Hard limits on the postselectability of optical graph states

Coherent control of large entangled graph states enables a wide variety of quantum information processing tasks, including error-corrected quantum computation. The linear optical approach offers excellent control and coherence, but today most photon sources and entangling gates---required for the construction of large graph states---are probabilistic and rely on postselection. In this work, we provide proofs and heuristics to aid experimental design using postselection. We derive a fundamental limitation on the generation of photonic qubit states using postselected entangling gates: experiments which contain a cycle of postselected gates cannot be postselected. Further, we analyse experiments that use photons from postselected photon pair sources, and lower bound the number of classes of graph state entanglement that are accessible in the non-degenerate case---graph state entanglement classes that contain a tree are are always accessible. Numerical investigation up to 9-qubits shows that the proportion of graph states that are accessible using postselection diminishes rapidly. We provide tables showing which classes are accessible for a variety of up to nine qubit resource states and sources. We also use our methods to evaluate near-term multi-photon experiments, and provide our algorithms for doing so.Comment: Our manuscript comprises 4843 words, 6 figures, 1 table, 47 references, and a supplementary material of 1741 words, 2 figures, 1 table, and a Mathematica code listin

Mapping graph state orbits under local complementation

Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation---the graph operation that links all local-Clifford equivalent graph states---allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by local complementation, mapping them up to 9 qubits and revealing a rich hidden structure. We provide programs to compute these orbits, along with our data for each of the 587 orbits up to 9 qubits and a means to visualise them. We find direct links between the connectivity of certain orbits with the entanglement properties of their component graph states. Furthermore, we observe the correlations between graph-theoretical orbit properties, such as diameter and colourability, with Schmidt measure and preparation complexity and suggest potential applications. It is well known that graph theory and quantum entanglement have strong interplay---our exploration deepens this relationship, providing new tools with which to probe the nature of entanglement

Defining an ageing-related pathology, disease or syndrome: International Consensus Statement

Around the world, individuals are living longer, but an increased average lifespan does not always equate to an increased health span. With advancing age, the increased prevalence of ageing-related diseases can have a significant impact on health status, functional capacity and quality of life. It is therefore vital to develop comprehensive classification and staging systems for ageing-related pathologies, diseases and syndromes. This will allow societies to better identify, quantify, understand and meet the healthcare, workforce, well-being and socioeconomic needs of ageing populations, whilst supporting the development and utilisation of interventions to prevent or to slow, halt or reverse the progression of ageing-related pathologies. The foundation for developing such classification and staging systems is to define the scope of what constitutes an ageing-related pathology, disease or syndrome. To this end, a consensus meeting was hosted by the International Consortium to Classify Ageing-Related Pathologies (ICCARP), on February 19, 2024, in Cardiff, UK, and was attended by 150 recognised experts. Discussions and voting were centred on provisional criteria that had been distributed prior to the meeting. The participants debated and voted on these. Each criterion required a consensus agreement of ≥ 70% for approval. The accepted criteria for an ageing-related pathology, disease or syndrome were (1) develops and/or progresses with increasing chronological age; (2) should be associated with, or contribute to, functional decline or an increased susceptibility to functional decline and (3) evidenced by studies in humans. Criteria for an ageing-related pathology, disease or syndrome have been agreed by an international consortium of subject experts. These criteria will now be used by the ICCARP for the classification and ultimately staging of ageing-related pathologies, diseases and syndromes