Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2012.14997 · Physical Review A

Bipartite Leggett-Garg and macroscopic Bell-inequality violations using cat states: Distinguishing weak and deterministic macroscopic realism

Manushan Thenabadu, M. D. Reid

Published May 16, 2022• 12 citations
arXivHTMLPDF

Abstract

We consider tests of Leggett-Garg's macrorealism and of macroscopic local realism, where for spacelike separated measurements the assumption of macroscopic noninvasive measurability is justified by that of macroscopic Bell locality. We give a mapping between the Bell and Leggett-Garg experiments for microscopic qubits based on spin-$1/2$ eigenstates and gedanken experiments for macroscopic qubits based on two macroscopically distinct coherent states $|\ensuremath{\alpha}\ensuremath{\rangle}$ and $|\ensuremath{-}\ensuremath{\alpha}\ensuremath{\rangle}$ (as $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$). In this mapping, the unitary rotation ${U}_{\ensuremath{\theta}}$ of the Stern-Gerlach analyzer or polarizing beam splitter is realized by a local interaction $H=\mathrm{\ensuremath{\Omega}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}^{4}$ where $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}$ is the number of quanta. By adjusting the time of interaction, one alters the measurement setting $\ensuremath{\theta}$. We thus predict violations of Leggett-Garg and Bell inequalities in a macroscopic regime where coarse-grained measurements $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ need only discriminate between two macroscopically distinct coherent states. To interpret the violations, we distinguish between different definitions of macroscopic realism. Deterministic macroscopic local realism (dMR) assumes the system is in a state with a definite outcome ${\ensuremath{\lambda}}_{\ensuremath{\theta}}$ for the measurement $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ prior to the unitary rotation ${U}_{\ensuremath{\theta}}$, and is negated by the violations. Weak macroscopic realism (wMR) assumes a definite outcome for systems prepared in a superposition ${\ensuremath{\psi}}_{\text{pointer}}$ of two macroscopically distinct eigenstates of $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$, after the unitary rotation ${U}_{\ensuremath{\theta}}$. We find that wMR can be viewed consistently with the violations and with the predictions of quantum mechanics for two tests of wMR. A model is presented in which wMR holds and the macroscopic violations emerge over the course of the unitary dynamics occurring at both sites. Implications for the realism of the micro-macro state generated during a quantum measurement are discussed. Finally, we point out an EPR-type paradox, which demonstrates inconsistency between wMR and the completeness of quantum mechanics at a microscopic level.

DOI
10.1103/physreva.105.052207

Related papers

Weak versus Deterministic Macroscopic Realism, and Einstein–Podolsky–Rosen’s Elements of Reality

Jesse Fulton, Manushan Thenabadu, Run Yan Teh +1 more

The violation of a Leggett–Garg inequality confirms the incompatibility between quantum mechanics and the combined premises (called macro-realism) of macroscopic realism (MR) and noninvasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails for systems in a superposition of macroscopically distinct states—or else, that NIM fails. In this paper, we consider a strong negation of macro-realism, involving superpositions of coherent states, where the NIM premise is replaced by Bell’s locality premise. We follow recent work and propose the validity of a subset of Einstein–Podolsky–Rosen (EPR) and Leggett–Garg premises, referred to as weak macroscopic realism (wMR). In finding consistency with wMR, we identify that the Leggett–Garg inequalities are violated because of failure of both MR and NIM, but also that both are valid in a weaker (less restrictive) sense. Weak MR is distinguished from deterministic macroscopic realism (dMR) by recognizing that a measurement involves a reversible unitary interaction that establishes the measurement setting. Weak MR posits that a predetermined value for the outcome of a measurement can be attributed to the system after the interaction, when the measurement setting is experimentally specified. An extended definition of wMR considers the “element of reality” defined by EPR for system A, where one can predict with certainty the outcome of a measurement on A by performing a measurement on system B. Weak MR posits that this element of reality exists once the unitary interaction determining the measurement setting at B has occurred. We demonstrate compatibility of systems violating Leggett–Garg inequalities with wMR but point out that dMR has been shown to be falsifiable. Other tests of wMR are proposed, the predictions of wMR agreeing with quantum mechanics. Finally, we compare wMR with macro-realism models discussed elsewhere. An argument in favour of wMR is presented: wMR resolves a potential contradiction pointed out by Leggett and Garg between failure of macro-realism and assumptions intrinsic to quantum measurement theory.

arXiv:2101.09476•Entropy•Dec 21, 2023•5 citations

Testing macroscopic local realism using local nonlinear dynamics and time settings

