Related papers: On a suggestion relating topological and quantum m…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
The topic of the review is the application of new ideas of unconventional quantum states to the physics of condensed matter, in particular of solid state, in the context of modern field theory. A comparison is made with classical papers on…
Few physical systems with topologies more complicated than simple gaussian linking have been explored in detail. Here we focus on examples with higher topologies in non-relativistic quantum mechanics and in QCD.
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
The coupling between two or more objects can generally be categorized as strong or weak. In cavity quantum electrodynamics for example, when the coupling strength is larger than the loss rate the coupling is termed strong, and otherwise it…
In this work, we present a quantum information framework for the entanglement behavior of the low energy quasiparticle (QP) excitations in various quantum phases in one-dimensional (1D) systems. We first establish an exact correspondence…
This is a survey article describing the relationship between quantum curves and topological recursion. A quantum curve is a Schr\"odinger operator-like noncommutative analogue of a plane curve which encodes (quantum) enumerative invariants…
We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On R^d the new theory differs from the original one by the spectrum of operators. Sometimes the local…
We give an elementary introduction to the notion of quantum entanglement between distinguishable parties and review a recent proposal about solid state quantum computation with spin-qubits in quantum dots. The indistinguishable character of…
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…
The essence of the famed long-range entanglement as revealed in topologically ordered state is the paradoxical coexistence of short-range correlation and nonlocal information that cannot be removed through constant-depth local quantum…
We discuss physical systems with topologies more complicated than simple gaussian linking. Our examples of these higher topologies are in non-relativistic quantum mechanics and in QCD.
This paper explores of the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang-Baxter Equation is a universal gate for quantum computing, in the…
We consider a quantum simulator of the Heisenberg chain with ferromagnetic interactions based on the two-component 1D Bose-Hubbard model at filling equal to two in the strong coupling regime. The entanglement properties of the ground state…
This article presents a local realistic interpretation of quantum entanglement. The entanglement is explained as innate interference between the non-empty state associated with the peaked piece of one particle and the empty states…
75 years after the term "entanglement" was coined to a peculiar feature inherent to quantum systems, the connection between quantum and classical mechanics remains an open problem. Drawing on recent results obtained in semiclassical…
Quantum entanglement describes superposition states in multi-dimensional systems, at least two partite, which cannot be factorized and are thus non-separable. Non-separable states exist also in classical theories involving vector spaces. In…
Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying…
In a topological description of elementary matter proposed by Bilson-Thompson, the leptons and quarks of a single generation, together with the electroweak gauge bosons, are represented as elements of the framed braid group of three…