Cloning of observables

We introduce the concept of cloning for classes of observables and classify cloning machines for qubit systems according to the number of parameters needed to describe the class under investigation. A no-cloning theorem for observables is derived and the connections between cloning of observables and joint measurements of noncommuting observables are elucidated. Relationships with cloning of states and non-demolition measurements are also analysed.

Tests of multimode quantum nonlocality with homodyne measurements

We investigate the violation of local realism in Bell tests involving homodyne measurements performed on multimode continuous-variable states. By binning the measurement outcomes in an appropriate way, we prove that the Mermin-Klyshko inequality can be violated by an amount that grows exponentially with the number of modes. Furthermore, the maximum violation allowed by quantum mechanics can be attained for any number of modes, albeit requiring a quantum state whose generation is hardly practicable. Interestingly, this exponential increase of the violation holds true even for simpler states, such as multipartite GHZ states. The resulting benefit of using more modes is shown to be significant in practical multipartite Bell tests by analyzing the increase of the robustness to noise with the number of modes. In view of the high efficiency achievable with homodyne detection, our results thus open a possible way to feasible loophole-free Bell tests that are robust to experimental imperfections. We provide an explicit example of a three-mode state (a superposition of coherent states) which results in a significantly high violation of the Mermin-Klyshko inequality (around 10%) with homodyne measurements.

Detecting the work statistics through Ramsey-like interferometry

Out-of-equilibrium statistical mechanics is attracting considerable interest due to the recent advances in the control and manipulations of systems at the quantum level. Recently, an interferometric scheme for the detection of the characteristic function of the work distribution following a time-dependent process has been proposed [L. Mazzola et al., Phys. Rev. Lett. 110 (2013) 230602]. There, it was demonstrated that the work statistics of a quantum system undergoing a process can be reconstructed by effectively mapping the characteristic function of work on the state of an ancillary qubit. Here, we expand that work in two important directions. We first apply the protocol to an interesting specific physical example consisting of a superconducting qubit dispersively coupled to the field of a microwave resonator, thus enlarging the class of situations for which our scheme would be key in the task highlighted above. We then account for the interaction of the system with an additional one (which might embody an environment), and generalize the protocol accordingly.

Vector bundles on the projective line and finite domination of chain complexes

We present an algebro-geometric approach to a theorem on finite domination of chain complexes over a Laurent polynomial ring. The approach uses extension of chain complexes to sheaves on the projective line, which is governed by a K-theoretical obstruction.

Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Local operator multipliers and positivity

We establish an unbounded version of Stinespring's Theorem and a lifting result for Stinespring representations of completely positive modular maps defined on the space of all compact operators. We apply these results to study positivity for Schur multipliers. We characterise positive local Schur multipliers, and provide a description of positive local Schur multipliers of Toeplitz type. We introduce local operator multipliers as a non-commutative analogue of local Schur multipliers, and characterise them extending both the characterisation of operator multipliers from [16] and that of local Schur multipliers from [27]. We provide a description of the positive local operator multipliers in terms of approximation by elements of canonical positive cones.

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

We consider the non-equilibrium dynamics of a simple system consisting of interacting spin-1/2 particles subjected to a collective damping. The model is close to situations that can be engineered in hybrid electro/opto-mechanical settings. Making use of large-deviation theory, we find a Gallavotti-Cohen symmetry in the dynamics of the system as well as evidence for the coexistence of two dynamical phases with different activity levels. We show that additional damping processes smooth out this behavior. Our analytical results are backed up by Monte Carlo simulations that reveal the nature of the trajectories contributing to the different dynamical phases.

Coherent and stochastic contributions of compound resonances in atomic processes: Electron recombination, photoionization, and scattering

In open-shell atoms and ions, processes such as photoionization, combination (Raman) scattering, electron scattering, and recombination are often mediated by many-electron compound resonances. We show that their interference (neglected in the independent-resonance approximation) leads to a coherent contribution, which determines the energy-averaged total cross sections of electron- and photon-induced reactions obtained using the optical theorem. In contrast, the partial cross sections (e.g., electron recombination or photon Raman scattering) are dominated by the stochastic contributions. Thus, the optical theorem provides a link between the stochastic and coherent contributions of the compound resonances. Similar conclusions are valid for reactions via compound states in molecules and nuclei.

Sets of p-multiplicity in locally compact groups

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E∗={(s,t):ts−1∈E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone–von Neumann Theorem.

Comments on “Wirtinger-based integral inequality: Application to time-delay systems [Automatica 49 (2013) 2860–2866]”

In a recent paper (Automatica 49 (2013) 2860–2866), the Wirtinger-based inequality has been introduced to derive tractable stability conditions for time-delay or sampled-data systems. We point out that there exist two errors in Theorem 8 for the stability analysis of sampled-data systems, and the correct theorem is presented.

Thermodynamics of trajectories and local fluctuation theorems for harmonic quantum networks

We present a general method to undertake a thorough analysis of the thermodynamics of the quantum jump trajectories followed by an arbitrary quantum harmonic network undergoing linear and bilinear dynamics. The approach is based on the phase-space representation of the state of a harmonic network. The large deviation function associated with this system encodes the full counting statistics of exchange and also allows one to deduce for fluctuation theorems obeyed by the dynamics. We illustrate the method showing the validity of a local fluctuation theorem about the exchange of excitations between a restricted part of the environment (i.e., a local bath) and a harmonic network coupled with different schemes.

Comparisons of anterior segment biometry between Chinese and Caucasians using anterior segment optical coherence tomography.

PURPOSE: To compare anterior segment parameters between eyes of Chinese and Caucasians using anterior segment optical coherence tomography and to evaluate the association between these parameters and anterior chamber angle width between the two ethnic groups. METHODS: 60 Chinese and 60 Caucasians, 30 with open angles and 30 with narrow angles (defined as Shaffer grade < or =2 in > or =3 quadrants during dark room gonioscopy) in each group, were consecutively enrolled. One eye of each subject was randomly selected for imaging in a completely darkened room. Measurements, including anterior chamber depth (ACD), scleral spur-to-scleral spur distance (anterior chamber width (ACW)), anterior chamber angle width, iris convexity and iris thickness, were compared between the groups. The associations between angle opening distance and biometric measurements were evaluated with univariate and multivariate regression analyses. RESULTS: There were no differences in age, axial length, anterior chamber angle measurements, pupil diameter and iris convexity between Chinese and Caucasians in both open-angle and narrow-angle groups. However, the ACD and ACW were smaller and the iris was thicker in Chinese. In the multivariate analysis, the ACD was the most influential biometric parameter for angle opening distance in both Chinese and Caucasians. After adjusting the effects of axial length, age and sex, ACD and ACW were significantly smaller in Chinese. CONCLUSIONS: Chinese eyes had smaller ACD, smaller ACW and greater iris thickness than Caucasians. ACD was the most influential parameter in determining the angle width in both ethnic groups.