Related papers: Generalised tensors and traces
We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…
We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure…
What does it mean for one quantum process to be more disordered than another? Here we provide a precise answer to this question in terms of a quantum-mechanical generalization of majorization. The framework admits a complete description in…
Generic computability has been studied in group theory and we now study it in the context of classical computability theory. A set A of natural numbers is generically computable if there is a partial computable function f whose domain has…
A measure of quantum non-Markovianity for an open system dynamics, based on revivals of the distinguishability between system states, has been introduced in the literature using the trace distance as quantifier for distinguishability.…
We show that in principle, $N$-partite unitary transformations can be perfectly discriminated under local measurement and classical communication (LOCC) despite of their nonlocal properties. Based on this result, some related topics,…
Classical tensors, the familiar mathematical objects denoted by symbols such as $t_{i}$, $t^{ij}$ and $t_{k}^{ij}$, are usually interpreted either as 'coordinatizable objects' with coordinates changing in a specific way under a change of…
We discuss conditional expectations that can be used as generalizations of the partial trace for quantum systems with an infinite-dimensional Hilbert space of states.
General relativity and quantum mechanics have both revealed the relativity of certain notions that were previously thought to be absolute. I clarify the precise sense in which these theories are relational, and I argue that the various…
Consistent tensor products on auxiliary spaces, hereafter denoted "fusion procedures", are defined for general quadratic algebras, non-dynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures…
Tensor models are measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as additionally to the…
The so-called quantum measurement problems are solved from a new perspective. One of the main observations is that the basic entities of our world are {\it particles}, elementary or composite. It follows that each elementary process, hence…
Sequences of commuting quantum operators can be parallelized using entanglement. This transformation is behind some optimal quantum metrology protocols and recent results on quantum circuit complexity. We show that dephasing quantum maps in…
We provide a systematic approach to quantum mechanics from an information-theoretic perspective using the language of tensor networks. Our formulation needs only a single kind of object, so-called positive *-tensors. Physical models…
We consider quantum quenches in integrable systems where complete factorisation of scattering, transmission and particle creation processes is assumed at all times. We show that under this assumption, the simultaneous transmission and…
A correspondence is established between the elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the hardware and dynamical operations of neural networks. The correspondence is framed as a general…
Causal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory…
Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this…
We present a generalized Schmidt decomposition for a pure system with any number of two-level subsystems. The basis is symmetric under the permutation of the parties and is derived from the product state defining the injective tensor norm…
Can quantum theory be applied on all scales? While there are many arguments for the universality of quantum theory, this question remains a subject of debate. It is unknown how far the existence of macroscopic irreversibility can be derived…