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n-Particle Quantum Statistics on Graphs

- J. Harrison, J. Keating, J. Robbins, A. Sawicki
- Mathematics, Physics
- 21 April 2013

We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum… Expand

Convexity of momentum map, Morse index, and quantum entanglement

- A. Sawicki, M. Oszmaniec, M. Ku's
- Mathematics, Physics
- 2 August 2012

We analyze from the topological perspective the space of all SLOCC (Stochastic Local Operations with Classical Communication) classes of pure states for composite quantum systems. We do it for both… Expand

Symplectic Geometry of Entanglement

- A. Sawicki, A. Huckleberry, M. Kus
- Physics, Mathematics
- 12 July 2010

We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of group… Expand

Universality of Single-Qudit Gates

- A. Sawicki, K. Karnas
- Mathematics, Physics
- 19 September 2016

We consider the problem of deciding if a set of quantum one-qudit gates $$\mathcal {S}=\{g_1,\ldots ,g_n\}\subset G$$S={g1,…,gn}⊂G is universal, i.e. if $${<}\mathcal {S}{>}$$ is dense in G, where G… Expand

When is a pure state of three qubits determined by its single-particle reduced density matrices?

- A. Sawicki, M. Walter, M. Ku's
- Mathematics, Physics
- 16 July 2012

Using techniques from symplectic geometry, we prove that a pure state of three qubits is up to local unitaries uniquely determined by its one-particle reduced density matrices exactly when their… Expand

Non-abelian Quantum Statistics on Graphs

- Tomasz Maciążek, A. Sawicki
- Mathematics, Physics
- Communications in Mathematical Physics
- 7 June 2018

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 general framework… Expand

How many invariant polynomials are needed to decide local unitary equivalence of qubit states

- Tomasz Maciążek, M. Oszmaniec, A. Sawicki
- Mathematics, Physics
- 16 May 2013

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 unitary (LU) equivalence… Expand

Universality of beamsplitters

- A. Sawicki
- Physics, Mathematics
- Quantum Inf. Comput.
- 29 July 2015

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Classical nonintegrability of a quantum chaotic SU(3) Hamiltonian system

- A. Sawicki, M. Ku's
- Mathematics, Physics
- 7 September 2009

Abstract We prove the nonintegrability of a model Hamiltonian system defined on the Lie algebra s u 3 suitable for investigation of connections between classical and quantum characteristics of chaos.

Are scattering properties of graphs uniquely connected to their shapes?

- Oleh Hul, M. Ławniczak, S. Bauch, A. Sawicki, M. Kus, L. Sirko
- Physics, Medicine
- Physical review letters
- 24 July 2012

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