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arXiv:1504.02707 · npj Quantum Information

Preserving entanglement during weak measurement demonstrated with a violation of the Bell–Leggett–Garg inequality

T. White, J. Mutus, Justin Dressel, J. Kelly, R. Barends, Evan R. Jeffrey, D. Sank, A. Megrant, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, Charles Neill, P. J. J. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, Alexander N. Korotkov, John M. Martinis

Published Feb 16, 2016• 61 citations

Abstract

Abstract Weak measurement has provided new insight into the nature of quantum measurement, by demonstrating the ability to extract average state information without fully projecting the system. For single-qubit measurements, this partial projection has been demonstrated with violations of the Leggett–Garg inequality. Here we investigate the effects of weak measurement on a maximally entangled Bell state through application of the Hybrid Bell–Leggett–Garg inequality (BLGI) on a linear chain of four transmon qubits. By correlating the results of weak ancilla measurements with subsequent projective readout, we achieve a violation of the BLGI with 27 s.d.s. of certainty.

DOI: 10.1038/npjqi.2015.22

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In the paper cited in the title, experimental results were presented that clearly prove that the quantum entanglement between two qubits is preserved after weak enough measurements are performed on them. The theoretical interpretation of the reported results, however, requires further consideration.

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Comment on White, Mutus, Dressel, et al., "Preserving entanglement..." [arXiv:1504.02707]

David H. Oaknin

In the cited paper [White, T., Mutus, J., Dressel, J. et al., Preserving entanglement during weak measurement demonstrated with a violation of the Bell-Leggett-Garg inequality, npj Quantum Information 2, 15022 (2016), arXiv:1504.02707], experimental results were presented that clearly prove that the quantum entanglement between two qubits is preserved after weak enough measurements are performed on them. The theoretical interpretation of the reported results, however, requires further consideration.

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Comment on White, Mutus, Dressel, et al., "Preserving entanglement during weak measurement ... " [arXiv:1504.02707]

David H. Oaknin

In the cited paper [White, T., Mutus, J., Dressel, J. et al., "Preserving entanglement during weak measurement demonstrated with a violation of the Bell-Leggett-Garg inequality", npj Quantum Information 2, 15022 (2016), arXiv:1504.02707], experimental results were presented that clearly prove that the quantum entanglement between two qubits is preserved after weak enough measurements are performed on them. The theoretical interpretation of the reported results, however, requires further consideration. The remarks made in this paper may have serious implications both for quantum foundations and for quantum cryptography.

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Abstract Weak measurement has provided new insight into the nature of quantum measurement, by demonstrating the ability to extract average state information without fully projecting the system. For single-qubit measurements, this partial projection has been demonstrated with violations of the Leggett–Garg inequality. Here we investigate the effects of weak measurement on a maximally entangled Bell state through application of the Hybrid Bell–Leggett–Garg inequality (BLGI) on a linear chain of four transmon qubits. By correlating the results of weak ancilla measurements with subsequent projective readout, we achieve a violation of the BLGI with 27 s.d.s. of certainty.

Leggett and Garg derived inequalities that probe the boundaries of classical and quantum physics by putting limits on the properties that classical objects can have. Historically, it has been suggested that Leggett-Garg inequalities are easily violated by quantum systems undergoing sequences of strong measurements, casting doubt on whether quantum mechanics correctly describes macroscopic objects. Here I show that Leggett-Garg inequalities cannot be violated by any projective measurement. The perceived violation of the inequalities found previously can be traced back to an inappropriate assumption of non-invasive measurability. Surprisingly, weak projective measurements cannot violate the Leggett-Garg inequalities either because even though the quantum system itself is not fully projected via weak measurements, the measurement devices are.

By weakly measuring the polarization of a photon between two strong polarization measurements, we experimentally investigate the correlation between the appearance of anomalous values in quantum weak measurements and the violation of realism and nonintrusiveness of measurements. A quantitative formulation of the latter concept is expressed in terms of a Leggett-Garg inequality for the outcomes of subsequent measurements of an individual quantum system. We experimentally violate the Leggett-Garg inequality for several measurement strengths. Furthermore, we experimentally demonstrate that there is a one-to-one correlation between achieving strange weak values and violating the Leggett-Garg inequality.

In the cited paper [White, T., Mutus, J., Dressel, J. et al., Preserving entanglement during weak measurement demonstrated with a violation of the Bell-Leggett-Garg inequality, npj Quantum Information 2, 15022 (2016), arXiv:1504.02707], experimental results were presented that clearly prove that the quantum entanglement between two qubits is preserved after weak enough measurements are performed on them. The theoretical interpretation of the reported results, however, requires further consideration.

In the cited paper [White, T., Mutus, J., Dressel, J. et al., "Preserving entanglement during weak measurement demonstrated with a violation of the Bell-Leggett-Garg inequality", npj Quantum Information 2, 15022 (2016), arXiv:1504.02707], experimental results were presented that clearly prove that the quantum entanglement between two qubits is preserved after weak enough measurements are performed on them. The theoretical interpretation of the reported results, however, requires further consideration. The remarks made in this paper may have serious implications both for quantum foundations and for quantum cryptography.

Quantum mechanics presents peculiar properties that, on the one hand, have been the subject of several theoretical and experimental studies about its very foundations and, on the other hand, provide tools for developing new technologies, the so-called quantum technologies. The nonclassicality pointed out by Leggett-Garg inequalities has represented, with Bell inequalities, one of the most investigated subjects. In this article we study the connection of Leggett-Garg inequalities with a new emerging field of quantum measurement, the weak values in the case of a series of sequential measurements on a single object. In detail, we perform an experimental study of the four-time-correlator Leggett-Garg test, by exploiting single and sequential weak measurements performed on heralded single photons.