the capacity is derived. We propose a general classification scheme of quantum states according to their usefulness for dense coding. In the bipartite case (for any dimensions), bound entanglement is not useful for this task.

Efficient use of quantum resources for the transmission of a reference frame.

We propose a covariant protocol for transmitting reference frames encoded on N spins, achieving sensitivity N-2 without the need of a preestablished reference frame and without using entanglement between sender and receiver. The protocol exploits the use of equivalent representations that were overlooked in the previous literature.

There exist nonorthogonal quantum measurements that are perfectly repeatable.

We show that, contrary to the widespread belief, in quantum mechanics repeatable measurements are not necessarily described by orthogonal projectors--the customary paradigm of observable. Nonorthogonal repeatability, however, occurs only for infinite dimensions. We also show that, when a nonorthogonal repeatable measurement is performed, the measured system retains some "memory" of the number of times that the measurement has been performed.

Detection of entanglement with polarized photons: experimental realization of an entanglement witness.

We report on the first experimental realization of an entanglement witness, a method to detect entanglement with few local measurements. The present demonstration has been performed with polarized photons in Werner states, a well-known family of mixed states that can be either separable or nonseparable. The Werner states are generated by a novel high brilliance source of bipartite entangled states by which the state mixedness can be easily adjusted.

Quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation.

Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. We present a general method based on quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation. As input the method needs only a single entangled state. The feasibility of the technique for the electromagnetic field is shown, and the experimental setup is illustrated based on homodyne tomography of a twin beam.

Continuous variable cloning via network of parametric gates.

We propose an experimental scheme for the cloning machine of continuous quantum variables through a network of parametric amplifiers working as input-output four-port gates.

Using entanglement improves the precision of quantum measurements.

We show how entanglement can be used to improve the estimation of an unknown transformation. Using entanglement is always of benefit in improving either the precision or the stability of the measurement. Examples relevant for applications are illustrated, for either qubits or continuous variables.

Toward a tomographic picture of a Bose-Einstein condensate.

The possibilities of applying tomographic techniques to a Bose-Einstein condensate to reconstruct its ground state are investigated by means of numerical simulations. Two situations for which the density-matrix elements can be retrieved from atom counting probabilities are considered. The methods presented here allow one to distinguish among various possible quantum states.

Investigation of the photon statistics of parametric fluorescence in a traveling-wave parametric amplifier by means of self-homodyne tomography.

Photon-number distributions for parametric fluorescence from a nondegenerate optical parametric amplifier are measured with a novel self-homodyne technique. These distributions exhibit the thermal-state character predicted by theory. However, a difference between the fluorescence gain and the signal gain of the parametric amplifier is observed. We attribute this difference to a change in the signal-beam profile during the traveling-wave pulsed amplification process.

Development of a computerized data base to evaluate pressure ulcers.

A computerized data base for collecting information on patients with pressure ulcers was developed following a review of selected literature including Allman (1986), Bergstrom (1987), Barbenel (1977), Reichert (1986), Black (1987) and others. The data base was piloted, revised, and used for data collection on 103 patients admitted to two hospitals. Standardized data allowed for correlations of spinal cord injury (SCI) and location of pressure ulcers. Sacral ulcers were more prevalent with patients who had SCI at C4-T1 while ischial ulcers were more common with SCI at T11-L1. Some of the other correlations differ from prior research and warrant further investigation with a larger sample size from multiple institutions.