Entanglement 25 years after Quantum Teleportation: testing joint measurements in quantum networks

Abstract

Twenty-five years after the invention of quantum teleportation, the concept of entanglement gained enormous popularity. This is especially nice to those who remember that entanglement was not even taught at universities until the 1990's. Today, entanglement is often presented as a resource, the resource of quantum information science and technology. However, entanglement is exploited twice in quantum teleportation. First, entanglement is the `quantum teleportation channel', i.e. entanglement between distant systems. Second, entanglement appears in the eigenvectors of the joint measurement that Alice, the sender, has to perform jointly on the quantum state to be teleported and her half of the `quantum teleportation channel', i.e. entanglement enabling entirely new kinds of quantum measurements. I emphasize how poorely this second kind of entanglement is understood. In particular, I use quantum networks in which each party connected to several nodes performs a joint measurement to illustrate that the quantumness of such joint measurements remains elusive, escaping today's available tools to detect and quantify it.

Feature paper, Celebrating the Silver Jubilee of Teleportation (7 pages). V2 (March'19): Many typos corrected (sorry) and a few comments added

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• Constraints on nonlocality in networks from no-signaling and independence
• A neural network oracle for quantum nonlocality problems in networks
• Machine Learning meets Quantum Foundations: A Brief Survey
• Entanglement swapping and quantum correlations via Elegant Joint Measurements
• Experimental Optimal Verification of Entangled States using Local Measurements
• Quantum nonlocality in networks can be demonstrated with an arbitrarily small level of independence between the sources
• Demonstrating the power of quantum computers, certification of highly entangled measurements and scalable quantum nonlocality
• Experimental optimal orienteering via parallel and antiparallel spins
• Quantum information
• Partial self-testing and randomness certification in the triangle network
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• Nonlocality, steering and quantum state tomography in a single experiment
• Towards a minimal example of quantum nonlocality without inputs
• Non-Local Boxes for Networks
• Experimental nonclassicality in a causal network without assuming freedom of choice
• Inequalities witnessing coherence, nonlocality, and contextuality
• Optimal discrimination between real and complex quantum theories
• Quantum violation of local causality in urban network with hybrid photonic technologies
• Compounds of symmetric informationally complete measurements and their application in quantum key distribution
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• Self-testing nonlocality without entanglement
• Bipartite quantum measurements with optimal single-sided distinguishability
• Correspondence between entangled states and entangled bases under local transformations
• Numerically assisted determination of local models in network scenarios
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• Topologically Robust Quantum Network Nonlocality
• Detecting quantum steering in networks
• Classification of joint quantum measurements based on entanglement cost of localization
• A Hierarchy of Multipartite Nonlocality and Device-Independent Effect Witnesses
• Quantum teleportation based on the elegant joint measurement
• Device-independent certification of non-classical joint measurements via causal models
• Towards a measurement theory in QFT: "Impossible" quantum measurements are possible but not ideal
• Noise-robust proofs of quantum network nonlocality
• A positive operator-valued measure for two-photon detection via sum-frequency generation
• Symmetric quantum joint measurements on multiple qubits
• Multipartite Nonlocality in Clifford Networks
• A more generalized two-qubit symmetric quantum joint measurement
• Closing the detection loophole in the triangle network with high-dimensional photonic states
• Tristochastic operations and convolutions of quantum states
• Bell nonlocality in quantum networks with unreliable sources: Loophole-free postelection via self-testing
• Non-projective Bell state measurements
• Violation of the Finner inequality in the four-output triangle network
• Symmetric Localizable Multipartite Quantum Measurements from Pauli Orbits
• Experimental genuine quantum nonlocality in the triangle network
• The Multiqubit Elegant Joint Measurement
• Exploring the Local Landscape in the Triangle Network
• Non-locality of conjugation symmetry: characterization and examples in quantum network sensing
• Quantum Communication -- Celebrating the Silver Jubilee of Teleportation
• Recycling the resource: Sequential usage of shared state in quantum teleportation with weak measurements
• Graph approach to quantum teleportation dynamics
• Semi-device-independent certification of number of measurements
• Localization of joint quantum measurements on ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ by entangled resources with Schmidt number at most $d$
• Entanglement concentration via measurement:- role of imaginarity
• Classical Communication Enhanced Quantum State Verification