Manushan Thenabadu, G.-L. Cheng, T. Pham +3 more

We show how one may test macroscopic local realism where, differently from conventional Bell tests, all relevant measurements that lead to a violation of a Bell inequality need only distinguish between two macroscopically distinct states of the system being measured. Here, measurements give macroscopically distinct outcomes for some property of the system and do not resolve microscopically (of order $\ensuremath{\hbar}$). To obtain a quantifiable test, we define $N$-scopic local realism where the outcomes are separated by an amount $\ensuremath{\sim}N$. We show for $N$ up to 20 that violations of $N$-scopic local realism are predicted for entangled systems of $N$ bosons at each of two sites. We further demonstrate for arbitrarily large $\ensuremath{\alpha}$ the violation of $\ensuremath{\alpha}$-scopic local realism, for entangled superpositions of coherent states with amplitudes $\ensuremath{\sim}\phantom{\rule{1.0pt}{0ex}}\ensuremath{\alpha}$, infinitely separated in phase space, as $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$. To achieve the Bell violations, the two separated subsystems evolve dynamically according to a local nonlinear unitary interaction. The tests may be understood in two ways. First, they are macroscopic Bell tests involving spacelike separated measurement events, where the choice of measurement setting at each site corresponds to a choice between two different times of local interaction. The interaction may be seen as the unitary stage of a local measurement process. Second, the proposal is a strong version of a Leggett-Garg test of "macrorealism" that uses two trajectories, where the usual assumption of noninvasive measurability as applied to measurements at one site is replaced by that of macroscopic locality. For $N=1$, tests are feasible and give a way to demonstrate ``no classical trajectories'' without the assumption of noninvasive measurability, using instead that of locality.

arXiv:1906.04900•Physical Review A•Aug 5, 2020•14 citations

Macroscopic delayed choice and retrocausality: Quantum eraser, Leggett-Garg, and dimension witness tests with cat states

Manushan Thenabadu, M. D. Reid

We propose delayed-choice experiments carried out with macroscopic qubits, realized as macroscopically distinct coherent states $|\ensuremath{\alpha}\ensuremath{\rangle}$ and $|\ensuremath{-}\ensuremath{\alpha}\ensuremath{\rangle}$. Quantum superpositions of $|\ensuremath{\alpha}\ensuremath{\rangle}$ and $|\ensuremath{-}\ensuremath{\alpha}\ensuremath{\rangle}$ are created via a unitary interaction $U(\ensuremath{\theta})$ based on a nonlinear Hamiltonian, in analogy with polarizing beam splitters used in photonic experiments. Macroscopic delayed-choice experiments give a compelling reason to develop interpretations not allowing macroscopic retrocausality: This would otherwise suggest changes to the macroscopic qubit value based on a future measurement setting $\ensuremath{\phi}$. We therefore consider weak macroscopic realism (wMR), which for the system at time $t$ specifies a hidden variable ${\ensuremath{\lambda}}_{\ensuremath{\theta}}$ to determine the macroscopic qubit value, independently of $\ensuremath{\phi}$. Using entangled cat states, we demonstrate a quantum eraser where the choice to measure a which-way or wave-type property is delayed. Consistency with wMR is possible, if we interpret the macroscopic qubit value to be determined by ${\ensuremath{\lambda}}_{\ensuremath{\theta}}$ without specification of the state at the level of $\ensuremath{\hbar}$. We then demonstrate violations of a delayed-choice Leggett-Garg inequality, and of the Wheeler-Chaves-Lemos-Pienaar dimension witness inequality, for the macroscopic qubits. This negates all two-dimensional nonretrocausal wMR models. However, one can interpret consistently with wMR, thus avoiding conclusions of macroscopic retrocausality, by noting extra dimensions, and that violations require further unitary dynamics $U$ after $t$. The violations are then explained as failure of deterministic macroscopic realism, which specifies the validity of ${\ensuremath{\lambda}}_{\ensuremath{\theta}}$ prior to the dynamics $U(\ensuremath{\theta})$ determining the measurement setting $\ensuremath{\theta}$. Finally, although there is consistency with wMR for macroscopic observations, Einstein-Podolsky-Rosen--type paradoxes pointing to the incompleteness of quantum mechanics exist at a microscopic level, based on fringe distributions.

arXiv:2109.12465•Physical Review A•Jun 8, 2022•9 citations

Bell inequalities for falsifying mesoscopic local realism via amplification of quantum noise

