Recently, Halder \emph{et al.} [Phys. Rev. Lett. \textbf{122}, 040403 (2019)] proposed the concept strong nonlocality without entanglement: an orthogonal set of fully product states in multipartite quantum systems that is locally irreducible for every bipartition subsystems. As difficulty problem, most results are restricted to tripartite systems. Here we consider a weaker form called local dis...

As we know, unextendible product basis (UPB) is an incomplete basis whose members cannot be perfectly distinguished by local operations and classical communication. However, very little is known about those incomplete and locally indistinguishable product bases that are not UPBs. In this paper, we first construct a series of orthogonal product bases that are completable but not locally distingu...

In a series of recent papers, Simon Saunders, Fred Muller and Michael Seevinck have collectively argued, against the folklore, that some non-trivial version of Leibniz’s principle of the identity of indiscernibles is upheld in quantum mechanics. They argue that all particles—fermions, paraparticles, anyons, even bosons—may be weakly discerned by some physical relation. Here I show that their ar...

A garbling scheme is used to garble a circuit C and an input x in a way that reveals the output C(x) but hides everything else. An adaptively secure scheme allows the adversary to specify the input x after seeing the garbled circuit. Applebaum et al. (CRYPTO ’13) showed that in any garbling scheme with adaptive simulation-based security, the size of the garbled input must exceed the output size...

We show that a number of graph invariants are, even combined, insufficient to distinguish between nonisomorphic trees or general graphs. Among these are: the spectrum of eigenvalues (equivalently, the characteristic polynomial), the number of independent sets of all sizes or the number of connected subgraphs of all sizes. We therefore extend the classical theorem of Schwenk that almost every tr...