Related papers: Group theoretical approach to entanglement
We describe quantum mechanical entanglement in terms of compact quantum groups. We prove an analog of positivity of partial transpose (PPT) criterion and formulate a Horodecki-type Theorem.
We introduce a reversible theory of exact entanglement manipulation by establishing a necessary and sufficient condition for state transfer under trace-preserving transformations that completely preserve the positivity of partial transpose…
Entanglement is a key feature in many quantum technologies, including secure communication protocols and quantum computing. However, detecting it in mixed quantum states remains a challenging task. While the positive partial transposition…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…
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…
We present here an overview of our work concerning entanglement properties of composite quantum systems. The characterization of entanglement, i.e. the possibility to assert if a given quantum state is entangled with others and how much…
We construct a set of PPT (positive partial transpose) states and show that these PPT states are not separable, thus present a class of bound entangled quantum states.
In recent years considerable progress has been made towards developing a general theory of quantum entanglement. In particular, criteria to decide whether a given quantum state is entangled are of high theoretical and practical interest.…
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…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems and we introduce the notion of coefficient of quantum correlations. Our presentation stems from rigorous…
In this paper, we initiate a systematic study of entanglements of division fields from a group theoretic perspective. For a positive integer $n$ and a subgroup $G\subseteq \text{GL}_2(\mathbb{Z}/{n}\mathbb{Z})$ with surjective determinant,…
Inspired by its fundamental importance in quantum mechanics, we define and study the notion of entanglement for abstract physical theories, investigating its profound connection with the concept of superposition. We adopt the formalism of…
Entanglement entropy plays a variety of roles in quantum field theory, including the connections between quantum states and gravitation through the holographic principle. This article provides a review of entanglement entropy from a mixed…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing, which is known to be an NP-hard problem in general. Despite the proposed many methods such as the positive partial…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
This brief article discusses some aspects of quantum theory and their impact on popular culture. The basic features of quantum entanglement between two or more parties are introduced in a language suitable for a general audience, and…