Symmetric Extension of Two-Qubit States

Quantum key distribution uses public discussion protocols to establish shared secret keys. In the exploration of ultimate limits to such protocols, the property of symmetric extendibility of underlying bipartite states $\rho_{AB}$ plays an important role. A bipartite state $\rho_{AB}$ is symmetric extendible if there exits a tripartite state $\rho_{ABB'}$, such that the $AB$ marginal state is identical to the $AB'$ marginal state, i.e. $\rho_{AB'}=\rho_{AB}$. For a symmetric extendible state $\rho_{AB}$, the first task of the public discussion protocol is to break this symmetric extendibility. Therefore to characterize all bi-partite quantum states that possess symmetric extensions is of vital importance. We prove a simple analytical formula that a two-qubit state $\rho_{AB}$ admits a symmetric extension if and only if \tr(\rho_B^2)\geq \tr(\rho_{AB}^2)-4\sqrt{\det{\rho_{AB}}}. Given the intimate relationship between the symmetric extension problem and the quantum marginal problem, our result also provides the first analytical necessary and sufficient condition for the quantum marginal problem with overlapping marginals.Comment: 10 pages, no figure. comments are welcome. Version 2: introduction rewritte

Minimum Entangling Power is Close to Its Maximum

Given a quantum gate $U$ acting on a bipartite quantum system, its maximum (average, minimum) entangling power is the maximum (average, minimum) entanglement generation with respect to certain entanglement measure when the inputs are restricted to be product states. In this paper, we mainly focus on the 'weakest' one, i.e., the minimum entangling power, among all these entangling powers. We show that, by choosing von Neumann entropy of reduced density operator or Schmidt rank as entanglement measure, even the 'weakest' entangling power is generically very close to its maximal possible entanglement generation. In other words, maximum, average and minimum entangling powers are generically close. We then study minimum entangling power with respect to other Lipschitiz-continuous entanglement measures and generalize our results to multipartite quantum systems. As a straightforward application, a random quantum gate will almost surely be an intrinsically fault-tolerant entangling device that will always transform every low-entangled state to near-maximally entangled state.Comment: 26 pages, subsection III.A.2 revised, authors list updated, comments are welcom

A zinc finger protein array for the visual detection of specific DNA sequences for diagnostic applications.

The visual detection of specific double-stranded DNA sequences possesses great potential for the development of diagnostics. Zinc finger domains provide a powerful scaffold for creating custom DNA-binding proteins that recognize specific DNA sequences. We previously demonstrated sequence-enabled reassembly of TEM-1 β-lactamase (SEER-LAC), a system consisting of two inactive fragments of β-lactamase each linked to engineered zinc finger proteins (ZFPs). Here the SEER-LAC system was applied to develop ZFP arrays that function as simple devices to identify bacterial double-stranded DNA sequences. The ZFP arrays provided a quantitative assay with a detection limit of 50 fmol of target DNA. The method could distinguish target DNA from non-target DNA within 5 min. The ZFP arrays provided sufficient sensitivity and high specificity to recognize specific DNA sequences. These results suggest that ZFP arrays have the potential to be developed into a simple and rapid point-of-care (POC) diagnostic for the multiplexed detection of pathogens

Water-based Recreation and Water Quality Indices: A Revealed Preference Approach

Benefit estimates of water pollution control policies rely heavily on water quality indices. Since the 1970s, these measures of water quality have been used extensively in stated preference surveys to estimate willingness to pay for water quality that is suitable for recreational use. However, there is little empirical evidence of how well these indices correspond to observed recreational behavior. This paper utilizes a unique micro-dataset of individual household recreational use and water quality in a revealed preference framework to explore how well several major water quality indices explain water-based recreational use