Quantum Error Correction with the Toric-GKP Code

We examine the performance of the single-mode GKP code and its concatenation with the toric code for a noise model of Gaussian shifts, or displacement errors. We show how one can optimize the tracking of errors in repeated noisy error correction for the GKP code. We do this by examining the maximum-likelihood problem for this setting and its mapping onto a 1D Euclidean path-integral modeling a particle in a random cosine potential. We demonstrate the efficiency of a minimum-energy decoding strategy as a proxy for the path integral evaluation. In the second part of this paper, we analyze and numerically assess the concatenation of the GKP code with the toric code. When toric code measurements and GKP error correction measurements are perfect, we find that by using GKP error information the toric code threshold improves from $10\%$ to $14\%$. When only the GKP error correction measurements are perfect we observe a threshold at $6\%$. In the more realistic setting when all error information is noisy, we show how to represent the maximum likelihood decoding problem for the toric-GKP code as a 3D compact QED model in the presence of a quenched random gauge field, an extension of the random-plaquette gauge model for the toric code. We present a new decoder for this problem which shows the existence of a noise threshold at shift-error standard deviation $\sigma_0 \approx 0.243$ for toric code measurements, data errors and GKP ancilla errors. If the errors only come from having imperfect GKP states, this corresponds to states with just 4 photons or more. Our last result is a no-go result for linear oscillator codes, encoding oscillators into oscillators. For the Gaussian displacement error model, we prove that encoding corresponds to squeezing the shift errors. This shows that linear oscillator codes are useless for quantum information protection against Gaussian shift errors.Comment: 50 pages, 14 figure

Community sewage sensors towards evaluation of drug use trends: detection of cocaine in wastewater with DNA-directed immobilization aptamer sensors

Illicit drug use has a global concern and effective monitoring and interventions are highly required to combat drug abuse. Wastewater-based epidemiology (WBE) is an innovative and cost-effective approach to evaluate community-wide drug use trends, compared to traditional population surveys. Here we report for the first time, a novel quantitative community sewage sensor (namely DNA-directed immobilization of aptamer sensors, DDIAS) for rapid and cost-effective estimation of cocaine use trends via WBE. Thiolated single-stranded DNA (ssDNA) probe was hybridized with aptamer ssDNA in solution, followed by co-immobilization with 6-mercapto-hexane onto the gold electrodes to control the surface density to effectively bind with cocaine. DDIAS was optimized to detect cocaine at as low as 10 nM with a dynamic range from 10 nM to 5 μM, which were further employed for the quantification of cocaine in wastewater samples collected from a wastewater treatment plant in seven consecutive days. The concentration pattern of the sampling week is comparable with that from mass spectrometry. Our results demonstrate that the developed DDIAS can be used as community sewage sensors for rapid and cost-effective evaluation of drug use trends, and potentially implemented as a powerful tool for on-site and real-time monitoring of wastewater by un-skilled personnel

Monitoring genetic population biomarkers for wastewater-based epidemiology

We report a rapid “sample-to-answer” platform that can be used for the quantitative monitoring of genetic biomarkers within communities through the analysis of wastewater. The assay is based on the loop-mediated isothermal amplification (LAMP) of nucleic acid biomarkers and shows for the first time the ability to rapidly quantify human-specific mitochondrial DNA (mtDNA) from raw untreated wastewater samples. mtDNA provides a model population biomarker associated with carcinogenesis including breast, renal and gastric cancers. To enable a sample-to-answer, field-based technology, we integrated a filter to remove solid impurities and perform DNA extraction and enrichment into a low cost lateral flow-based test. We demonstrated mtDNA detection over seven consecutive days, achieving a limit of detection of 40 copies of human genomic DNA per reaction volume. The assay can be performed at the site of sample collection, with minimal user intervention, yielding results within 45 min and providing a method to monitor public health from wastewater

Irreversibility for all bound entangled states

We derive a new inequality for entanglement for a mixed four-partite state. Employing this inequality, we present a one-shot lower bound for entanglement cost and prove that entanglement cost is strictly larger than zero for any entangled state. We demonstrate that irreversibility occurs in the process of formation for all non-distillable entangled states. In this way we solve a long standing problem, of how "real" is entanglement of bound entangled states. Using the new inequality we also prove impossibility of local-cloning of a known entangled state.Comment: The publication version. As noted in quant-ph/0510035, the result also implies that the mathematical definition of entangled states is equivalent to the physical definition in the sense of states preparation by LOC