The laplacian of a graph as a density matrix: a basic combinatorial approach to separability of mixed states

We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that the density matrix of a graph can be always written as a uniform mixture of pure density matrices of graphs. We consider the von Neumann entropy of these matrices and we characterize the graphs for which the minimum and maximum values are attained. We then discuss the problem of separability by pointing out that separability of density matrices of graphs does not always depend on the labelling of the vertices. We consider graphs with a tensor product structure and simple cases for which combinatorial properties are linked to the entanglement of the state. We calculate the concurrence of all graph on four vertices representing entangled states. It turns out that for some of these graphs the value of the concurrence is exactly fractional.Comment: 20 pages, 11 figure

The disentangling power of unitaries

We define the disentangling power of a unitary operator in a similar way as the entangling power defined by Zanardi et al. [P. Zanardi, C. Zalka, L. Faoro, Phys. Rev. A 62 (2000) 030301(R), quant-ph/0005031]. A general formula is derived and it is shown that both quantities are directly proportional. All results concerning the entangling power can simply be translated into similar statements for the disentangling power. In particular, the disentangling power is maximal for certain permutations derived from orthogonal Latin squares. These permutations can therefore be interpreted as those that distort entanglement in a maximal way

Is there a need for greater integration and shift in policy to tackle food waste? Insights from a review of European Union legislations

Within the European Union, there is an increasing recognition about the negative environmental impacts of food waste making it a prominent policy issue. But there is no clarity whether policies aimed at food waste minimisation are based on sound legislative frameworks that actually empower the relevant actors. By carefully reviewing existing European Union legislations that are linked directly or indirectly to food waste, we identify the difficulties encountered by stakeholders and assess whether adaptations to the rules-in-use are beneficial and desirable. Our general finding is that liability for donated foodstuffs, date marking provisions, the flexibility principle provided by the European Union Hygiene Package and fiscal rules are the main policy elements affecting, either positively or negatively, food waste generation and management. Food donation for charitable purposes emerges as the predominant Pan-European Union waste management solution. While removing existing barriers for food donors and banks is fundamental—as it makes redistribution more effective—this does not tackle prevention of excess food generation. We conclude that while there are several European Union food legislations which include and impact food waste management options, they are hardly direct. Moreover, they often generate incentives that are at odds across stakeholders, thereby dampening the intended impact. There is, therefore, need for an integrated policy framework to tackle food waste specifically. For that to happen though, a pre-requisite is lot more empirical research on the interaction effects of various food waste legislations

Estimation of pure qubits on circles

Gisin and Popescu [PRL, 83, 432 (1999)] have shown that more information about their direction can be obtained from a pair of anti-parallel spins compared to a pair of parallel spins, where the first member of the pair (which we call the pointer member) can point equally along any direction in the Bloch sphere. They argued that this was due to the difference in dimensionality spanned by these two alphabets of states. Here we consider similar alphabets, but with the first spin restricted to a fixed small circle of the Bloch sphere. In this case, the dimensionality spanned by the anti-parallel versus parallel alphabet is now equal. However, the anti-parallel alphabet is found to still contain more information in general. We generalize this to having N parallel spins and M anti-parallel spins. When the pointer member is restricted to a small circle these alphabets again span spaces of equal dimension, yet in general, more directional information can be found for sets with smaller |N-M| for any fixed total number of spins. We find that the optimal POVMs for extracting directional information in these cases can always be expressed in terms of the Fourier basis. Our results show that dimensionality alone cannot explain the greater information content in anti-parallel combinations of spins compared to parallel combinations. In addition, we describe an LOCC protocol which extract optimal directional information when the pointer member is restricted to a small circle and a pair of parallel spins are supplied.Comment: 23 pages, 8 figure

Accelerating Tactile Internet with QUIC: A Security and Privacy Perspective

The Tactile Internet paradigm is set to revolutionize human society by enabling skill-set delivery and haptic communication over ultra-reliable, low-latency networks. The emerging sixth-generation (6G) mobile communication systems are envisioned to underpin this Tactile Internet ecosystem at the network edge by providing ubiquitous global connectivity. However, apart from a multitude of opportunities of the Tactile Internet, security and privacy challenges emerge at the forefront. We believe that the recently standardized QUIC protocol, characterized by end-to-end encryption and reduced round-trip delay would serve as the backbone of Tactile Internet. In this article, we envision a futuristic scenario where a QUIC-enabled network uses the underlying 6G communication infrastructure to achieve the requirements for Tactile Internet. Interestingly this requires a deeper investigation of a wide range of security and privacy challenges in QUIC, that need to be mitigated for its adoption in Tactile Internet. Henceforth, this article reviews the existing security and privacy attacks in QUIC and their implication on users. Followed by that, we discuss state-of-the-art attack mitigation strategies and investigate some of their drawbacks with possible directions for future workComment: 7 pages, 3 figures, 1 tabl

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

Spectroscopic Definition of the CuZ° Intermediate in Turnover of Nitrous Oxide Reductase and Molecular Insight into the Catalytic Mechanism

