Improving Einstein-Podolsky-Rosen Steering Inequalities with State Information

We discuss the relationship between entropic Einstein-Podolsky-Rosen (EPR)-steering inequalities and their underlying uncertainty relations, along with the hypothesis that improved uncertainty relations lead to tighter EPR-steering inequalities. In particular, we discuss how the intrinsic uncertainty in a mixed quantum state is used to improve existing uncertainty relations and how this information affects one's ability to witness EPR-steering. As an example, we consider the recent improvement (using a quantum memory) to the entropic uncertainty relation between pairs of discrete observables (Nat. Phys. 6, 659 (2010)) and show that a trivial substitution of the tighter bound in the steering inequality leads to contradictions, due in part to the fact that the improved bound depends explicitly on the state being measured. By considering the assumptions that enter into the development of a steering inequality, we derive correct steering inequalities from these improved uncertainty relations and find that they are identical to ones already developed (Phys. Rev. A, 87, 062103 (2013)). In addition, we consider how one can use the information about the quantum state to improve our ability to witness EPR-steering, and develop a new symmetric EPR-steering inequality as a result.Comment: 6 page

Uncertainty Relation for Mutual Information

We postulate the existence of a universal uncertainty relation between the quantum and classical mutual informations between pairs of quantum systems. Specifically, we propose that the sum of the classical mutual information, determined by two mutually unbiased pairs of observables, never exceeds the quantum mutual information. We call this the complementary-quantum correlation (CQC) relation and prove its validity for pure states, for states with one maximally mixed subsystem, and for all states when one measurement is minimally disturbing. We provide results of a Monte Carlo simulation suggesting the CQC relation is generally valid. Importantly, we also show that the CQC relation represents an improvement to an entropic uncertainty principle in the presence of a quantum memory, and that it can be used to verify an achievable secret key rate in the quantum one-time pad cryptographic protocol.Comment: 6 pages, 2 figure

EPR Steering Inequalities from Entropic Uncertainty Relations

We use entropic uncertainty relations to formulate inequalities that witness Einstein-Podolsky-Rosen (EPR) steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the differing natures of the correlations captured by one-way and symmetric steering inequalities, and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator valued measures (POVMs), and we also derive hybrid-steering inequalities between alternate degrees of freedom.Comment: 10 pages, 2 figure

Improving Einstein–Podolsky–Rosen Steering Inequalities with State Information

We discuss the relationship between entropic Einstein–Podolsky–Rosen (EPR)-steering inequalities and their underlying uncertainty relations along with the hypothesis that improved uncertainty relations lead to tighter EPR-steering inequalities. In particular, we discuss how using information about the state of a quantum system affects oneʼs ability to witness EPR-steering. As an example, we consider the recent improvement to the entropic uncertainty relation between pairs of discrete observables (Berta et al., 2010 [10]). By considering the assumptions that enter into the development of a steering inequality, we derive correct steering inequalities from these improved uncertainty relations and find that they are identical to ones already developed (Schneeloch et al., 2013 [9]). In addition, we consider how one can use state information to improve our ability to witness EPR-steering, and develop a new continuous variable symmetric EPR-steering inequality as a result

Health state utility values for diabetic retinopathy: protocol for a systematic review and meta-analysis

Background People with diabetic retinopathy tend to have lower levels of health-related quality of life than individuals with no retinopathy. Strategies for screening and treatment have been shown to be cost-effective. In order to reduce the bias in cost-effectiveness estimates, systematic reviews of health state utility values (HSUVs) are crucial for health technology assessment and the development of decision analytic models. A review and synthesis of HSUVs for the different stages of disease progression in diabetic retinopathy has not previously been conducted. Methods/Design We will conduct a systematic review of the available literature that reports HSUVs for people with diabetic retinopathy, in correspondence with current stage of disease progression and/or visual acuity. We will search Medline, EMBASE, Web of Science, Cost-Effectiveness Analysis Registry, Centre for Reviews and Dissemination Database, and EconLit to identify relevant English-language articles. Data will subsequently be synthesized using linear mixed effects modeling meta-regression. Additionally, reported disease severity classifications will be mapped to a four-level grading scale for diabetic retinopathy. Discussion The systematic review and meta-analysis will provide important evidence for future model-based economic evaluations of technologies for diabetic retinopathy. The meta-regression will enable the estimation of utility values at different disease stages for patients with particular characteristics and will also highlight where the design of the study and HSUV instrument have influenced the reported utility values. We believe this protocol to be the first of its kind to be published

Einstein-Podolsky-Rosen Steering Inequalities from Entropic Uncertainty Relations

We use entropic uncertainty relations to formulate inequalities that witness Einstein-Podolsky-Rosen (EPR)-steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the differing natures of the correlations captured by one-way and symmetric steering inequalities and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator-valued measures, and we also derive hybrid steering inequalities between alternate degrees of freedom

Violation of Continuous-Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements

In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous-variable systems using only experimentally measured discrete probability distributions and details of the measurement apparatus. We use this inequality to witness EPR steering between the positions and momenta of photon pairs generated in spontaneous parametric down-conversion. We examine the asymmetry between parties in this inequality, and show that this asymmetry can be used to reduce the technical requirements of experimental setups intended to demonstrate the EPR paradox. Furthermore, we develop a more stringent steering inequality that is symmetric between parties, and use it to show that the down-converted photon pairs also exhibit symmetric EPR steering

The melanoma-specific graded prognostic assessment does not adequately discriminate prognosis in a modern population with brain metastases from malignant melanoma

The melanoma-specific graded prognostic assessment (msGPA) assigns patients with brain metastases from malignant melanoma to 1 of 4 prognostic groups. It was largely derived using clinical data from patients treated in the era that preceded the development of newer therapies such as BRAF, MEK and immune checkpoint inhibitors. Therefore, its current relevance to patients diagnosed with brain metastases from malignant melanoma is unclear. This study is an external validation of the msGPA in two temporally distinct British populations.Performance of the msGPA was assessed in Cohort I (1997-2008, n=231) and Cohort II (2008-2013, n=162) using Kaplan-Meier methods and Harrell's c-index of concordance. Cox regression was used to explore additional factors that may have prognostic relevance.The msGPA does not perform well as a prognostic score outside of the derivation cohort, with suboptimal statistical calibration and discrimination, particularly in those patients with an intermediate prognosis. Extra-cerebral metastases, leptomeningeal disease, age and potential use of novel targeted agents after brain metastases are diagnosed, should be incorporated into future prognostic models.An improved prognostic score is required to underpin high-quality randomised controlled trials in an area with a wide disparity in clinical care