相关论文: Breaking global symmetries with locality-preservin…
Model checking large networks of processes is challenging due to state explosion. In many cases, individual processes are isomorphic, but there is insufficient global symmetry to simplify model checking. This work considers the verification…
Quantum resources such as entanglement, information redundancy, and coherence enable revolutionary advantages but obey fundamental tradeoffs. We present a unified geometric constraint governing three core operational tasks: teleportation…
The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and…
Universality of local unitary transformations is one of the cornerstones of quantum computing with many applications and implications that go beyond this field. However, it has been recently shown that this universality does not hold in the…
We identify a non-local symmetry for Yang-Mills theories in 1+1 and 2+1 spacetime dimensions. The symmetry mixes a vector current with the gauge field. The current involved in the symmetry is required to satisfy certain constraints. The…
We present a strategy for the quantum simulation of many-body lattice models with constrained Hilbert spaces. We focus on lattice gauge theories (LGTs), which underlie a wide range of phenomena in particle physics, condensed matter, and…
We study a five-dimensional supergravity model with boundary-localized visible sector exhibiting anomaly-mediated supersymmetry breaking, in which the central requirements of sequestering and radius stabilization are achieved…
Generalized symmetries and their spontaneous breakdown serve as the fundamental concept to constrain the many-body entanglement structure, which allows us to characterize quantum phases of matter and emergent collective excitations. For…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
Quantum multifractality is a fundamental property of systems such as non-interacting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental…
We examined the possibility of recovering the losses of entanglement and the non-local advantage by using the local symmetric operations. The improvement efficiency may be increased by applying the symmetric operations on both qubits. The…
We consider the problem of creating locally supersymmetric theories in signature (10,2). The most natural algebraic starting point is the F-algebra, which is the de Sitter-type (10,2) extension of the super-Poincare algebra. We derive the…
Local gauge symmetries reduce to the identity on the observables, as well as on the physical states (apart from reflexes of the local gauge group topology) and therefore their use in Quantum Field Theory (QFT) asks for a justification of…
Topological order in two dimensions can be described in terms of deconfined quasiparticle excitations - anyons - and their braiding statistics. However, it has recently been realized that this data does not completely describe the situation…
Entanglement is an useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and is not locally possible. We focus on orthogonal states, which can…
We undertake a detailed study of the sets of multiplicity in a second countable locally compact group $G$ and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space $\mathcal{B}(L^2(G))$…
We investigate the local preservation of $A$-orthogonality at a point by $A$-bounded operators within the semi-Hilbertian framework induced by a positive operator $A$ on a Hilbert space $\mathbb{H}.$ We provide complete characterizations of…
Symmetries play a central role in single-particle localization. Recent research focused on many-body localized (MBL) systems, characterized by new kind of integrability, and by the area-law entanglement of eigenstates. We investigate the…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
Resource theories provide a general framework for the characterization of properties of physical systems in quantum mechanics and beyond. Here, we introduce methods for the quantification of resources in general probabilistic theories…