Structure of Quantum Entanglement at a Finite Temperature Critical Point

We propose a scheme to characterize long-range quantum entanglement close to a finite temperature critical point using tripartite entanglement negativity. As an application, we study a model with mean-field Ising critical exponents and find that the tripartite negativity does not exhibit any singularity in the thermodynamic limit across the transition. This indicates that the long-distance critical fluctuations are completely classical, allowing one to define a `quantum correlation length' that remains finite at the transition despite a divergent physical correlation length. Motivated by our model, we also study mixed state entanglement in tight-binding models of bosons with $U(1)$ and time-reversal symmetry. By employing Glauber-Sudarshan `P-representation', we find a surprising result that such states have zero entanglement.Comment: 12 pages, 12 figure

Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality

We study the growth of entanglement between two adjacent regions in a tripartite, one-dimensional many-body system after a quantum quench. Combining a replica trick with a space-time duality transformation, we derive an exact, universal relation between the entanglement negativity and Renyi-1/2 mutual information which holds at times shorter than the sizes of all subsystems. Our proof is directly applicable to any translationally invariant local quantum circuit, i.e., any lattice system in discrete time characterised by local interactions, irrespective of the nature of its dynamics. Our derivation indicates that such a relation can be directly extended to any system where information spreads with a finite maximal velocity.Comment: 8 pages, 3 figures; v2 improved discussio

State Differences in the Reporting of Diabetes-Related Incorrect Cause-of-Death Causal Sequences on Death Certificates

OBJECTIVE To examine state differences in the reporting of diabetes-related incorrect cause-of-death (COD) causal sequences on death certificates in the U.S. RESEARCH DESIGN AND METHODS We conducted a cross-sectional descriptive study to determine the prevalence of two types of incorrect COD causal sequences with data from the Multiple Cause Mortality File of the year 2004. RESULTS Among deaths in which diabetes was reported as the first diagnosis on line a, b, c, or d in Part I of the death certificate in the U.S., 21% had below diabetes placement error (ranged from 30% in Maryland to 7% in Hawaii) and 11% had above diabetes placement error (ranged from 18% in Kentucky to 5% in California). The net effects of the two types of error ranged from −0.7% in Nevada to 19.6% in the District of Columbia. CONCLUSIONS Because the rates of incorrect reporting of diabetes-related COD causal sequence varied across states, the comparability of the diabetes death rate between states may have been compromised

Mixed-state long-range order and criticality from measurement and feedback

We propose a general framework for using local measurements, local unitaries, and non-local classical communication to construct quantum channels which can efficiently prepare mixed states with long-range quantum order or quantum criticality. As an illustration, symmetry-protected topological (SPT) phases can be universally converted into mixed-states with long-range entanglement, which can undergo phase transitions with quantum critical correlations of local operators and a logarithmic scaling of the entanglement negativity, despite coexisting with volume-law entropy. Within the same framework, we present two applications using fermion occupation number measurement to convert (i) spinful free fermions in one dimension into a quantum-critical mixed state with enhanced algebraic correlations between spins and (ii) Chern insulators into a mixed state with critical quantum correlations in the bulk. The latter is an example where mixed-state quantum criticality can emerge from a gapped state of matter in constant depth using local quantum operations and non-local classical communication.Comment: 25 pages, 11 figure