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arXiv:1506.05353 · Physical Review Letters

Efficient Measurement of Multiparticle Entanglement with Embedding Quantum Simulator

Ming-Cheng Chen, Dian Wu, Zu-En Su, Xin-Dong Cai, Xi‐Lin Wang, Tao Yang, Li Li, Nai-Le Liu, Chao‐Yang Lu, Jian-Wei Pan

Published Feb 18, 2016• 18 citations
arXivHTMLPDF

Abstract

The quantum measurement of entanglement is a demanding task in the field of quantum information. Here, we report the direct and scalable measurement of multiparticle entanglement with embedding photonic quantum simulators. In this embedding framework [R. Di Candia et al. Phys. Rev. Lett. 111, 240502 (2013)], the N-qubit entanglement, which does not associate with a physical observable directly, can be efficiently measured with only two (for even N) and six (for odd N) local measurement settings. Our experiment uses multiphoton quantum simulators to mimic dynamical concurrence and three-tangle entangled systems and to track their entanglement evolutions.

DOI
10.1103/physrevlett.116.070502

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The quantum measurement of entanglement is a demanding task in the field of quantum information. Here, we report the direct and scalable measurement of multiparticle entanglement with embedding photonic quantum simulators. In this embedding framework [R. Di Candia et al. Phys. Rev. Lett. 111, 240502 (2013)], the N-qubit entanglement, which does not associate with a physical observable directly, can be efficiently measured with only two (for even N) and six (for odd N) local measurement settings. Our experiment uses multiphoton quantum simulators to mimic dynamical concurrence and three-tangle entangled systems and to track their entanglement evolutions.
Measuring entanglement is a demanding task that usually requires full tomography of a quantum system, involving a number of observables that grows exponentially with the number of parties. Recently, it was suggested that adding a single ancillary qubit would allow for the efficient measurement of concurrence, and indeed any entanglement monotone associated with antilinear operations. Here, we report on the experimental implementation of such a device-an embedding quantum simulator-in photonics, encoding the entangling dynamics of a bipartite system into a tripartite one. We show that bipartite concurrence can be efficiently extracted from the measurement of merely two observables, instead of 15, without full tomographic information.
We implement an embedding quantum simulator (EQS) in nuclear spin systems. The experiment consists of a simulator of up to three qubits, plus a single ancillary qubit, where we are able to efficiently measure the concurrence and the three-tangle of two-qubit and three-qubit systems as they undergo entangling dynamics. The EQS framework allows us to drastically reduce the number of measurements needed for this task, which otherwise would require full-state reconstruction of the qubit system. Our simulator is built of the nuclear spins of four 13C^{13}\mathrm{C}13C atoms in a molecule of trans-crotonic acid manipulated with NMR techniques.
Abstract Entanglement is a key ingredient for quantum technologies and a fundamental signature of quantumness in a broad range of phenomena encompassing many-body physics, thermodynamics, cosmology and life sciences. For arbitrary multiparticle systems, entanglement quantification typically involves nontrivial optimisation problems, and it may require demanding tomographical techniques. Here, we develop an experimentally feasible approach to the evaluation of geometric measures of multiparticle entanglement. Our framework provides analytical results for particular classes of mixed states of N qubits, and computable lower bounds to global, partial, or genuine multiparticle entanglement of any general state. For global and partial entanglement, useful bounds are obtained with minimum effort, requiring local measurements in just three settings for any N. For genuine entanglement, a number of measurements scaling linearly with N are required. We demonstrate the power of our approach to estimate and quantify different types of multiparticle entanglement in a variety of N-qubit states useful for quantum information processing and recently engineered in laboratories with quantum optics and trapped ion setups.
Randomized measurements constitute a simple measurement primitive that exploits the information encoded in the outcome statistics of samples of local quantum measurements defined through randomly selected bases. In this work we exploit the potential of randomized measurements in order to probe the amount of entanglement contained in multiparticle quantum systems as quantified by the multiparticle concurrence. We further present a detailed statistical analysis of the underlying measurement resources required for a confident estimation of the introduced quantifiers using analytical tools from the theory of random matrices. The introduced framework is demonstrated by a series of numerical experiments analyzing the concurrence of typical multiparticle entangled states as well as of ensembles of output states produced by random quantum circuits. Finally, we examine the multiparticle entanglement of mixed states produced by noisy quantum circuits consisting of single- and two-qubit gates with nonvanishing depolarization errors, thus showing that our framework is directly applicable in the noisy intermediate-scale regime.
Entanglement plays a fundamental role in quantum physics and information processing. Here, we develop an unbiased estimator for mixed-state entanglement in the few-shot scenario and directly estimate it using random unitary evolution in a photonic system. As a supplement to traditional projective measurements, we incorporate Bell measurements on qubit-pairs, enriching the previous randomized measurement scheme, which is no-go in this task with only local unitary evolution. The scheme is scalable to n-qubits via Bell measurements on qubit-pairs. The estimator can be derived directly from a few consecutive outcomes while exhibiting greater robustness to system errors and noise compared to schemes based on shadow estimation. We find that, under a fixed measurement resource, the way with more versatile measurement settings with fewer repeats per setting is more efficient. Our protocol and demonstration advance the direct characterization of quantum states in practice.
In this Brief Report we discuss entanglement of multiparticle quantum systems. We propose a potential measure of a type of entanglement of pure states of nnn qubits, the $n\ensuremath{-}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}.$ For a system of two qubits the $n\ensuremath{-}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}$ is equal to the square of the concurrence, and for systems of three qubits it is equal to the ``residual entanglement.'' We show that the $n\ensuremath{-}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}$ is also equal to a generalization of the concurrence squared for even n,n,n, and use this fact to prove that the $n\ensuremath{-}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}$ is an entanglement monotone. However, the $n\ensuremath{-}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}$ is undefined for odd n>3.n>3.n>3. Finally, we propose a measure related to the $n\ensuremath{-}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}$ for mixed-state systems of nnn qubits, and find an analytical formula for this measure for even n.n.n.