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Oliver Rudolph

Publications and source records attributed to Oliver Rudolph.

At least 19 recordsLinked to original sources

Enhancing Manufacturing Knowledge Access with LLMs and Context-aware Prompting

Knowledge graphs (KGs) have transformed data management within the manufacturing industry, offering effective means for integrating disparate data sources through shared and structured conceptual schemas. However, harnessing the power of KGs can be daunting for non-experts, as it often requires formulating complex SPARQL queries to retrieve specific information. With the advent of Large Language Models (LLMs), there is a growing potential to automatically translate natural language queries into the SPARQL format, thus bridging the gap between user-friendly interfaces and the sophisticated architecture of KGs. The challenge remains in adequately informing LLMs about the relevant context and structure of domain-specific KGs, e.g., in manufacturing, to improve the accuracy of generated queries. In this paper, we evaluate multiple strategies that use LLMs as mediators to facilitate information retrieval from KGs. We focus on the manufacturing domain, particularly on the Bosch Line Information System KG and the I40 Core Information Model. In our evaluation, we compare various approaches for feeding relevant context from the KG to the LLM and analyze their proficiency in transforming real-world questions into SPARQL queries. Our findings show that LLMs can significantly improve their performance on generating correct and complete queries when provided only the adequate context of the KG schema. Such context-aware prompting techniques help LLMs to focus on the relevant parts of the ontology and reduce the risk of hallucination. We anticipate that the proposed techniques help LLMs to democratize access to complex data repositories and empower informed decision-making in manufacturing settings.

cs.AI

Smallest disentangling state spaces for general entangled bipartite quantum states

Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct `smallest' local sets of operators that achieve this. In other words, given an arbitrary bipartite quantum state we construct convex sets of local operators that allow for a separable decomposition, but that cannot be made smaller while continuing to do so. We then consider two further variants of the problem where the local state spaces are required to contain the local quantum states, and obtain solutions for a variety of cases including a region of pure states around the maximally entangled state. The methods involve calculating certain forms of cross norm. Two of the variants of the problem have a strong relationship to theorems on ensemble decompositions of positive operators, and our results thereby give those theorems an added interpretation. The results generalise those obtained in our previous work on this topic [New J. Phys. 17, 093047 (2015)].

quant-ph

Smallest state spaces for which bipartite entangled quantum states are separable

According to usual definitions, entangled states cannot be given a separable decomposition in terms of products of local density operators. If we relax the requirement that the local density operators be positive, then an entangled quantum state may admit a separable decomposition in terms of more general sets of single-system operators. This form of separability can be used to construct classical models and simulation methods when only restricted set of measurements are available. With such motivations in mind, we ask what are the smallest such sets of local operators such that a pure bipartite entangled quantum state becomes separable? We find that in the case of maximally entangled states there are many inequivalent solutions, including for example the sets of phase point operators that arise in the study of discrete Wigner functions. We therefore provide a new way of interpreting these operators, and more generally, provide an alternative method for constructing local hidden variable models for entangled quantum states under subsets of quantum measurements.

quant-ph

Families of pure PEPS with efficiently simulatable local hidden variable models for most measurements

An important problem in quantum information theory is to understand what makes entangled quantum systems non-local or hard to simulate efficiently. In this work we consider situations in which various parties have access to a restricted set of measurements on their particles, and construct entangled quantum states that are essentially classical for those measurements. In particular, given any set of local measurements on a large enough Hilbert space whose dual strictly contains (i.e. contains an open neighborhood of) a pure state, we use the PEPS formalism and ideas from generalized probabilistic theories to construct pure multiparty entangled states that have (a) local hidden variable models, and (b) can be efficiently simulated classically. We believe that the examples we construct cannot be efficiently classically simulated using previous techniques. Without the restriction on the measurements, the states that we construct are non-local, and in some proof-of-principle cases are universal for measurement based quantum computation.

quant-ph

On extremal quantum states of composite systems with fixed marginals

We study the convex set of all bipartite quantum states with fixed marginal states. The extremal states in this set have recently been characterized by Parthasarathy [Ann. Henri Poincaré (to appear), quant-ph/0307182, [1]]. Here we present an alternative necessary and sufficient condition for a state with given marginals to be extremal. Our approach is based on a canonical duality between bipartite states and a certain class of completely positive maps and has the advantage that it is easier to check and to construct explicit examples of extremal states. In dimension 2 x 2 we give a simple new proof for the fact that all extremal states with maximally mixed marginals are precisely the projectors onto maximally entangled wave functions. We also prove that in higher dimension this does not hold and construct an explicit example of an extremal state with maximally mixed marginals in dimension 3 x 3 that is not maximally entangled. Generalizations of this result to higher dimensions are also discussed.

quant-ph

Some Properties of the Computable Cross Norm Criterion for Separability

The computable cross norm (CCN) criterion is a new powerful analytical and computable separability criterion for bipartite quantum states, that is also known to systematically detect bound entanglement. In certain aspects this criterion complements the well-known Peres positive partial transpose (PPT) criterion. In the present paper we study important analytical properties of the CCN criterion. We show that in contrast to the PPT criterion it is not sufficient in dimension 2 x 2. In higher dimensions we prove theorems connecting the fidelity of a quantum state with the CCN criterion. We also analyze the behaviour of the CCN criterion under local operations and identify the operations that leave it invariant. It turns out that the CCN criterion is in general not invariant under local operations.

