Generalized conditional entropy in bipartite quantum systems

We analyze, for a general concave entropic form, the associated conditional entropy of a quantum system A+B, obtained as a result of a local measurement on one of the systems (B). This quantity is a measure of the average mixedness of A after such measurement, and its minimum over all local measurements is shown to be the associated entanglement of formation between A and a purifying third system C. In the case of the von Neumann entropy, this minimum determines also the quantum discord. For classically correlated states and mixtures of a pure state with the maximally mixed state, we show that the minimizing measurement can be determined analytically and is universal, i.e., the same for all concave forms. While these properties no longer hold for general states, we also show that in the special case of the linear entropy, an explicit expression for the associated conditional entropy can be obtained, whose minimum among projective measurements in a general qudit-qubit state can be determined analytically, in terms of the largest eigenvalue of a simple 3x3 correlation matrix. Such minimum determines the maximum conditional purity of A, and the associated minimizing measurement is shown to be also universal in the vicinity of maximal mixedness. Results for X states, including typical reduced states of spin pairs in XY chains at weak and strong transverse fields, are also provided and indicate that the measurements minimizing the von Neumann and linear conditional entropies are typically coincident in these states, being determined essentially by the main correlation. They can differ, however, substantially from that minimizing the geometric discord.Comment: 11 pages, 2 figures; References adde

Generalized conditional entropy optimization for qudit-qubit states

We derive a general approximate solution to the problem of minimizing the conditional entropy of a qudit-qubit system resulting from a local projective measurement on the qubit, which is valid for general entropic forms and becomes exact in the limit of weak correlations. This entropy measures the average conditional mixedness of the post-measurement state of the qudit, and its minimum among all local measurements represents a generalized entanglement of formation. In the case of the von Neumann entropy, it is directly related to the quantum discord. It is shown that at the lowest non-trivial order, the problem reduces to the minimization of a quadratic form determined by the correlation tensor of the system, the Bloch vector of the qubit and the local concavity of the entropy, requiring just the diagonalization of a $3\times 3$ matrix. A simple geometrical picture in terms of an associated correlation ellipsoid is also derived, which illustrates the link between entropy optimization and correlation access and which is exact for a quadratic entropy. The approach enables a simple estimation of the quantum discord. Illustrative results for two-qubit states are discussed.Comment: 11 pages, 6 figures. Final published versio

Conditional purity and quantum correlation measures in two qubit mixed states

We analyze and show experimental results of the conditional purity, the quantum discord and other related measures of quantum correlation in mixed two-qubit states constructed from a pair of photons in identical polarization states. The considered states are relevant for the description of spin pair states in interacting spin chains in a transverse magnetic field. We derive clean analytical expressions for the conditional local purity and other correlation measures obtained as a result of a remote local projective measurement, which are fully verified by the experimental results. A simple exact expression for the quantum discord of these states in terms of the maximum conditional purity is also derived.Comment: 16 pages, 5 figures, minor changes, to be published in J. Phys.

Biased Random Access Codes

A Random Access Code (RAC) is a communication task in which the sender encodes a random message into a shorter one to be decoded by the receiver so that a randomly chosen character of the original message is recovered with some probability. Both the message and the character to be recovered are assumed to be uniformly distributed. In this paper, we extend this protocol by allowing more general distributions of these inputs, which alters the encoding and decoding strategies optimizing the protocol performance, either with classical or quantum resources. We approach the problem of optimizing the performance of these biased RACs with both numerical and analytical tools. On the numerical front, we present algorithms that allow a numerical evaluation of the optimal performance over both classical and quantum strategies and provide a Python package designed to implement them, called RAC-tools. We then use this numerical tool to investigate single-parameter families of biased RACs in the $n^2 \mapsto 1$ and $2^d \mapsto 1$ scenarios. For RACs in the $n^2 \mapsto 1$ scenario, we derive a general upper bound for the cases in which the inputs are not correlated, which coincides with the quantum value for $n=2$ and, in some cases for $n=3$. Moreover, it is shown that attaining this upper bound self-tests pairs or triples of rank-1 projective measurements, respectively. An analogous upper bound is derived for the value of RACs in the $2^d \mapsto 1$ scenario which is shown to be always attainable using mutually unbiased measurements if the distribution of input strings is unbiased

Quantum Discord and entropic measures of quantum correlations: Optimization and behavior in finite XYXY spin chains

We discuss a generalization of the conditional entropy and one-way information deficit in quantum systems, based on general entropic forms. The formalism allows to consider simple entropic forms for which a closed evaluation of the associated optimization problem in qudit-qubit systems is shown to become feasible, allowing to approximate that of the quantum discord. As application, we examine quantum correlations of spin pairs in the exact ground state of finite $XY$ spin chains in a magnetic field through the quantum discord and information deficit. While these quantities show a similar behavior, their optimizing measurements exhibit significant differences, which can be understood and predicted through the previous approximations. The remarkable behavior of these quantities in the vicinity of transverse and non-transverse factorizing fields is also discussed.Comment: 10 pages, 3 figure

World Addiction Medicine Reports : formation of the International Society of Addiction Medicine (ISAM) Global Expert Network (ISAM-GEN) and Its global surveys

Funding: All the infrastructure funding of this initiative is supported by the International Society of Addiction Medicine (ISAM). We will be open to fundraising for specific projects within the platform and future collaboration with external partners.Addiction medicine is a dynamic field that encompasses clinical practice and research in the context of societal, economic, and cultural factors at the local, national, regional, and global levels. This field has evolved profoundly during the past decades in terms of scopes and activities with the contribution of addiction medicine scientists and professionals globally. The dynamic nature of drug addiction at the global level has resulted in a crucial need for developing an international collaborative network of addiction societies, treatment programs and experts to monitor emerging national, regional, and global concerns. This protocol paper presents methodological details of running longitudinal surveys at national, regional, and global levels through the Global Expert Network of the International Society of Addiction Medicine (ISAM-GEN). The initial formation of the network with a recruitment phase and a round of snowball sampling provided 354 experts from 78 countries across the globe. In addition, 43 national/regional addiction societies/associations are also included in the database. The surveys will be developed by global experts in addiction medicine on treatment services, service coverage, co-occurring disorders, treatment standards and barriers, emerging addictions and/or dynamic changes in treatment needs worldwide. Survey participants in categories of (1) addiction societies/associations, (2) addiction treatment programs, (3) addiction experts/clinicians and (4) related stakeholders will respond to these global longitudinal surveys. The results will be analyzed and cross-examined with available data and peer-reviewed for publication.Peer reviewe