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- Published: Friday, 19 April 2019

# Coincidence helps with quantum measurements

Experimentally, quantum phenomena are notoriously difficult to deal with; the effort needed to characterise systems involving quantum phenomena increases dramatically with the size of the system. Engineered quantum systems consisting of tens of individually controllable interacting quantum particles are currently being developed using multiple different physical platforms [1-3] – including in our own group in Innsbruck, where trapped ions are used.

Such quantum simulators and quantum computers are considered to be promising early applications of quantum technologies – with the potential to solve problems where simulations on conventional, so-called “classical” computers fail, due to the complexity of the problems.

However, the quantum systems used as quantum simulators must continue to grow in size for this stage to be reached. In order to operate a quantum simulator consisting of ten or more particles in the laboratory, the states of the system must be characterised as accurately as possible. So far, methods such as quantum state tomography have been used for the characterisation of quantum states, with which the state of the system can be completely described. This method, however, involves a very high measuring and computing effort, and so becomes unfeasible for systems with more than half a dozen particles.

M.R.Knabl

An important property to measure in engineered quantum systems is entanglement, which is a key feature of many-body systems, and a phenomenon that is still difficult to understand. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. A theory-experiment collaboration between researchers in our group, researchers in the group of Peter Zoller, and the IQOQI Innsbruck, have presented and experimentally demonstrated a protocol to measure the second-order Rényi entropy. The new method is based on the repeated measurements of randomly selected transformations of individual particles [4]. The statistical evaluation of the measurement results then provides information about the entanglement in the system. 500 local transformations were performed on each ion, with the measurements repeated a total of 150 times in order to use statistical correlations between measurements to determine information about the entanglement of the state.

The experiments were performed using a trapped-ion quantum simulator with partition sizes of up to 10 qubits. The platform consisted of up to 20 ions confined in a linear Paul trap, with each experiment consisting of either ten ions, or a ten-ion subsystem of a 20-ion chain. Starting from a simple product state, the individual particles interacted through the use of laser pulses. The dynamical development of the system was subsequently characterised using the protocol, with the results proving the overall coherent character of the system dynamics, as well as revealing the growth of entanglement between its parts – in both the absence and presence of disorder. Our protocol represents a universal tool for probing and characterising engineered quantum systems in the laboratory, and is applicable to arbitrary quantum states of up to several tens of qubits.

In the laboratory, this new method provides an unprecedented ability to understand our quantum simulator in more detail than ever before, as well as providing access to quantities such as the purity and entanglement in the system.

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The work financially supported by the European Research Council ERC, the Austrian Science Fund FWF, QTFLAG-QuantERA, and the Quantum Flagship project PASQuanS

Literature

[1] I. Bloch, J. Dalibard, S. Nascimbène, Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012). doi:10.1038/nphys2259

[2] A. Browaeys, D. Barredo, T. Lahaye, Experimental investigations of dipole–dipole interactions between a few Rydberg atoms. J. Phys. B 49, 152001 (2016). doi:10.1088/0953-4075/49/15/152001

[3] J. M. Gambetta, J. M. Chow, M. Steffen, Building logical qubits in a superconducting quantum computing system. npj Quantum Inf. 3, 2 (2017). doi:10.1038/s41534-016-0004-0

[4] A. Elben, B. Vermersch, C. F. Roos, P. Zoller, Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states. arXiv:1812.02624 [quant-ph] (6 Dec 2018).