quant-ph

The Uniqueness Theorem for Entanglement Measures

We explore and develop the mathematics of the theory of entanglement measures. After a careful review and analysis of definitions, of preliminary results, and of connections between conditions on entanglement measures, we prove a sharpened version of a uniqueness theorem which gives necessary and sufficient conditions for an entanglement measure to coincide with the reduced von Neumann entropy on pure states. We also prove several versions of a theorem on extreme entanglement measures in the case of mixed states. We analyse properties of the asymptotic regularization of entanglement measures proving, for example, convexity for the entanglement cost and for the regularized relative entropy of entanglement.

quant-ph

Further results on the cross norm criterion for separability

In the present paper the cross norm criterion for separability of density matrices is studied. In the first part of the paper we determine the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the second part we show that the greatest cross norm criterion induces a novel computable separability criterion for bipartite systems. This new criterion is a necessary but in general not a sufficient criterion for separability. It is shown, however, that for all pure states, for Bell diagonal states, for Werner states in dimension d=2 and for isotropic states in arbitrary dimensions the new criterion is necessary and sufficient. Moreover, it is shown that for Werner states in higher dimensions (d greater than 2), the new criterion is only necessary.

quant-ph

A new class of entanglement measures

We introduce new entanglement measures on the set of density operators on tensor product Hilbert spaces. These measures are based on the greatest cross norm on the tensor product of the sets of trace class operators on Hilbert space. We show that they satisfy the basic requirements on entanglement measures discussed in the literature, including convexity, invariance under local unitary operations and non-increase under local quantum operations and classical communication.

math-ph

A uniqueness theorem for entanglement measures

We obtain a mathematically simple characterization of all functionals coinciding with the von Neumann reduced entropy on pure states based on the Khinchin-Faddeev axiomatization of Shannon entropy and give a physical interpretation of the axioms in terms of entanglement.

quant-ph

On unentangled Gleason theorems for quantum information theory

It is shown here that a strengthening of Wallach's Unentangled Gleason Theorem can be obtained by applying results of the present authors on generalised Gleason theorems for quantum multi-measures arising from investigations of quantum decoherence functionals.

quant-ph

Super Hilbert Spaces

The basic mathematical framework for super Hilbert spaces over a Grassmann algebra with a Grassmann number-valued inner product is formulated. Super Hilbert spaces over infinitely generated Grassmann algebras arise in the functional Schroedinger representation of spinor quantum field theory in a natural way.

math-ph

A separability criterion for density operators

We give a necessary and sufficient condition for a mixed quantum mechanical state to be separable. The criterion is formulated as a boundedness condition in terms of the greatest cross norm on the tensor product of trace class operators.

quant-ph

The representation theory of decoherence functionals in history quantum theories

In the first part of this paper the general perspective of history quantum theories is reviewed. History quantum theories provide a conceptual and mathematical framework for formulating quantum theories without a globally defined Hamiltonian time evolution and for introducing the concept of space time event into quantum theory. On a mathematical level a history quantum theory is characterized by the space of histories, which represent the space time events, and by the space of decoherence functionals which represent the quantum mechanical states in the history approach. The second part of this paper is devoted to the study of the structure of the space of decoherence functionals for some physically reasonable spaces of histories in some detail. The temporal reformulation of standard Hamiltonian quantum theories suggests to consider the case that the space of histories is given by (i) the lattice of projection operators on some Hilbert space or -- slightly more general -- (ii) the set of projection operators in some von Neumann algebra. In the case (i) the conditions are identified under which decoherence functionals can be represented by, respectively, trace class operators, bounded operators or families of trace class operators on the tensor product of the underlying Hilbert space by itself. Moreover we shall discuss the naturally arising representations of decoherence functionals as sesquilinear forms. The paper ends with a discussion of the consequences of the results for the general axiomatic framework of history theories.

math-ph

Temporal Quantum Theory

We propose a framework for temporal quantum theories for the purpose of describing states and observables associated with extended regions of space time quantum mechanically. The proposal is motivated by Isham's history theories. We discuss its relation to Isham's history theories and to standard quantum mechanics. We generalize the Isham-Linden information entropy to the present context.

math-ph

Homogeneous decoherence functionals in standard and history quantum mechanics

General history quantum theories are quantum theories without a globally defined notion of time. Decoherence functionals represent the states in the history approach and are defined as certain bivariate complex-valued functionals on the space of all histories. However, in practical situations -- for instance in the history formulation of standard quantum mechanics -- there often is a global time direction and the homogeneous decoherence functionals are specified by their values on the subspace of homogeneous histories. In this work we study the analytic properties of (i) the standard decoherence functional in the history version of standard quantum mechanics and (ii) homogeneous decoherence functionals in general history theories. We restrict ourselves to the situation where the space of histories is given by the lattice of projections on some Hilbert space H. Among other things we prove the non-existence of a finitely valued extension for the standard decoherence functional to the space of all histories, derive a representation for the standard decoherence functional as an unbounded quadratic form with a natural representation on a Hilbert space and prove the existence of an Isham-Linden-Schreckenberg (ILS) type representation for the standard decoherence functional.

math-ph

On Tracial Operator Representations of Quantum Decoherence Functionals

A general `quantum history theory' can be characterised by the space of histories and by the space of decoherence functionals. In this note we consider the situation where the space of histories is given by the lattice of projection operators on an infinite dimensional Hilbert space $H$. We study operator representations for decoherence functionals on this space of histories. We first give necessary and sufficient conditions for a decoherence functional being representable by a trace class operator on $H \otimes H$, an infinite dimensional analogue of the Isham-Linden-Schreckenberg representation for finite dimensions. Since this excludes many decoherence functionals of physical interest, we then identify the large and physically important class of decoherence functionals which can be represented, canonically, by bounded operators on $H \otimes H$.

quant-ph