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arXiv:1706.00252 · Physical Review A

Entanglement measures in embedding quantum simulators with nuclear spins

Tao Xin, Julen Simon Pedernales, E. Solano, Gui‐Lu Long

Published Feb 14, 2018• 15 citations
arXivHTMLPDF

Abstract

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 $^{13}\mathrm{C}$ atoms in a molecule of trans-crotonic acid manipulated with NMR techniques.

DOI
10.1103/physreva.97.022322

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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.
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 propose and experimentally demonstrate an efficient framework for the quantum simulation of quantum channels in nuclear magnetic resonance (NMR). Our approach relies on the suitable decomposition of nonunitary operators in a linear combination of ddd unitary ones, which can be then experimentally implemented with the assistance of a number of ancillary qubits that grows logarithmically in ddd. As a proof-of-principle demonstration, we realize the quantum simulation of three quantum channels for a single-qubit: phase damping, amplitude damping, and depolarizing channels. For these paradigmatic cases, we measure key features, such as the fidelity of the initial state and the associated von Neumann entropy for a qubit evolving through these channels. Our experiments are carried out using nuclear spins in a liquid sample and NMR control techniques.
We report the implementation of two- and three-spin quantum erasers using nuclear magnetic resonance (NMR). Quantum erasers provide a means of manipulating quantum entanglement, an important resource for quantum information processing. Here, we first use a two-spin system to illustrate the essential features of quantum erasers. The extension to a three-spin ``disentanglement eraser'' shows that entanglement in a subensemble can be recovered if a proper measurement of the ancillary system is carried out. Finally, we use the same pair of orthogonal decoherent operations used in quantum erasers to probe the two classes of entanglement in tripartite quantum systems: the Greenberger-Horne-Zeilinger state and the W state. A detailed presentation is given of the experimental decoherent control methods that emulate the loss of phase information in strong measurements, and the use of NMR decoupling techniques to implement partial trace operations.
In recent years, the performance of different entanglement indicators obtained directly from tomograms has been assessed in continuous-variable and hybrid quantum systems. In this paper, we carry out this task in the case of spin systems. We compute the entanglement indicators from actual experimental data obtained from three liquid-state nuclear magnetic resonance (NMR) experiments and compare them with standard entanglement measures calculated from the corresponding density matrices, both experimentally reconstructed and numerically computed. The gross features of entanglement dynamics and spin squeezing properties are found to be reproduced by these entanglement indicators. However, the extent to which these indicators and spin squeezing track the entanglement during time evolution of the multipartite systems in the NMR experiments is very sensitive to the precise nature and strength of interactions as well as the manner in which the full system is partitioned into subsystems. We also use the IBM quantum computer to implement equivalent circuits that capture the dynamics of the multipartite system in one of the NMR experiments and carry out a similar comparative assessment of the performance of tomographic indicators. This exercise shows that these indicators can estimate the degree of entanglement without necessitating detailed state reconstruction procedures, establishing the advantage of the tomographic approach.
In this work, we have been working on the concept of quantum entanglement. At first, we studied the theory of entanglement in its characterization and measurement, introducing a new scheme for detection of entanglement. The new approach links molecular-spin entities involving nuclear spins to quantum computing as more appropriate physical systems of interest. Then, we continued with the realization of entanglement in experiments. NMR has been the first choice due to its well approved advantages for quantum computing. NMR, however, has not been an appropriate system for demonstrating entangled states. Through a mathematical proof, NMR with low spin polarization has been invalidated for true implementations of non-local quantum algorithms, particularly supserdense coding. The point is that high spin polarization is inevitably required to acquire entanglement while in the current NMR it has been a formidable task to get highly polarized nuclear spins. In order to acquire high spin polarization, introducing electron spins can be much effective because of its three-order-of-magnitude larger gyromagnetic ratio compared to nuclear spins. Electron Nuclear DOuble Resonance (ENDOR) is spin manipulation technology that enables us to deal with both electron and nuclear spins. Thus, in this context, it can be more appropriate device for quantum computing. We emphasize that (pseudo)entanglement and interconversion between the entangled states have been realized with ENDOR on extremely stable organic molecular-spin entities. The required experimental conditions to obtain true quantum entanglement are also discussed. The appropriate entanglement witness for the corresponding ensemble quantum computing is introduced and examined.