Optimal Entanglement Generation from Quantum Operations

We consider how much entanglement can be produced by a non-local two-qubit unitary operation, $U_{AB}$ - the entangling capacity of $U_{AB}$. For a single application of $U_{AB}$, with no ancillas, we find the entangling capacity and show that it generally helps to act with $U_{AB}$ on an entangled state. Allowing ancillas, we present numerical results from which we can conclude, quite generally, that allowing initial entanglement typically increases the optimal capacity in this case as well. Next, we show that allowing collective processing does not increase the entangling capacity if initial entanglement is allowed.Comment: v1.0 15 pages, 3 figures, written in revtex4. v2.0 References updated. Submitted to Phys. Rev. A v3.0 16 pages, 4 figures. Expanded explanation in section 3A, figures corrected and made clearer. Definition of entangling capacity in section 4 made explicit. Other minor typos correcte

All Inequalities for the Relative Entropy

The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party to a smaller number $m$ of parties is always less than or equal to the relative entropy of the two original n-party states. This is the monotonicity of relative entropy. Using techniques from convex geometry, we prove that monotonicity under restrictions is the only general inequality satisfied by relative entropies. In doing so we make a connection to secret sharing schemes with general access structures. A suprising outcome is that the structure of allowed relative entropy values of subsets of multiparty states is much simpler than the structure of allowed entropy values. And the structure of allowed relative entropy values (unlike that of entropies) is the same for classical probability distributions and quantum states.Comment: 15 pages, 3 embedded eps figure

Identifying patients' support needs following critical illness:A scoping review of the qualitative literature

BACKGROUND: Intensive care survivors suffer chronic and potentially life-changing physical, psychosocial and cognitive sequelae, and supporting recovery is an international priority. As survivors' transition from the intensive care unit to home, their support needs develop and change. METHODS: In this scoping review, we categorised patients' support needs using House's Social Support Needs framework (informational, emotional, instrumental, appraisal) and mapped these against the Timing it Right framework reflecting the patient's transition from intensive care (event/diagnosis) to ward (stabilisation/preparation) and discharge home (implementation/adaptation). We searched electronic databases from 2000 to 2017 for qualitative research studies reporting adult critical care survivors' experiences of care. Two reviewers independently screened, extracted and coded data. Data were analysed using a thematic framework approach. RESULTS: From 3035 references, we included 32 studies involving 702 patients. Studies were conducted in UK and Europe (n = 17, 53%), Canada and the USA (n = 6, 19%), Australasia (n = 6, 19%), Hong Kong (n = 1, 3%), Jordan (n = 1, 3%) and multi-country (n = 1, 3%). Across the recovery trajectory, informational, emotional, instrumental, appraisal and spiritual support needs were evident, and the nature and intensity of need differed when mapped against the Timing it Right framework. Informational needs changed from needing basic facts about admission, to detail about progress and treatments and coping with long-term sequelae. The nature of emotional needs changed from needing to cope with confusion, anxiety and comfort, to a need for security and family presence, coping with flashbacks, and needing counselling and community support. Early instrumental needs ranged from managing sleep, fatigue, pain and needing nursing care and transitioned to needing physical and cognitive ability support, strength training and personal hygiene; and at home, regaining independence, strength and return to work. Appraisal needs related to obtaining feedback on progress, and after discharge, needing reassurance from others who had been through the ICU experience. CONCLUSIONS: This review is the first to identify the change in social support needs among intensive care survivors as they transition from intensive care to the home environment. An understanding of needs at different transition periods would help inform health service provision and support for survivors

Normal forms and entanglement measures for multipartite quantum states

A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular value decomposition. The analysis naturally leads to the introduction of entanglement measures quantifying the multipartite entanglement (as generalizations of the concurrence and the 3-tangle), and the optimal local filtering operations maximizing these entanglement monotones are obtained. Moreover a natural extension of the definition of GHZ-states to e.g. $2\times 2\times N$ systems is obtained.Comment: Proof of uniqueness of normal form adde

The Flare-energy Distributions Generated by Kink-unstable Ensembles of Zero-net-current Coronal Loops

It has been proposed that the million degree temperature of the corona is due to the combined effect of barely-detectable energy releases, so called nanoflares, that occur throughout the solar atmosphere. Alas, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release and so we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory, i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold

Local transformation of mixed states of two qubits to Bell diagonal states

The optimal entanglement manipulation for a single copy of mixed states of two qubits is to transform it to a Bell diagonal state. In this paper we derive an explicit form of the local operation that can realize such a transformation. The result obtained is universal for arbitrary entangled two-qubit states and it discloses that the corresponding local filter is not unique for density matrices with rank $n=2$ and can be exclusively determined for that with $n=3$ and 4. As illustrations, a four-parameters family of mixed states are explored, the local filter as well as the transformation probability are given explicitly, which verify the validity of the general result.Comment: 5 pages, to be published in Phys. Rev.