Epistemic vs Ontic Classification of quantum entangled states?

In this brief paper, starting from recent works, we analyze from conceptual point of view this basic question: can be the nature of quantum entangled states interpreted ontologically or epistemologically? According some works, the degrees of freedom (and the tool of quantum partitions) of quantum systems permit us to establish a possible classification between factorizables and entangled states. We suggest, that the "choice" of degree of freedom (or quantum partitions), even if mathematically justified introduces epistemic element, not only in the systems but also in their classification. We retain, instead, that there are not two classes of quantum states, entangled and factorizables, but only a single classes of states: the entangled states. In fact, the factorizable states become entangled for a different choice of their degrees of freedom (i.e. they are entangled with respect to other observables). In the same way, there are not partitions of quantum system which have an ontological superior status with respect to any other. For all these reasons, both mathematical tools utilized (i.e quantum partitions or degrees of freedom) are responsible of improper classification of quantum systems. Finally, we argue that we cannot speak about a classification of quantum systems: all the quantum states exhibit a unique objective nature, they are all entangled states

Balanced Judicious Bipartition is Fixed-Parameter Tractable

The family of judicious partitioning problems, introduced by Bollob\u27as and Scott to the field of extremal combinatorics, has been extensively studied from a structural point of view for over two decades. This rich realm of problems aims to counterbalance the objectives of classical partitioning problems such as Min Cut, Min Bisection and Max Cut. While these classical problems focus solely on the minimization/maximization of the number of edges crossing the cut, judicious (bi)partitioning problems ask the natural question of the minimization/maximization of the number of edges lying in the (two) sides of the cut. In particular, Judicious Bipartition (JB) seeks a bipartition that is "judicious" in the sense that neither side is burdened by too many edges, and Balanced JB also requires that the sizes of the sides themselves are "balanced" in the sense that neither of them is too large. Both of these problems were defined in the work by Bollob\u27as and Scott, and have received notable scientific attention since then. In this paper, we shed light on the study of judicious partitioning problems from the viewpoint of algorithm design. Specifically, we prove that BJB is FPT (which also proves that JB is FPT)