M. D. Reid

Macroscopic realism (MR) per se specifies that a system which has two macroscopically distinct states available to it (such as a cat being dead or alive) is at all times predetermined to be in one or other of those two states. A minimal assumption of a macroscopic realistic theory therefore is the validity of a hidden variable ${\ensuremath{\lambda}}_{M}$ that predetermines the outcome (whether dead or alive) of a measurement $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ distinguishing the two states. Proposals to test MR generally introduce a second premise to further qualify the meaning of MR. Thus, we consider a model, macroscopic local realism (MLR), where the second premise is that measurements at one location cannot cause an instantaneous macroscopic change $\ensuremath{\delta}$ to the results of measurements made on a second system at another location. To provide a practical test, we define the intermediate concept of $\ensuremath{\delta}$-scopic local realism ($\ensuremath{\delta}$-LR), where $\ensuremath{\delta}\ensuremath{\ne}0$ can be quantified, but need not be macroscopic. By considering the amplification of quantum fluctuations, we show how negation of $\ensuremath{\delta}$-LR is possible using fields violating a continuous variable Bell inequality. A modified Bell-Clauser-Horne-Shimony-Holt inequality is derived that tests $\ensuremath{\delta}$-LR, and a quantitative proposal given for experiments based on polarization entanglement. In the proposal, $\ensuremath{\delta}$ is the magnitude of the quantum noise scaled by an adjustable coherent amplitude $\ensuremath{\alpha}$ that can also be considered part of the measurement apparatus. Thus, $\ensuremath{\delta}$ is large in an absolute sense, but scales inversely with the square root of the system size, which is proportional to ${|\ensuremath{\alpha}|}^{2}$. We discuss how the proposed experiment gives a realization of a type of Schr\"odinger-cat experiment without problems of decoherence.

arXiv:1612.08883•Physical Review A•Apr 19, 2018•13 citations

Quantum- vs. Macro- Realism: What does the Leggett-Garg Inequality actually test?

O. J. E. Maroney, Christopher G. Timpson

Macroscopic Realism (MR) says that a macroscopic system is always determinately in one or other of the macroscopically distinguishable states available to it. The Leggett-Garg (LG) inequality was derived to allow experimental test of whether or not this doctrine is true; it is also often thought of as a temporal version of a Bell-inequality. Despite recent interest in the inequality, controversy remains regarding what would be shown by its violation. Here we resolve this controversy, which arises due to an insufficiently general and model-independent approach to the question so far. We argue that LG's initial characterisation of MR does not pick out a particularly natural realist position, so we articulate an operationally well-defined and well-motivated position in its place. We show that much weaker conditions than LG's are sufficient to derive the inequality: in the first instance, its violation only demonstrates that certain measurements fail to be non-disturbing at the operational level. We articulate three distinct species of MR-ist position, and argue that it is only the first of these which can be refuted by LG inequality violation. This first position is an attractive one, so ruling it out remains of interest, however. A crucial role is played in LG's argument by the assumption of noninvasive measurability. We show that this notion is ambiguous between the weaker notion of disturbance at the operational level, and the stronger notion of invasiveness at the ontic level of properties of the system. Ontic noninvasiveness would be required to rule out MR per se but this property is not entailed by MR, and its presence cannot be established in a model-independent way. It follows that despite the formal parallels, Bell's and LG's inequalities are not methodologically on a par. We close with some reflections on the implications of our analysis for the pedagogy of quantum superposition.

arXiv:1412.6139•Dec 18, 2014•23 citations

Light polarization measurements in tests of macrorealism

Eugenio Roldán, Johannes Kofler, Carlos Navarrete–Benlloch

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.

