Some families of density matrices for which separability is easily tested

We reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree condition") to test separability of density matrices of graphs. The condition is directly related to the PPT-criterion. We prove that the degree condition is necessary for separability and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest point graphs and perfect matchings. We observe that the degree condition appears to have value beyond density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. The paper isolates a number of problems and delineates further generalizations.Comment: 14 pages, 4 figure

Crypto collectibles, museum funding and openGLAM: Challenges, opportunities and the potential of non-fungible tokens (NFTs)

Non-fungible tokens (NFTs) make it technically possible for digital assets to be owned and traded, introducing the concept of scarcity in the digital realm for the first time. Resulting from this technical development, this paper asks the question, do they provide an opportunity for fundraising for galleries, libraries, archives and museums (GLAM), by selling ownership of digital copies of their collections? Although NFTs in their current format were first invented in 2017 as a means for game players to trade virtual goods, they reached the mainstream in 2021, when the auction house Christie’s held their first-ever sale exclusively for an NFT of a digital image, that was eventually sold for a record 69 million USD. The potential of NFTs to generate significant revenue for artists and museums by selling effectively a cryptographically signed copy of a digital image (similar to real-world limited editions, which are signed and numbered copies of a given artwork), has sparked the interest of the financially deprived museum and heritage sector with world-renowned institutions such as the Uffizi Gallery and the Hermitage Museum, having already employed NFTs in order to raise funds. Concerns surrounding the environmental impact of blockchain technology and the rise of malicious projects, exploiting previously digitised heritage content made available through OpenGLAM licensing, have attracted criticism over the speculative use of the technology. In this paper, we present the current state of affairs in relation to NFTs and the cultural heritage sector, identifying challenges, whilst highlighting opportunities that they create for revenue generation, in order to help address the ever-increasing financial challenges of galleries and museums

Classicality in discrete Wigner functions

Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that the only pure states having non-negative W for all such functions are stabilizer states, as conjectured by one of us [Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving non-negativity of W for all definitions of W form a subgroup of the Clifford group. This means pure states with non-negative W and their associated unitary dynamics are classical in the sense of admitting an efficient classical simulation scheme using the stabilizer formalism.Comment: 10 pages, 1 figur

Drinfeld Twists and Algebraic Bethe Ansatz of the Supersymmetric t-J Model

We construct the Drinfeld twists (factorizing $F$-matrices) for the supersymmetric t-J model. Working in the basis provided by the $F$-matrix (i.e. the so-called $F$-basis), we obtain completely symmetric representations of the monodromy matrix and the pseudo-particle creation operators of the model. These enable us to resolve the hierarchy of the nested Bethe vectors for the $gl(2|1)$ invariant t-J model.Comment: 23 pages, no figure, Latex file, minor misprints are correcte

Trace Formulae and Spectral Statistics for Discrete Laplacians on Regular Graphs (I)

Trace formulae for d-regular graphs are derived and used to express the spectral density in terms of the periodic walks on the graphs under consideration. The trace formulae depend on a parameter w which can be tuned continuously to assign different weights to different periodic orbit contributions. At the special value w=1, the only periodic orbits which contribute are the non back- scattering orbits, and the smooth part in the trace formula coincides with the Kesten-McKay expression. As w deviates from unity, non vanishing weights are assigned to the periodic walks with back-scatter, and the smooth part is modified in a consistent way. The trace formulae presented here are the tools to be used in the second paper in this sequence, for showing the connection between the spectral properties of d-regular graphs and the theory of random matrices.Comment: 22 pages, 3 figure

Traces on the Sklyanin algebra and correlation functions of the eight-vertex model

We propose a conjectural formula for correlation functions of the Z-invariant (inhomogeneous) eight-vertex model. We refer to this conjecture as Ansatz. It states that correlation functions are linear combinations of products of three transcendental functions, with theta functions and derivatives as coefficients. The transcendental functions are essentially logarithmic derivatives of the partition function per site. The coefficients are given in terms of a linear functional on the Sklyanin algebra, which interpolates the usual trace on finite dimensional representations. We establish the existence of the functional and discuss the connection to the geometry of the classical limit. We also conjecture that the Ansatz satisfies the reduced qKZ equation. As a non-trivial example of the Ansatz, we present a new formula for the next-nearest neighbor correlation functions.Comment: 35 pages, 2 figures, final versio

