Related papers: Unitary induced channels and Tsirelson's problem
In a well-known result [Werner2001], Werner classified all tight quantum teleportation and dense coding schemes, showing that they correspond to unitary error bases. Here tightness is a certain dimensional restriction: the quantum system to…
Quantum causality is an emerging field of study which has the potential to greatly advance our understanding of quantum systems. In this paper, we put forth a theoretical framework for merging quantum information science and causal…
We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg's QWEP conjecture) are essentially equivalent.…
Tsirelson's problem asks whether the commuting operator model for two-party quantum correlations is equivalent to the tensor-product model. We give a negative answer to this question by showing that there are non-local games which have…
In this note, we consider quantum correlations of bipartite systems having a slight interaction, and reinterpret Tsirelson's problem (and hence Kirchberg's and Connes's conjectures) in terms of finite-dimensional asymptotically commuting…
In this work we design a specific simulation tool for quantum channels which is based on the use of a control system. This allows us to simulate an average quantum channel which is expressed in terms of an ensemble of channels, even when…
Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of…
We study general ``normally'' distributed random unitary transformations. These distributions can be defined in terms of a diffusive random walk in the respective group manifold, formally underpinned by the concept of infinite divisibility.…
One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of quantum channel which is a basic building block of any data-transmitting or data-processing…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
We argue that the quantum-theoretical structures studied in several recent lines of research cannot be adequately described within the standard framework of quantum circuits. This is in particular the case whenever the combination of…
Compound channel models offer a simple and straightforward way of analyzing the stability of decoder design under model variations. With this work we provide a coding theorem for a large class of practically relevant compound channel…
Deep neural networks generalize well on unseen data though the number of parameters often far exceeds the number of training examples. Recently proposed complexity measures have provided insights to understanding the generalizability in…
We establish an operator algebra generalization of Watrous' theorem \cite{watrous2009} on mixing unital quantum channels (completely positive trace-preserving maps) with the completely depolarizing channel, wherein the more general objects…
Quantum kernel methods are one of the most explored approaches to quantum machine learning. However, the structural properties and inductive bias of quantum kernels are not fully understood. In this work, we introduce the notion of…
The purpose of this paper is to challenge the existing paradigm on which contemporary models of generalised uncertainty relations (GURs) are based, that is, the assumption of modified commutation relations. We review an array of theoretical…
Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
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…
The recognition that large classes of quantum many-body systems have limited entanglement in the ground and low-lying excited states led to dramatic advances in their numerical simulation via so-called tensor networks. However, global…