arXiv subjects
Publications and source records attributed to Cole Kelson-Packer.
We use linear programming to prove a separable version of Ky Fan's majorization relation for a sum of two operators that are each a tensor product of $n$ positive semidefinite operators. We give an example showing that such a relation does not hold in general for sums of three or more tensor products of three or more positive semidefinite operators.
The interplay of unitary evolution and projective measurements is a modern interest in the study of many-body entanglement. On the one hand, the competition between these two processes leads to the recently discovered measurement-induced phase transition (MIPT). On the other hand, measurement-based quantum computation (MBQC) is a well-known computational paradigm where measurements simulate unitary evolution by utilizing the entanglement of special resources such as the two-dimensional (2D) cluster state. The entanglement properties enabling MBQC may be attributed to symmetry-protected topological (SPT) orders, particularly subsystem-symmetric topological (SSPT) orders. It was recently found that the one-dimensional cluster state may be associated with an SPT phase in random circuits respecting a global $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry, and furthermore that all phase transitions in this scenario belong to the same universality class. As resources with greater computational power feature greater symmetry, it is fruitful to investigate further any relationship between levels of symmetry in MIPTs and MBQC. In this paper we investigate MIPTs on a torus with three levels of symmetry-respecting unitary evolution interspersed by measurements. Although we find two area-law phases and one volume-law phase with distinct entanglement structures for each ensemble, the phase transition from the volume-law phase to the area-law phase associated with the 2D SSPT cluster state has variable correlation length exponent $\nu$. Whereas $\nu\approx 0.90$ for unconstrained Clifford unitaries and $\nu\approx0.83$ for globally-symmetric Cliffords, subsystem-symmetric Cliffords feature a much smaller value $\nu\approx 0.38$. We discuss how these distinct $\nu$'s quantify spacetime response scales where quantum information is manipulated by single-qubit measurements as in MBQC.
Expanding upon our previous study of competing critical phenomena in black hole formation, we numerically investigate the behavior of dominant exponents across the boundary separating asymptotically dispersing and collapsing regions in a two-dimensional configuration space of initial data. We find that across the Type II boundary section the dominant exponent remains constant, equal to the reciprocal of Choptuik's well-known quasi-universal value, whereas across the Type I section the exponent noticeably varies. We postulate that this change reflects the existence of a third critical solution in addition to the two primary competing solutions, possibly another member of the family of metastable soliton stars constituting the Type I attractor.
The critical formation of low-mass black holes is a historical cornerstone of numerical General Relativity, with important implications in cosmology for censorship conjectures and the production of primordial black holes (PBHs). Concurrent with the surge in black hole observational physics in recent years has been an increased interest in these subjects. Critical formation is often suggested as a mechanism for PBH production, but it is possible that the existence of different types of critical processes potentially accompanying more realistic scenarios may affect this conclusion more than has been considered thus far. This paper numerically investigates, as a toy model, the interplay of multiple near-critical fields in the collapse of spherically symmetric scalar fields. It is found that a combination of type~I and type~II near-critical fields results in a kind of competition between their respective critical evolutions and propose. A heuristic explanation for this phenomenon is given employing ideas from the theory of dynamical systems.