We provide an in-depth investigation of parameter estimation in nested Mach-Zehnder interferometers (NMZIs) using two information measures: the Fisher information and the Shannon mutual information. Protocols for counterfactual communication have, so far, been based on two different definitions of counterfactuality. In particular, some schemes have been based on NMZI devices, and have recently been subject to criticism. We provide a methodology for evaluating the counterfactuality of these protocols, based on an information-theoretical framework. More specifically, we make the assumption that any realistic quantum channel in MZI structures will have some weak uncontrolled interaction. We then use the Fisher information of this interaction to measure counterfactual violations. The measure is used to evaluate the suggested counterfactual communication protocol of H. Salih et al. [ Phys. Rev. Lett. 110, 170502 (2013)]. The protocol of D. R. M. Arvidsson-Shukur and C. H. W. Barnes [ Phys. Rev. A 94, 062303 (2016)], based on a different definition, is evaluated with a probability measure. Our results show that the definition of Arvidsson-Shukur and Barnes is satisfied by their scheme, while that of Salih et al. is only satisfied by perfect quantum channels. For realistic devices the latter protocol does not achieve its objective.

We derive a deterministic protocol to implement a general single-qubit positive operator-valued measure (POVM) on near-term circuit-based quantum computers. The protocol has a modular structure such that an $n$-element POVM is implemented as a sequence of $(n-1)$ circuit modules. Each module performs a two-element POVM. Two variations of the protocol are suggested—one optimal in terms of number of ancilla qubits, the other optimal in terms of number of qubit gate operations and quantum circuit depth. We use the protocol to implement two- and three-element POVMs on two publicly available quantum computing devices. The results we obtain suggest that implementing nontrivial POVMs could be within the reach of the current noisy quantum computing devices.

We have carried out both experimental and theoretical studies of the magnetic properties of thin films of oxygen-deficient EuO. Accurate control of the oxygen vacancy concentration in these films was achieved by sputter codeposition of Eu and ${\text{Eu}}_2{\text{O}}_3$. The films were characterized by superconducting quantum interference device, x-ray reflectometry and polarized neutron reflectometry and the magnetic moment was found to increase monotonically with oxygen vacancy concentration. The electronic structure of ${\text{EuO}}_{1-x}$ was calculated using density-functional theory $\left(\text{DFT}+U\right)$. In agreement with previous studies, these calculations show that oxygen vacancies act as $n$-type dopants in EuO and that the excess electrons preferentially populate the majority spin branch of the spin-polarized conduction band. The observed increase in the magnetic moment originating from these excess electrons was accurately determined experimentally and found to be in good agreement with our quantitative predictions.

Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or entanglement to sample the unitary $N_{\mathrm{tot}}$ times, the variance of the estimates can scale as $O(1/N_{\mathrm{tot}}^2)$, compared to the best “classical” strategy with $O(1/N_{\mathrm{tot}})$. The original algorithm for quantum phase estimation cannot be implemented on near-term hardware as it requires large-scale entangled probes and fault-tolerant quantum computing. Therefore, alternative algorithms have been introduced that rely on coherence and statistical inference. These algorithms produce quantum-boosted phase estimates without interprobe entanglement. This family of phase-estimation algorithms have, until now, never exhibited the possibility of achieving optimal scaling $O(1/N_{\mathrm{tot}}^2)$. Moreover, previous works have not considered the effect of noise on these algorithms. Here, we present a coherence-based phase-estimation algorithm which can achieve the optimal quadratic scaling in the mean absolute error and the mean squared error. In the presence of noise, our algorithm produces errors that approach the theoretical lower bound. The optimality of our algorithm stems from its adaptive nature: Each step is determined, iteratively, using a Bayesian protocol that analizes the results of previous steps.

Magnetic domain walls in patterned permalloy ring elements of different widths and thicknesses have been probed by magnetic force microscopy and micromagnetic simulations. We report the experimental observation of antivortex structures in single-layer magnetic rings, previously only theoretically predicted. Furthermore, vortex-antivortex chains are observed on occasion in wider rings that prefer a circulating flux closure state. It is possible that they are pinned transient states of the relaxation path from the magnetically saturated to the circulating flux closure state. Similar tendencies are seen in micromagnetic simulations implying that vortex-antivortex pair nucleation and annihilation are fundamental parts of the said relaxation. Finally we present a phase diagram of different domain-wall configurations as a function of ring width and thickness.