Precision characterisation of two-qubit Hamiltonians via entanglement mapping

We show that the general Heisenberg Hamiltonian with non-uniform couplings can be characterised by mapping the entanglement it generates as a function of time. Identification of the Hamiltonian in this way is possible as the coefficients of each operator control the oscillation frequencies of the entanglement function. The number of measurements required to achieve a given precision in the Hamiltonian parameters is determined and an efficient measurement strategy designed. We derive the relationship between the number of measurements, the resulting precision and the ultimate discrete error probability generated by a systematic mis-characterisation, when implementing two-qubit gates for quantum computing.Comment: 6 Pages, 3 figure

Scheme for direct measurement of a general two-qubit Hamiltonian

The construction of two-qubit gates appropriate for universal quantum computation is of enormous importance to quantum information processing. Building such gates is dependent on accurate knowledge of the interaction dynamics between two qubit systems. This letter will present a systematic method for reconstructing the full two-qubit interaction Hamiltonian through experimental measures of concurrence. This not only gives a convenient method for constructing two qubit quantum gates, but can also be used to experimentally determine various Hamiltonian parameters in physical systems. We show explicitly how this method can be employed to determine the first and second order spin-orbit corrections to the exchange coupling in quantum dots.Comment: 4 Pages, 1 Figur

Quantum system characterization with limited resources

The construction and operation of large scale quantum information devices presents a grand challenge. A major issue is the effective control of coherent evolution, which requires accurate knowledge of the system dynamics that may vary from device to device. We review strategies for obtaining such knowledge from minimal initial resources and in an efficient manner, and apply these to the problem of characterization of a qubit embedded into a larger state manifold, made tractable by exploiting prior structural knowledge. We also investigate adaptive sampling for estimation of multiple parameters

Optimality of entropic uncertainty relations

The entropic uncertainty relation proven by Maassen and Uffink for arbitrary pairs of two observables is known to be non-optimal. Here, we call an uncertainty relation optimal, if the lower bound can be attained for any value of either of the corresponding uncertainties. In this work we establish optimal uncertainty relations by characterising the optimal lower bound in scenarios similar to the Maassen-Uffink type. We disprove a conjecture by Englert et al. and generalise various previous results. However, we are still far from a complete understanding and, based on numerical investigation and analytical results in small dimension, we present a number of conjectures.Comment: 24 pages, 10 figure

Games for query inseparability of description logic knowledge bases

We consider conjunctive query inseparability of description logic knowledge bases with respect to a given signature---a fundamental problem in knowledge base versioning, module extraction, forgetting and knowledge exchange. We give a uniform game-theoretic characterisation of knowledge base conjunctive query inseparability and develop worst-case optimal decision algorithms for fragments of Horn-ALCHI, including the description logics underpinning OWL 2 QL and OWL 2 EL. We also determine the data and combined complexity of deciding query inseparability. While query inseparability for all of these logics is P-complete for data complexity, the combined complexity ranges from P- to ExpTime- to 2ExpTime-completeness. We use these results to resolve two major open problems for OWL 2 QL by showing that TBox query inseparability and the membership problem for universal conjunctive query solutions in knowledge exchange are both ExpTime-complete for combined complexity. Finally, we introduce a more flexible notion of inseparability which compares answers to conjunctive queries in a given signature over a given set of individuals. In this case, checking query inseparability becomes NP-complete for data complexity, but the ExpTime- and 2ExpTime-completeness combined complexity results are preserved

Information-theoretic equilibrium and observable thermalization

To understand under which conditions thermodynamics emerges from the microscopic dynamics is the ultimate goal of statistical mechanics. Despite the fact that the theory is more than 100 years old, we are still discussing its foundations and its regime of applicability. A point of crucial importance is the definition of the notion of thermal equilibrium, which is given as the state that maximises the von Neumann entropy. Here we argue that it is necessary to propose a new way of describing thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise the notion of thermal equilibrium, for a given observable, via the maximisation of its Shannon entropy and highlight the thermal properties that such a principle heralds. The relation with Gibbs ensembles is brought to light. Furthermore, we apply such a notion of equilibrium to a closed quantum systems and prove that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, we bring to light an intimate connection of such a principle with the Eigenstate Thermalisation Hypothesis.Comment: Accepted by Scientific Repor

UNDERSTANDING PREPOSITIONS THROUGH COGNITIVE GRAMMAR. A CASE OF IN

Poly - semantic nature of prepositions has been discussed in linguistic literature and confirmed by language data. In the majority of research within cognitive linguistics prepositions have been approached as predicates organising entities in space, with less attention paid to the search for a meaning schema sanctioning the numerous uses. Cognitive Grammar analytic tools allow for the analysis which results in discovering one meaning schema sanctioning the uses of the English preposition in. The present analysis is based on the assumption that the meaning schema of in profiles a relation of conceptual enclosure between two symbolic structures, one of which conceptually fits in the other. Accordingly, I argue that the speaker employs in to structure a real scene not because one element of the scene can physically enclose the other one, but due to conceptual ‘fitting in’ holding between the predication ‘preceding’ the preposition and the one that ‘follows’. In formal terms, the usage of in is conditioned and sanctioned by compatibility of active zones in the predications used to form the complex language expression involved. Peculiarities of physical organization may be ignored in such conceptualisation, though the speaker can choose to encode all peculiarities of physical organisation of real world objects employing different linguistic devices