A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control

We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of which arbitrary transfer filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental filter-functions set suffices to characterize the error suppression capabilities of the control protocol in both the time and frequency domain. We prove that the resulting notion of filtering order reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the order of error cancellation, traditionally defined in the Magnus sense. Examples and implications are discussed.Comment: Paper plus supplementary material. 10 pages, 1 figure. Unnumbered equation between 2 and 3 corrected. Results are unchange

Total correlations as fully additive entanglement monotones

We generalize the strategy presented in Refs. [1, 2], and propose general conditions for a measure of total correlations to be an entanglement monotone using its pure (and mixed) convex-roof extension. In so doing, we derive crucial theorems and propose a concrete candidate for a total correlations measure which is a fully additive entanglement monotone.Comment: 8 pages, 3 figures. Title changed, new result

Multifunctional metal-organic frameworks : from academia to industrial applications

After three decades of intense and fundamental research on metal-organic frameworks (MOFs), is there anything left to say or to explain? The synthesis and properties of MOFs have already been comprehensively described elsewhere. It is time, however, to prove the nature of their true usability: technological applications based on these extended materials require development and implementation as a natural consequence of the up-to-known intensive research focused on their design and preparation. The current large number of reviews on MOFs emphasizes practical strategies to develop novel networks with varied crystal size, shape and topology, being mainly devoted to academic concerns. The present survey intends to push the boundaries and summarise the state-of-the-art on the preparation of promising (multi) functional MOFs in worldwide laboratories and their use as materials for industrial implementation. This review starts, on the one hand, to describe several tools and striking examples of remarkable and recent (multi) functional MOFs exhibiting outstanding properties (e.g., in gas adsorption and separation, selective sorption of harmful compounds, heterogeneous catalysis, luminescent and corrosion protectants). On the other hand, and in a second part, it intends to use these examples of MOFs to incite scientists to move towards the transference of knowledge from the laboratories to the industry. Within this context, we exhaustively review the many efforts of several worldwide commercial companies to bring functional MOFs towards the daily use, analysing the various patents and applications reported to date. Overall, this review goes from the very basic concepts of functional MOF engineering and preparation ending up in their industrial production on a large scale and direct applications in society

Communicating via ignorance: Increasing communication capacity via superposition of order

Classically, no information can be transmitted through a depolarising, that is a completely noisy, channel. We show that by combining a depolarising channel with another channel in an indefinite causal order---that is, when there is superposition of the order that these two channels were applied---it becomes possible to transmit significant information. We consider two limiting cases. When both channels are fully-depolarising, the ideal limit is communication of 0.049 bits; experimentally we achieve $(3.4{\pm}0.2){\times}10^{-2}$ bits. When one channel is fully-depolarising, and the other is a known unitary, the ideal limit is communication of 1 bit. We experimentally achieve 0.64${\pm}$0.02 bits. Our results offer intriguing possibilities for future communication strategies beyond conventional quantum Shannon theory

On the dynamics of initially correlated open quantum systems: theory and applications

We show that the dynamics of any open quantum system that is initially correlated with its environment can be described by a set of (or less) completely positive maps, where d is the dimension of the system. Only one such map is required for the special case of no initial correlations. The same maps describe the dynamics of any system-environment state obtained from the initial state by a local operation on the system. The reduction of the system dynamics to a set of completely positive maps allows known numerical and analytic tools for uncorrelated initial states to be applied to the general case of initially correlated states, which we exemplify by solving the qubit dephasing model for such states, and provides a natural approach to quantum Markovianity for this case. We show that this set of completely positive maps can be experimentally characterised using only local operations on the system, via a generalisation of noise spectroscopy protocols. As further applications, we first consider the problem of retrodicting the dynamics of an open quantum system which is in an arbitrary state when it becomes accessible to the experimenter, and explore the conditions under which retrodiction is possible. We also introduce a related one-sided or limited-access tomography protocol for determining an arbitrary bipartite state, evolving under a sufficiently rich Hamiltonian, via local operations and measurements on just one component. We simulate this protocol for a physical model of particular relevance to nitrogen-vacancy centres, and in particular show how to reconstruct the density matrix of a set of three qubits, interacting via dipolar coupling and in the presence of local magnetic fields, by measuring and controlling only one of them.Comment: 19 pages. Comments welcom