Related papers: Generalised tensors and traces
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…
We present a notion of generalized entanglement which goes beyond the conventional definition based on quantum subsystems. This is accomplished by directly defining entanglement as a property of quantum states relative to a distinguished…
Trace decreasing quantum operations naturally emerge in experiments involving postselection. However, the experiments usually focus on dynamics of the conditional output states as if the dynamics were trace preserving. Here we show that…
We introduce a generalization of entanglement based on the idea that entanglement is relative to a distinguished subspace of observables rather than a distinguished subsystem decomposition. A pure quantum state is entangled relative to such…
The expected indefinite causal structure in quantum gravity poses a challenge to the notion of entanglement: If two parties are in an indefinite causal relation of being spacelike and timelike, can they still be entangled? If so, how does…
New quantum distance is introduced as a half-sum of several singular values of difference between two density operators. This is, up to factor, the metric induced by so-called Ky Fan norm. The partitioned trace distances enjoy similar…
Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of…
It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multi-partite tensor product structure of the state-space and the…
The notion of a tensor captures three great ideas: equivariance, multilinearity, separability. But trying to be three things at once makes the notion difficult to understand. We will explain tensors in an accessible and elementary way…
A novel measure, quantumness of correlations is introduced here for bipartite states, by incorporating the required measurement scheme crucial in defining any such quantity. Quantumness coincides with the previously proposed measures in…
A 'process theory' is any theory of systems and processes which admits sequential and parallel composition. `Terminality' unifies normalisation of pure states, trace-preservation of CP-maps, and adding up to identity of positive operators…
Tensor universality often implies that multi-partite quantum-state processing is determined by what happens in totally disentangled cases. In independent systems relative time direction for the parts is arbitrary. This hints that time may…
The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role…
Quantum correlations, crucial for the advantage and advancement of quantum science and technology, arise from the impossibility of expressing a quantum state as a tensor product over a given set of parties. In this work, a generalized…
When we work with information from multiple sources, the formalism each employs to handle uncertainty may not be uniform. In order to be able to combine these knowledge bases of different formats, we need to first establish a common basis…
Standard quantum mechanics undeniably violates the notion of separability that classical physics accustomed us to consider as valid. By relating the phenomenon of quantum nonseparability to the all-important concept of potentiality, we…
We extend the usual process-theoretic view on locality and causality in subsystems (based on the tensor product case) to general quantum systems (i.e.\ possibly non-factor, finite-dimensional von Neumann algebras). To do so, we introduce a…
We show that Coecke's compositionality theorem for quantum information flow follows by the universal property of tensor products from the case in which all relevant states are totally disentangled, for which the proof is almost trivial.…
Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and…
In the reductionistic approach, mechanisms are divided into simpler parts interconnected in some standard way (e.g. by a mechanical transmission). We explore the possibility of porting reductionism in quantum operations. Conceptually, first…