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arXiv:1701.04630 · Physical Review A

Optimal experimental demonstration of error-tolerant quantum witnesses

Kunkun Wang, George C. Knee, Xiang Zhan, Zhihao Bian, Jian Li, Peng Xue

Published Mar 17, 2017• 35 citations
arXivHTMLPDF

Abstract

Testing quantum theory on macroscopic scales is a longstanding challenge whose solution could have a significant impact on physics. For example, laboratory tests (such as those anticipated in nanomechanical or biological systems) may look to rule out macroscopic realism: the idea that the properties of macroscopic objects exist objectively and can be noninvasively measured. Such investigations are likely to suffer from (i) stringent experimental requirements, (ii) marginal statistical significance, and (iii) logical loopholes. We address all of these problems by refining two tests of macroscopic realism, or ``quantum witnesses'', and implementing them in a microscopic test on a photonic qubit and qutrit. The first witness heralds the invasiveness of a blind measurement; its maximum violation has been shown to grow with the dimensionality of the system under study. The second witness heralds the invasiveness of a generic quantum channel and can achieve its maximum violation in any dimension; it therefore allows for the highest quantum signal-to-noise ratio and most significant refutation of the classical point of view.

DOI
10.1103/physreva.95.032122

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Testing quantum theory on macroscopic scales is a longstanding challenge whose solution could have a significant impact on physics. For example, laboratory tests (such as those anticipated in nanomechanical or biological systems) may look to rule out macroscopic realism: the idea that the properties of macroscopic objects exist objectively and can be noninvasively measured. Such investigations are likely to suffer from (i) stringent experimental requirements, (ii) marginal statistical significance, and (iii) logical loopholes. We address all of these problems by refining two tests of macroscopic realism, or ``quantum witnesses'', and implementing them in a microscopic test on a photonic qubit and qutrit. The first witness heralds the invasiveness of a blind measurement; its maximum violation has been shown to grow with the dimensionality of the system under study. The second witness heralds the invasiveness of a generic quantum channel and can achieve its maximum violation in any dimension; it therefore allows for the highest quantum signal-to-noise ratio and most significant refutation of the classical point of view.
Macroscopic realism is the name for a class of modifications to quantum theory that allow macroscopic objects to be described in a measurement-independent manner, while largely preserving a fully quantum mechanical description of the microscopic world. Objective collapse theories are examples which aim to solve the quantum measurement problem through modified dynamical laws. Whether such theories describe nature, however, is not known. Here we describe and implement an experimental protocol capable of constraining theories of this class, that is more noise tolerant and conceptually transparent than the original Leggett-Garg test. We implement the protocol in a superconducting flux qubit, and rule out (by ∼84 s.d.) those theories which would deny coherent superpositions of 170 nA currents over a ∼10 ns timescale. Further, we address the 'clumsiness loophole' by determining classical disturbance with control experiments. Our results constitute strong evidence for the superposition of states of nontrivial macroscopic distinctness.
We consider the quantum-witness test of macroscopic realism and derive an upper bound for possible violations of this equality due to quantum mechanics. The bound depends only on the number of possible outcomes for the blind measurement at the heart of the witness protocol. Mirroring recent results for the related Leggett-Garg inequality, we show that quantum mechanics can saturate the algebraic bound for large systems. We also establish a connection between the quantum witness and the trace distance between density matrices and discuss how the quantum witness can be used to obtain a bound on the Hilbert-space dimension of the system under study.
According to the world view of macrorealism, the properties of a given system exist prior to and independent of measurement, which is incompatible with quantum mechanics. Leggett and Garg put forward a practical criterion capable of identifying violations of macrorealism, and so far experiments performed on microscopic and mesoscopic systems have always agreed with quantum mechanics. However, a macrorealist can always assign the cause of such violations to the perturbation that measurements effect on such small systems, and hence a definitive test would require using noninvasive measurements, preferably on macroscopic objects, where such measurements seem more plausible. However, the generation of truly macroscopic quantum superposition states capable of violating macrorealism remains a big challenge. In this work we propose a setup that makes use of measurements on the polarization of light, a property that has been extensively manipulated both in classical and quantum contexts, hence establishing the perfect link between the microscopic and macroscopic worlds. In particular, we use Leggett-Garg inequalities and the criterion of no signaling in time to study the macrorealistic character of light polarization for different kinds of measurements, in particular with different degrees of coarse graining. Our proposal is noninvasive for coherent input states by construction. We show for states with well-defined photon number in two orthogonal polarization modes, that there always exists a way of making the measurement sufficiently coarse grained so that a violation of macrorealism becomes arbitrarily small, while sufficiently sharp measurements can always lead to a significant violation.
Macroscopic realism is the thesis that macroscopically observable properties must always have definite values. The idea was introduced by Leggett and Garg (1985), who wished to show a conflict with the predictions of quantum theory, by using it to derive an inequality that quantum theory violates. However, Leggett and Garg's analysis required not just the assumption of macroscopic realism per se, but also that the observable properties could be measured non-invasively. In recent years there has been increasing interest in experimental tests of the violation of the Leggett-Garg inequality, but it has remained a matter of controversy whether this second assumption is a reasonable requirement for a macroscopic realist view of quantum theory. In a recent critical assessment Maroney and Timpson (2014) identified three different categories of macroscopic realism, and argued that only the simplest category could be ruled out by Leggett-Garg inequality violations. Allen, Maroney, and Gogioso (2016) then showed that the second of these approaches was also incompatible with quantum theory in Hilbert spaces of dimension 4 or higher. However, we show that the distinction introduced by Maroney and Timpson between the second and third approaches is not noise tolerant, so unfortunately Allen's result, as given, is not directly empirically testable. In this paper we replace Maroney and Timpson's three categories with a parameterization of macroscopic realist models, which can be related to experimental observations in a noise tolerant way, and recover the original definitions in the noise-free limit. We show how this parameterization can be used to experimentally rule out classes of macroscopic realism in Hilbert spaces of dimension 3 or higher, without any use of the non-invasive measurability assumption. Even for relatively low precision experiments, this will rule out the original category of macroscopic realism, that is tested by the Leggett-Garg inequality, while as the precision of the experiments increases, all cases of the second category and many cases of the third category, will become experimentally ruled out.