Related papers: A recipe for topological observables of density ma…
Quantum-enhanced metrology can be achieved by entangling a probe with an auxiliary system, passing the probe through an interferometer, and subsequently making measurements on both the probe and auxiliary system. Conceptually, this…
Bundle gerbes are simple examples of higher geometric structures that show their utility in dealing with topological subtleties of physical theories. I review a recent construction of torsion topological invariants for condensed matter…
The mixed states are important in quantum optics since they frequently appear in the decoherence problems. When one of the components of the system is prepared in the mixed state and the evolution operator of this system is not available,…
Topological aspects represent currently a boosting area in condensed matter physics. Yet there are very few suggestions for technical applications of topological phenomena. Still, the most important is the calibration of resistance…
We consider families of invertible many-body quantum states in $d$ spatial dimensions that are parameterized over some parameter space $X$. The space of such families is expected to have topologically distinct sectors classified by the…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
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…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
The predictions of mean-field electrodynamics can now be probed using direct numerical simulations of random flows and magnetic fields. When modelling astrophysical MHD, it is important to verify that such simulations are in agreement with…
Topological phases support edge states that can be robust to material deformations and other perturbations. While well-studied in quantum systems, topological phases have also been observed in stochastic and biochemical systems, yet it…
We define topological invariants in terms of the ground states wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magneto-electric $\theta$ term in…
Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological…
If an extensive partition in two dimensions yields a gapful entanglement spectrum of the reduced density matrix, the Berry curvature based on the corresponding entanglement eigenfunction defines the Chern number. We propose such an…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
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 persistence of sub-Planck structure in phase space with loss of coherence is demonstrated in a mixed state, which comprises two terms in the density matrix. Its utility in carrying out Heisenberg-limited measurement and quantum…
The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective…
The classification of topological phases of matter is fundamental to understand and characterize the properties of quantum materials. In this paper we study phases of matter in one-dimensional open quantum systems. We define two mixed…
Preparing highly entangled quantum states is a key challenge in quantum metrology and quantum information science. Measurements, especially those of global observables, offer a simple and efficient way to generate entanglement between…
With any state of a multipartite quantum system its separability polytope is associated. This is an algebro-topological object (non-trivial only for mixed states) which captures the localisation of entanglement of the state. Particular…