arXiv:1708.00713•Physical Review A•Jun 18, 2018•0 citations
We consider tests of Leggett-Garg's macrorealism and of macroscopic local realism, where for spacelike separated measurements the assumption of macroscopic noninvasive measurability is justified by that of macroscopic Bell locality. We give a mapping between the Bell and Leggett-Garg experiments for microscopic qubits based on spin-1/21/21/2 eigenstates and gedanken experiments for macroscopic qubits based on two macroscopically distinct coherent states ∣\ensuremathα\ensuremath⟩|\ensuremath{\alpha}\ensuremath{\rangle}∣\ensuremathα\ensuremath⟩ and ∣\ensuremath−\ensuremathα\ensuremath⟩|\ensuremath{-}\ensuremath{\alpha}\ensuremath{\rangle}∣\ensuremath−\ensuremathα\ensuremath⟩ (as \ensuremathα\ensuremath→\ensuremath∞\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}\ensuremathα\ensuremath→\ensuremath∞). In this mapping, the unitary rotation U\ensuremathθ{U}_{\ensuremath{\theta}}U\ensuremathθ​ of the Stern-Gerlach analyzer or polarizing beam splitter is realized by a local interaction H=\ensuremathΩn\ifmmode^\elseˆ\fi4H=\mathrm{\ensuremath{\Omega}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}^{4}H=\ensuremathΩn\ifmmode^\elseˆ\fi4 where n\ifmmode^\elseˆ\fi\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}n\ifmmode^\elseˆ\fi is the number of quanta. By adjusting the time of interaction, one alters the measurement setting \ensuremathθ\ensuremath{\theta}\ensuremathθ. We thus predict violations of Leggett-Garg and Bell inequalities in a macroscopic regime where coarse-grained measurements M\ifmmode^\elseˆ\fi\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}M\ifmmode^\elseˆ\fi​ need only discriminate between two macroscopically distinct coherent states. To interpret the violations, we distinguish between different definitions of macroscopic realism. Deterministic macroscopic local realism (dMR) assumes the system is in a state with a definite outcome \ensuremathλ\ensuremathθ{\ensuremath{\lambda}}_{\ensuremath{\theta}}\ensuremathλ\ensuremathθ​ for the measurement M\ifmmode^\elseˆ\fi\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}M\ifmmode^\elseˆ\fi​ prior to the unitary rotation U\ensuremathθ{U}_{\ensuremath{\theta}}U\ensuremathθ​, and is negated by the violations. Weak macroscopic realism (wMR) assumes a definite outcome for systems prepared in a superposition \ensuremathψpointer{\ensuremath{\psi}}_{\text{pointer}}\ensuremathψpointer​ of two macroscopically distinct eigenstates of M\ifmmode^\elseˆ\fi\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}M\ifmmode^\elseˆ\fi​, after the unitary rotation U\ensuremathθ{U}_{\ensuremath{\theta}}U\ensuremathθ​. We find that wMR can be viewed consistently with the violations and with the predictions of quantum mechanics for two tests of wMR. A model is presented in which wMR holds and the macroscopic violations emerge over the course of the unitary dynamics occurring at both sites. Implications for the realism of the micro-macro state generated during a quantum measurement are discussed. Finally, we point out an EPR-type paradox, which demonstrates inconsistency between wMR and the completeness of quantum mechanics at a microscopic level.
The violation of a Leggett–Garg inequality confirms the incompatibility between quantum mechanics and the combined premises (called macro-realism) of macroscopic realism (MR) and noninvasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails for systems in a superposition of macroscopically distinct states—or else, that NIM fails. In this paper, we consider a strong negation of macro-realism, involving superpositions of coherent states, where the NIM premise is replaced by Bell’s locality premise. We follow recent work and propose the validity of a subset of Einstein–Podolsky–Rosen (EPR) and Leggett–Garg premises, referred to as weak macroscopic realism (wMR). In finding consistency with wMR, we identify that the Leggett–Garg inequalities are violated because of failure of both MR and NIM, but also that both are valid in a weaker (less restrictive) sense. Weak MR is distinguished from deterministic macroscopic realism (dMR) by recognizing that a measurement involves a reversible unitary interaction that establishes the measurement setting. Weak MR posits that a predetermined value for the outcome of a measurement can be attributed to the system after the interaction, when the measurement setting is experimentally specified. An extended definition of wMR considers the “element of reality” defined by EPR for system A, where one can predict with certainty the outcome of a measurement on A by performing a measurement on system B. Weak MR posits that this element of reality exists once the unitary interaction determining the measurement setting at B has occurred. We demonstrate compatibility of systems violating Leggett–Garg inequalities with wMR but point out that dMR has been shown to be falsifiable. Other tests of wMR are proposed, the predictions of wMR agreeing with quantum mechanics. Finally, we compare wMR with macro-realism models discussed elsewhere. An argument in favour of wMR is presented: wMR resolves a potential contradiction pointed out by Leggett and Garg between failure of macro-realism and assumptions intrinsic to quantum measurement theory.
