Related papers: New techniques for bounding stabilizer rank
How complex is the structure of quantum geometry? In several approaches, the spacetime atoms are obtained by the SU(2) intertwiner called quantum tetrahedron. The complexity of this construction has a concrete consequence in recent efforts…
Understanding quantum phases and phase transitions in the presence of symmetries is a central objective of quantum many-body physics. A powerful modern paradigm for investigating this problem is topological holography, which relates…
Geometrical structures of quantum mechanics provide us with new insightful results about the nature of quantum theory. In this work we consider mixed quantum states represented by finite rank density operators. We review our geometrical…
We initiate an investigation into a notion of state complexity for discrete-variable quantum systems. Specifically, we propose an information-theoretic quantifier for the complexity of quantum states within the stabilizer formalism of…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Deciding if a given family of quantum states is topologically ordered is an important but nontrivial problem in condensed matter physics and quantum information theory. We derive necessary and sufficient conditions for a family of graph…
This thesis seeks to develop a general method for solving so-called quantum realizability problems, which are questions of the following form: under which conditions does there exist a quantum state exhibiting a given collection of…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
We demonstrate a new approach to the generation of custom entangled many-body states through reservoir engineering, using the symmetry properties of bosonic lattice systems coupled to a local squeezed reservoir. We outline an algorithm…
The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is…
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…
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…
We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be…
The standard stabilizer formalism provides a setting to show that quantum computation restricted to operations within the Clifford group are classically efficiently simulable: this is the content of the well-known Gottesman-Knill theorem.…
Full reconstruction of quantum states from measurement samples is often a prohibitively complex task, both in terms of the experimental setup and the scaling of the sample size with the system. This motivates the relatively easier task of…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
By applying the projector to the filled lattice eigenstates on a specific position, or applying the local electron annihilation operator on the many-body ground state, one can construct a quantum state localized around a specific position…