Exponentially decreasing critical detection efficiency for any Bell inequality

Abstract

We address the problem of closing the detection efficiency loophole in Bell experiments, which is crucial for real-world applications. Every Bell inequality has a critical detection efficiency $\eta$ that must be surpassed to avoid the detection loophole. Here, we propose a general method for reducing the critical detection efficiency of any Bell inequality to arbitrary low values. This is accomplished by entangling two particles in $N$ orthogonal subspaces (e.g., $N$ degrees of freedom) and conducting $N$ Bell tests in parallel. Furthermore, the proposed method is based on the introduction of penalized $N$-product (PNP) Bell inequalities, for which the so-called simultaneous measurement loophole is closed, and the maximum value for local hidden-variable theories is simply the $N$th power of the one of the Bell inequality initially considered. We show that, for the PNP Bell inequalities, the critical detection efficiency decays exponentially with $N$. The strength of our method is illustrated with a detailed study of the PNP Bell inequalities resulting from the Clauser-Horne-Shimony-Holt inequality.

5 + 2 pages, 2 figures. v4: Construction of PNP Bell inequalities is improved

References in corpus (36)

• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Device-independent security of quantum cryptography against collective attacks
• Significant-loophole-free test of Bell's theorem with entangled photons
• Random Numbers Certified by Bell's Theorem
• A strong loophole-free test of local realism
• No Signalling and Quantum Key Distribution
• Device-independent quantum key distribution secure against collective attacks
• Advances in High Dimensional Quantum Entanglement
• Bounding the set of quantum correlations
• Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes
• Self-testing of quantum systems: a review
• A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality
• Closing the detection loophole in Bell experiments using qudits
• Device-independent randomness expansion against quantum side information
• Quantum nonlocality, Bell inequalities and the memory loophole
• Detection loophole in asymmetric Bell experiments
• Device-independent Randomness Expansion with Entangled Photons
• Non locality, closing the detection loophole and communication complexity
• Minimum detection efficiency for a loophole-free atom-photon Bell experiment
• Algorithm 950: Ncpol2sdpa---Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables
• Quantum key distribution overcoming extreme noise: simultaneous subspace coding using high-dimensional entanglement
• Detection Loophole in Bell experiments: How post-selected local correlations can look non-local
• Fully nonlocal, monogamous, and random genuinely multipartite quantum correlations
• Device-Independent Certification of a Nonprojective Qubit Measurement
• Necessary and sufficient detection efficiency for the Mermin inequalities
• Strict detector-efficiency bounds for n-site Clauser-Horne inequalities
• Device-Independent Secret Sharing and a Stronger Form of Bell Nonlocality
• Parallel Device-Independent Quantum Key Distribution
• Experimental certification of an informationally complete quantum measurement in a device-independent protocol
• Device-independent tests of structures of measurement incompatibility
• Bipartite Bell inequalities for hyperentangled states
• Bell nonlocality with a single shot
• Minimum Detection Efficiencies for a Loophole-Free Bell-type Test
• Closing the detection loophole in multipartite Bell tests using GHZ states
• Tests of Bell inequality with arbitrarily low photodetection efficiency and homodyne measurements
• The influence of the choice of post-processing method on Bell inequalities

Cited by in corpus (13)

• Advances in device-independent quantum key distribution
• Energy-time and time-bin entanglement: past, present and future
• Complete hierarchy for high-dimensional steering certification
• Graph-theoretic approach to Bell experiments with low detection efficiency
• The future of secure communications: device independence in quantum key distribution
• Bounding the detection efficiency threshold in Bell tests using multiple copies of the maximally entangled two-qubit state carried by a single pair of particles
• The Schmidt rank for the commuting operator framework
• Self-testing tilted strategies for maximal loophole-free nonlocality
• Coincidence postselection for genuine multipartite nonlocality: Causal diagrams and threshold efficiencies
• Loophole-free Bell tests with randomly chosen subsets of measurement settings
• Entanglement witnessing with untrusted detectors
• Semi-device-independent certification of number of measurements
• How Likely Are You to Observe Non-locality with Imperfect Detection Efficiency and Random Measurement Settings?