Witnessing Entanglement in Experiments with Correlated Noise
arXiv:2002.12400 · doi:10.1088/2058-9565/ab8d88
Abstract
The purpose of an entanglement witness experiment is to certify the creation of an entangled state from a finite number of trials. The statistical confidence of such an experiment is typically expressed as the number of observed standard deviations of witness violations. This method implicitly assumes that the noise is well-behaved so that the central limit theorem applies. In this work, we propose two methods to analyze witness experiments where the states can be subject to arbitrarily correlated noise. Our first method is a rejection experiment, in which we certify the creation of entanglement by rejecting the hypothesis that the experiment can only produce separable states. We quantify the statistical confidence by a p-value, which can be interpreted as the likelihood that the observed data is consistent with the hypothesis that only separable states can be produced. Hence a small p-value implies large confidence in the witnessed entanglement. The method applies to general witness experiments and can also be used to witness genuine multipartite entanglement. Our second method is an estimation experiment, in which we estimate and construct confidence intervals for the average witness value. This confidence interval is statistically rigorous in the presence of correlated noise. The method applies to general estimation problems, including fidelity estimation. To account for systematic measurement and random setting generation errors, our model takes into account device imperfections and we show how this affects both methods of statistical analysis. Finally, we illustrate the use of our methods with detailed examples based on a simulation of NV centers.
arXiv commentAccepted for publication in Quantum Science and Technology (2020). v2 (minor changes): title changed, additional clarification in several places, added simulation details. 21 pages + 12 pages appendices, 7 figures, 6 tables
References in corpus (35)
- Quantum entanglement
- Separability Criterion for Density Matrices
- Separability of Mixed States: Necessary and Sufficient Conditions
- Entanglement detection
- Efficient classical simulation of slightly entangled quantum computations
- A quantum network of clocks
- Deterministic delivery of remote entanglement on a quantum network
- Witnessing multipartite entanglement
- 18-qubit entanglement with photon's three degrees of freedom
- 10-qubit entanglement and parallel logic operations with a superconducting circuit
- Longer-Baseline Telescopes Using Quantum Repeaters
- 12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion
- Quantum Clock Synchronization Based on Shared Prior Entanglement
- Observation of Entangled States of a Fully Controlled 20-Qubit System
- Quantum Cryptography Beyond Quantum Key Distribution
- Measurement-Device-Independent Entanglement Witnesses for All Entangled Quantum States
- On Hoeffding's inequalities
- Imperfect measurements settings: implications on quantum state tomography and entanglement witnesses
- Self-testing multipartite entangled states through projections onto two systems
- Active resonator reset in the nonlinear dispersive regime of circuit QED
- Entanglement Witnesses for Graph States: General Theory and Examples
- Asymptotically optimal data analysis for rejecting local realism
- Quantum cryptography: key distribution and beyond
- Practical, Reliable Error Bars in Quantum Tomography
- Resource-efficient verification of quantum computing using Serfling's bound
- Detecting multipartite entanglement structure with minimal resources
- Switchable phonon diodes using nonlinear topological Maxwell lattices
- Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states
- (Nearly) optimal P-values for all Bell inequalities
- Entanglement witnesses and a loophole problem
- Experimental detection of entanglement with optimal-witness families
- Experimental implementation of a NMR entanglement witness
- Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement
- Entanglement witness game
- Lower Bounds for Quantum Parameter Estimation