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In quantum information theory and statistical physics, symmetries of multiple copies, or replicas, of a system play a pivotal role. For unitary ensembles, these symmetries are encoded in the replicated commutant: the algebra of operators…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
The set of doubly-stochastic quantum channels and its subset of mixtures of unitaries are investigated. We provide a detailed analysis of their structure together with computable criteria for the separation of the two sets. When applied to…
Higher-dimensional quantum systems (qudits) offer advantages in information encoding, error resilience, and compact gate implementations, and naturally arise in platforms such as superconducting and solid-state systems. However, realistic…
Recent advancements in quantum computing, alongside successful deployments of quantum communication, hold promises for revolutionizing mobile networks. While Quantum Machine Learning (QML) presents opportunities, it contends with challenges…
We derive the general formula for the capacity of a noiseless quantum channel assisted by an arbitrary amount of noisy entanglement. In this capacity formula, the ratio of the quantum mutual information and the von Neumann entropy of the…
Within the C*-algebraic framework of the resolvent algebra for canonical quantum systems, the structure of oscillating lattice systems with bounded nearest neighbor interactions is studied in any number of dimensions. The global dynamics of…
Quantum Machine Learning (QML) has emerged as a promising field that combines the power of quantum computing with the principles of machine learning. One of the significant challenges in QML is dealing with noise in quantum systems,…
When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity -- a fundamental synergy which…
Cluster algebras were introduced by S. Fomin and A. Zelevinsky in math.RT/0104151; their study continued in math.RA/0208229, math.RT/0305434. This is a family of commutative rings designed to serve as an algebraic framework for the theory…
We compute the C*-algebra generated by a group of composition operators acting on certain reproducing kernel Hilbert spaces over the disk, where the symbols belong to a non-elementary Fuchsian group. We show that such a C*-algebra contains…
It is well-known that every commutative separable unital C*-algebra of real rank zero is a quotient of the C*-algebra of all compex continous functions defined on the Cantor cube. We prove a non-commutative version of this result by showing…
Universal control of quantum systems is a major goal to be achieved for quantum information processing, which demands thorough understanding of fundamental quantum mechanics and promises applications of quantum technologies. So far, most…
Distributed quantum information processing protocols such as quantum entanglement distillation and quantum state discrimination rely on local operations and classical communications (LOCC). Existing LOCC-based protocols typically assume the…
The gravitational-wave detector is a complex and sensitive collection of advanced instruments that are impacted not only by mechanical/electronics systems but also by the surrounding environment. Hence, it is of great importance to classify…
The standard C*-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does…
We study quantum channels with respect to their image, i.e., the image of the set of density operators under the action of the channel. We first characterize the set of quantum channels having polytopic images and show that additivity of…
The implementation of realistic quantum devices requires a solid understanding of the nonlocal resources present in quantum channels, and the effects of decoherence on them. Here we quantify nonlocality of bipartite quantum channels and…
The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole system-algebra. If the physical algebra commutes with the interaction…
To a given tiling a non commutative space and the corresponding C*-algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for…