22 citations · 135 across the 16 of their papers we have counts for
16 papers
Natural orbitals and their occupation numbers for free anyons in the magnetic gauge
Jerzy Cioslowski, Oliver M. Brown, Tomasz Maciazek
We investigate the properties of natural orbitals and their occupation numbers of the ground state of two non-interacting anyons characterised by the fractional statistics paramete…
Extending the planar theory of anyons to quantum wire networks
Tomasz Maciazek, Mia Conlon, Gert Vercleyen +1
The braiding of the worldlines of particles restricted to move on a network (graph) is governed by the graph braid group, which can be strikingly different from the standard braid…
Can one hear a matrix? Recovering a real symmetric matrix from its spectral data
Tomasz Maciążek, Uzy Smilansky
The spectrum of a real and symmetric matrix determines the matrix up to unitary equivalence. More spectral data is needed together with some sign indicators to remove t…
Repulsively diverging gradient of the density functional in the Reduced Density Matrix Functional Theory
Tomasz Maciążek
The Reduced Density Matrix Functional Theory (RDMFT) is a remarkable tool for studying properties of ground states of strongly interacting quantum many body systems. As it gives ac…
Designing locally maximally entangled quantum states with arbitrary local symmetries
Oskar Słowik, Adam Sawicki, Tomasz Maciążek
One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local…
Universal properties of anyon braiding on one-dimensional wire networks
Tomasz Maciążek, Byung Hee An
We demonstrate that anyons on wire networks have fundamentally different braiding properties than anyons in 2D. Our analysis reveals an unexpectedly wide variety of possible non-ab…
Geometric presentations of braid groups for particles on a graph
Byung Hee An, Tomasz Maciazek
We study geometric presentations of braid groups for particles that are constrained to move on a graph, i.e. a network consisting of nodes and edges. Our proposed set of generators…
Implications of pinned occupation numbers for natural orbital expansions. II: Rigorous derivation and extension to non-fermionic systems
Tomasz Maciążek, Adam Sawicki, David Gross +2
We have explained and comprehensively illustrated in Part I that the generalized Pauli constraints suggest a natural extension of the concept of active spaces. In the present Part…
Implications of pinned occupation numbers for natural orbital expansions. I: Generalizing the concept of active spaces
Christian Schilling, Carlos L. Benavides-Riveros, Alexandre Lopes +2
The concept of active spaces simplifies the description of interacting quantum many-body systems by restricting to a neighbourhood of active orbitals around the Fermi level. The re…
Non-abelian Quantum Statistics on Graphs
Tomasz Maciążek, Adam Sawicki
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a…
Asymptotic properties of entanglement polytopes for large number of qubits
Tomasz Maciążek, Adam Sawicki
Entanglement polytopes have been recently proposed as the way of witnessing the SLOCC multipartite entanglement classes using single particle information. We present first asymptot…
Quantum marginals from pure doubly excited states
Tomasz Maciazek, Valdemar Tsanov
The possible spectra of one-particle reduced density matrices that are compatible with a pure multipartite quantum system of finite dimension form a convex polytope. We introduce a…
Multipartite quantum correlations: symplectic and algebraic geometry approach
A. Sawicki, T. Maciążek, M. Oszmaniec +3
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating…
On momentum images of representations and secant varieties
Elitza Hristova, Tomasz Maciazek, Valdemar V. Tsanov
Let be a connected compact semisimple group and be an irreducible unitary representation with highest weight . We study the momentum map $μ:\mathbb P(V_λ)\to\mathfrak…
Critical points of the linear entropy for pure L-qubit states
Tomasz Maciazek, Adam Sawicki
We present a substancially improved version of the method proposed in Sawicki et al (2012, 2014) for finding critical points of the linear entropy for L-qubit system. The new appro…
How many invariant polynomials are needed to decide local unitary equivalence of qubit states?
Tomasz Maciazek, Michał Oszmaniec, Adam Sawicki
Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitar…