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Violations of a Leggett-Garg inequality without signaling for a photonic qutrit probed with ambiguous measurements

Kunkun Wang, Clive Emary, Mengyan Xu, Xiang Zhan, Zhihao Bian, Lei Xiao, Peng Xue

Published Feb 5, 2018• 0 citations
Publisher

Abstract

© 2018 American Physical Society. We realize a quantum three-level system with photons distributed among three different spatial and polarization modes. Ambiguous measurements of the state of the qutrit are realized by blocking one out for the three modes at any one time. Using these measurements we construct a test of a Leggett-Garg inequality as well as tests of no-signaling-in-time for the measurements. We observe violations of the Leggett-Garg inequality that cannot be accounted for in terms of signaling. Moreover, we tailor the qutrit dynamics such that both ambiguous and unambiguous measurements are simultaneously nonsignaling, which is an essential step for the justification of the use of ambiguous measurements in Leggett-Garg tests.

DOI
10.25405/ncl.34349691

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© 2018 American Physical Society. We realize a quantum three-level system with photons distributed among three different spatial and polarization modes. Ambiguous measurements of the state of the qutrit are realized by blocking one out for the three modes at any one time. Using these measurements we construct a test of a Leggett-Garg inequality as well as tests of no-signaling-in-time for the measurements. We observe violations of the Leggett-Garg inequality that cannot be accounted for in terms of signaling. Moreover, we tailor the qutrit dynamics such that both ambiguous and unambiguous measurements are simultaneously nonsignaling, which is an essential step for the justification of the use of ambiguous measurements in Leggett-Garg tests.
We realize a quantum three-level system with photons distributed among three different spatial and polarization modes. Ambiguous measurements of the state of the qutrit are realized by blocking one out for the three modes at any one time. Using these measurements we construct a test of a Leggett-Garg inequality as well as tests of no-signaling-in-time for the measurements. We observe violations of the Leggett-Garg inequality that cannot be accounted for in terms of signaling. Moreover, we tailor the qutrit dynamics such that both ambiguous and unambiguous measurements are simultaneously nonsignaling, which is an essential step for the justification of the use of ambiguous measurements in Leggett-Garg tests.
Ambiguous measurements do not reveal complete information about the system under test. Their quantum-mechanical counterparts are semiweak (or in the limit, weak) measurements and here we discuss their role in tests of the Leggett-Garg inequalities. We show that, while ambiguous measurements allow one to forgo the usual noninvasive measurability assumption, to derive a Leggett-Garg inequality that may be violated, we are forced to introduce another assumption that equates the invasive influence of ambiguous and unambiguous detectors. Based on this assumption, we derive signaling conditions that should be fulfilled for the plausibility of the Leggett-Garg test. We then propose an experiment on a three-level system with a direct quantum-optics realization that satisfies all signaling constraints and violates a Leggett-Garg inequality.
Leggett-Garg inequalities are tests of macroscopic realism that can be violated by quantum mechanics. In this letter, we realise photonic Leggett-Garg tests on a three-level system and implement measurements that admit three distinct measurement outcomes, rather than the usual two. In this way we obtain violations of three- and four-time Leggett-Garg inequalities that are significantly in excess of those obtainable in standard Leggett-Garg tests. We also report violations the quantum-witness equality up to the maximum permitted for a three-outcome measurement. Our results highlight differences between spatial and temporal correlations in quantum mechanics.
Leggett-Garg inequalities are tests of macroscopic realism that can be violated by quantum mechanics. In this letter, we realise photonic Leggett-Garg tests on a three-level system and implement measurements that admit three distinct measurement outcomes, rather than the usual two. In this way we obtain violations of three- and four-time Leggett-Garg inequalities that are significantly in excess of those obtainable in standard Leggett-Garg tests. We also report violations the quantum-witness equality up to the maximum permitted for a three-outcome measurement. Our results highlight differences between spatial and temporal correlations in quantum mechanics.
In contrast to the spatial Bell's inequalities which probe entanglement between spatially separated systems, the Leggett–Garg inequalities test the correlations of a single system measured at different times. Violation of a genuine Leggett–Garg test implies either the absence of a realistic description of the system or the impossibility of measuring the system without disturbing it. Quantum mechanics violates the inequalities on both accounts and the original motivation for these inequalities was as a test for quantum coherence in macroscopic systems. The last few years has seen a number of experimental tests and violations of these inequalities in a variety of microscopic systems such as superconducting qubits, nuclear spins, and photons. In this article, we provide an introduction to the Leggett–Garg inequalities and review these latest experimental developments. We discuss important topics such as the significance of the non-invasive measurability assumption, the clumsiness loophole, and the role of weak measurements. Also covered are some recent theoretical proposals for the application of Leggett–Garg inequalities in quantum transport, quantum biology and nano-mechanical systems.
Macrorealistic description governing the classical realm is known to get uprooted in the quantum domain. The Leggett-Garg inequality [A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985)] proposes to probe the macrorealistic limit emerging from the quantum scenario. It places a bound on the linear combinations of temporal correlations of observables measured sequentially at different time intervals. Violation of the Leggett-Garg inequality, up to the so-called temporal Tsirelson bound (TTB), has been realized in the quantum domain. It is important to understand whether quantum theory permits larger violation beyond the TTB and up to the algebraic maximum value of the Leggett-Garg inequality. To this end, it has been shown [C. Budroni and C. Emary, Phys. Rev. Lett. 113, 050401 (2014)] that a three-term Leggett-Garg inequality can be violated beyond the TTB 3/23/23/2 in the time evolution of N>2N>2N>2 level quantum systems by choosing suitable measurement schemes and state-update rules. Furthermore, it is revealed that the algebraic maximum value 3 can be realized in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$. Their measurement scheme rules out violation of the Leggett-Garg inequality beyond the TTB by a qubit. Being genuinely quantum in nature, we ask whether such enhanced violation of the Leggett-Garg inequality could be witnessed in a qubit itself. Here, we show that a qubit undergoing time evolution generated by a non-Hermitian PT\mathcal{P}\mathcal{T}PT-symmetric Hamiltonian indeed violates the three-term Leggett-Garg inequality beyond the TTB and up to its algebraic maximum value 3.