Exploring new business models for monetising digitisation beyond image licensing to promote adoption of OpenGLAM

Ever since the Rijksmuseum pioneered the OpenGLAM movement in 2011, releasing to the public domain images of artworks in its collection, several other museums have followed its lead, including the Metropolitan Museum of Art and the Finnish National Gallery. Although studies have demonstrated that OpenGLAM provides numerous benefits to museums, ranging from the dissemination of their collections to increased sponsorship opportunities, the movement’s adoption remains limited. One of the main barriers for joining OpenGLAM is the “fear of losing image licensing revenue”, as participant museums have yet to invent new business models to recover lost image fees. Current efforts to address this challenge include Rijksmuseum’s Rijksstudio, a Print-on-Demand service for creating and purchasing products featuring the museum’s artworks. However, Rijksstudio is very similar to existing Print-on-Demand solutions for museums, which have barely evolved over the last decade and, subsequently, it shares their limitations (e.g. offering wall art products only). Α radically different approach that integrates Print-on-Demand automation with emerging technologies (i.e. image recognition and progressive web applications) to generate revenue from digitisation is the Infinite Museum Store (IMS). In [citation] we presented the technical aspects and innovation features of IMS, as well as the results of a pilot study held at the State Museum of Contemporary Art (SMCA) in Thessaloniki, Greece, which demonstrated its significant potential for generating revenue from digitised collections. This paper examines IMS from a business model perspective. It focuses on aspects such as viability, maintenance and long-term sustainability, and investigates ways technical innovation can be applied and utilised as a business model that generates revenue from digitisation, helping promote wider adoption of OpenGLAM

Examining Mobile Print-on-Demand as an Alternative to Image Licensing for Monetising Digitisation to Promote OpenGLAM

Although studies have demonstrated that OpenGLAM provides numerous benefits to participant institutions, such as the dissemination of collections and increased sponsorship opportunities (Kapsalis, 2016; Kelly, 2013), the movement’s adoption remains limited. For museums and galleries, the fear of losing image fees, poses as one of the main barriers for participation (Kapsalis, 2016), since image licensing remains the most widely adopted method for monetising digitisation, despite the fact that its profitability has repeatedly been questioned (Tanner, 2004; Grosvenor, 2018). On-demand printing provides an alternative for generating revenue from digitised collections; however, print-on-demand solutions for museums appear to have stalled in the last decade, remaining almost exclusively a privilege of the well-resourced institutions. Α radically different implementation that takes advantage of emerging technologies (i.e. image recognition and progressive web applications) to provide a mobile print-on-demand solution for all museums with digitised collections is the Infinite Museum Store (IMS). In (Valeonti et al., 2018a) we presented the technical aspects and innovation features of IMS, as well as the results of a pilot study held at the State Museum of Contemporary Art (SMCA) in Thessaloniki, Greece, which demonstrated a significant potential for generating revenue from digitisation. Based on IMS, this paper examines mobile print-on-demand as an alternative solution for monetising digitisation, also exploring ways that smaller, not as well-resourced museums, can take advantage of on-demand printing to generate revenue from their digitised collections. With museums claiming that it is a "challenge . . . to keep on top of the large numbers of [image] requests” (Smith, 2009), developing alternative ways to monetise digitisation would not only allow more institutions to join OpenGLAM, but it would also contribute to improving their profitability

Form factor expansion for thermal correlators

We consider finite temperature correlation functions in massive integrable Quantum Field Theory. Using a regularization by putting the system in finite volume, we develop a novel approach (based on multi-dimensional residues) to the form factor expansion for thermal correlators. The first few terms are obtained explicitly in theories with diagonal scattering. We also discuss the validity of the LeClair-Mussardo proposal.Comment: 41 pages; v2: minor corrections, v3: minor correction