Fundacao para a Ciencia e Tecnologia - PTDC/QUI-BIQ/116481/2010, PTDC/BBB-BQB/0129/2014, SFRH/BD/87898/2012 ; Unidade de Ciencias Biomoleculares Aplicadas-UCIBIO - FCT/MEC - UID/Multi/04378/2013 ; ERDF - POCI-01-0145-FEDER-007728Spectroscopic methods and density functional theory (DFT) calculations are used to determine the geometric and electronic structure of CuZ°, an intermediate form of the Cu4S active site of nitrous oxide reductase (N2OR) that is observed in single turnover of fully reduced N2OR with N2O. Electron paramagnetic resonance (EPR), absorption, and magnetic circular dichroism (MCD) spectroscopies show that CuZ° is a 1-hole (i.e., 3CuICuII) state with spin density delocalized evenly over CuI and CuIV. Resonance Raman spectroscopy shows two Cu-S vibrations at 425 and 413 cm-1, the latter with a -3 cm-1 O18 solvent isotope shift. DFT calculations correlated to these spectral features show that CuZ° has a terminal hydroxide ligand coordinated to CuIV, stabilized by a hydrogen bond to a nearby lysine residue. CuZ° can be reduced via electron transfer from CuA using a physiologically relevant reductant. We obtain a lower limit on the rate of this intramolecular electron transfer (IET) that is >104 faster than the unobserved IET in the resting state, showing that CuZ° is the catalytically relevant oxidized form of N2OR. Terminal hydroxide coordination to CuIV in the CuZ° intermediate yields insight into the nature of N2O binding and reduction, specifying a molecular mechanism in which N2O coordinates in a μ-1,3 fashion to the fully reduced state, with hydrogen bonding from Lys397, and two electrons are transferred from the fully reduced μ4S2- bridged tetranuclear copper cluster to N2O via a single Cu atom to accomplish N-O bond cleavage.authorsversionpublishe

Joint cosmological and gravitational-wave population inference using dark sirens and galaxy catalogues

In the absence of numerous gravitational-wave detections with confirmed electromagnetic counterparts, the "dark siren" method has emerged as a leading technique of gravitational-wave cosmology. The method allows redshift information of such events to be inferred statistically from a catalogue of potential host galaxies. Due to selection effects, dark siren analyses necessarily depend on the mass distribution of compact objects and the evolution of their merger rate with redshift. Informative priors on these quantities will impact the inferred posterior constraints on the Hubble constant ($H_0$). It is thus crucial to vary these unknown distributions during an $H_0$ inference. This was not possible in earlier analyses due to the high computational cost, restricting them to either excluding galaxy catalogue information, or fixing the gravitational-wave population mass distribution and risking introducing bias to the $H_0$ measurement. This paper introduces a significantly enhanced version of the Python package GWCOSMO, which allows joint estimation of cosmological and compact binary population parameters. This thereby ensures the analysis is now robust to a major source of potential bias. The gravitational-wave events from the Third Gravitational-Wave Transient Catalogue are reanalysed with the GLADE+ galaxy catalogue, and an updated, more reliable measurement of $H_0=69^{+12}_{-7}$ km s$^{-1}$ Mpc$^{-1}$ is found (maximum a posteriori probability and 68% highest density interval). This improved method will enable cosmological analyses with future gravitational-wave detections to make full use of the information available (both from galaxy catalogues and the compact binary population itself), leading to promising new independent bounds on the Hubble constant.Comment: 30 pages, 11 figure

ICAROGW: A python package for inference of astrophysical population properties of noisy, heterogeneous and incomplete observations

We present icarogw 2.0, a pure CPU/GPU python code developed to infer astrophysical and cosmological population properties of noisy, heterogeneous, and incomplete observations. icarogw 2.0 is mainly developed for compact binary coalescence (CBC) population inference with gravitational wave (GW) observations. The code contains several models for masses, spins, and redshift of CBC distributions, and is able to infer population distributions as well as the cosmological parameters and possible general relativity deviations at cosmological scales. We present the theoretical and computational foundations of icarogw, and we describe how the code can be employed for population and cosmological inference using (i) only GWs, (ii) GWs and galaxy surveys and (iii) GWs with electromagnetic counterparts. Although icarogw 2.0 has been developed for GW science, we also describe how the code can be used for any physical and astrophysical problem involving observations from noisy data in the presence of selection biases. With this paper, we also release tutorials on Zenodo.Comment: 33 pages, code available at (https://github.com/simone-mastrogiovanni/icarogw), tutorials available at (https://zenodo.org/record/7846415#.ZG0l0NJBxQo

The impacts of COVID-19 restrictions on care-givers of people with cognitive impairment and their support needs: A mixed-methods systematic review

The COVID-19 pandemic and ensuing restrictions/lockdowns have caused significant physical and psychological consequences for people with cognitive impairment who are heavily dependent on their care-givers. However, little is known about the impact on care-givers, the factors that exacerbate their situation and what supports they need. The aims of this paper are threefold: (a) to examine the impact of COVID-19 physical restrictions on both formal and informal care-givers of people with cognitive impairment; (b) to identify attributing factors influencing this impact; and (c) to recognise their support needs. Further, this paper informs future research, policy and practice. Guided by the Joanna Briggs Institute framework, a systematic review was conducted using a mixed-methods convergent integrated approach. Eight databases were searched using keywords related to COVID-19 restriction, dementia care-givers, impacts and care settings, followed by a manual search. The study was limited to primary research published in English between January 2020 and December 2021. Of the 840 records identified, 30 met the inclusion criteria. Service withdrawal and social distancing has effectively led to the reprivatisation of care to the family, particularly women. Care-givers experienced negative impacts including reduced psychological wellbeing and physical health, increased care burden and financial difficulties. A number of clinical attributes and socio-demographic factors influenced the COVID-19 impact on care-givers. Consequently, counselling services, assistance with care and financial support were identified as support needs. Implementation of new support and the strengthening of existing services are recommended to enhance resilience, build capacity to support care-givers in any given situation and mitigate the effects of future outbreaks