We show how one may test macroscopic local realism where, differently from conventional Bell tests, all relevant measurements that lead to a violation of a Bell inequality need only distinguish between two macroscopically distinct states of the system being measured. Here, measurements give macroscopically distinct outcomes for some property of the system and do not resolve microscopically (of order $\ensuremath{\hbar}$). To obtain a quantifiable test, we define NNN-scopic local realism where the outcomes are separated by an amount $\ensuremath{\sim}N$. We show for NNN up to 20 that violations of NNN-scopic local realism are predicted for entangled systems of NNN bosons at each of two sites. We further demonstrate for arbitrarily large $\ensuremath{\alpha}$ the violation of $\ensuremath{\alpha}$-scopic local realism, for entangled superpositions of coherent states with amplitudes $\ensuremath{\sim}\phantom{\rule{1.0pt}{0ex}}\ensuremath{\alpha}$, infinitely separated in phase space, as $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$. To achieve the Bell violations, the two separated subsystems evolve dynamically according to a local nonlinear unitary interaction. The tests may be understood in two ways. First, they are macroscopic Bell tests involving spacelike separated measurement events, where the choice of measurement setting at each site corresponds to a choice between two different times of local interaction. The interaction may be seen as the unitary stage of a local measurement process. Second, the proposal is a strong version of a Leggett-Garg test of "macrorealism" that uses two trajectories, where the usual assumption of noninvasive measurability as applied to measurements at one site is replaced by that of macroscopic locality. For N=1N=1N=1, tests are feasible and give a way to demonstrate ``no classical trajectories'' without the assumption of noninvasive measurability, using instead that of locality.
We propose delayed-choice experiments carried out with macroscopic qubits, realized as macroscopically distinct coherent states $|\ensuremath{\alpha}\ensuremath{\rangle}$ and $|\ensuremath{-}\ensuremath{\alpha}\ensuremath{\rangle}$. Quantum superpositions of $|\ensuremath{\alpha}\ensuremath{\rangle}$ and $|\ensuremath{-}\ensuremath{\alpha}\ensuremath{\rangle}$ are created via a unitary interaction $U(\ensuremath{\theta})$ based on a nonlinear Hamiltonian, in analogy with polarizing beam splitters used in photonic experiments. Macroscopic delayed-choice experiments give a compelling reason to develop interpretations not allowing macroscopic retrocausality: This would otherwise suggest changes to the macroscopic qubit value based on a future measurement setting $\ensuremath{\phi}$. We therefore consider weak macroscopic realism (wMR), which for the system at time ttt specifies a hidden variable ${\ensuremath{\lambda}}_{\ensuremath{\theta}}$ to determine the macroscopic qubit value, independently of $\ensuremath{\phi}$. Using entangled cat states, we demonstrate a quantum eraser where the choice to measure a which-way or wave-type property is delayed. Consistency with wMR is possible, if we interpret the macroscopic qubit value to be determined by ${\ensuremath{\lambda}}_{\ensuremath{\theta}}$ without specification of the state at the level of $\ensuremath{\hbar}$. We then demonstrate violations of a delayed-choice Leggett-Garg inequality, and of the Wheeler-Chaves-Lemos-Pienaar dimension witness inequality, for the macroscopic qubits. This negates all two-dimensional nonretrocausal wMR models. However, one can interpret consistently with wMR, thus avoiding conclusions of macroscopic retrocausality, by noting extra dimensions, and that violations require further unitary dynamics UUU after ttt. The violations are then explained as failure of deterministic macroscopic realism, which specifies the validity of ${\ensuremath{\lambda}}_{\ensuremath{\theta}}$ prior to the dynamics $U(\ensuremath{\theta})$ determining the measurement setting $\ensuremath{\theta}$. Finally, although there is consistency with wMR for macroscopic observations, Einstein-Podolsky-Rosen--type paradoxes pointing to the incompleteness of quantum mechanics exist at a microscopic level, based on fringe distributions.
Macroscopic realism (MR) per se specifies that a system which has two macroscopically distinct states available to it (such as a cat being dead or alive) is at all times predetermined to be in one or other of those two states. A minimal assumption of a macroscopic realistic theory therefore is the validity of a hidden variable ${\ensuremath{\lambda}}_{M}$ that predetermines the outcome (whether dead or alive) of a measurement $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ distinguishing the two states. Proposals to test MR generally introduce a second premise to further qualify the meaning of MR. Thus, we consider a model, macroscopic local realism (MLR), where the second premise is that measurements at one location cannot cause an instantaneous macroscopic change $\ensuremath{\delta}$ to the results of measurements made on a second system at another location. To provide a practical test, we define the intermediate concept of $\ensuremath{\delta}$-scopic local realism ($\ensuremath{\delta}$-LR), where $\ensuremath{\delta}\ensuremath{\ne}0$ can be quantified, but need not be macroscopic. By considering the amplification of quantum fluctuations, we show how negation of $\ensuremath{\delta}$-LR is possible using fields violating a continuous variable Bell inequality. A modified Bell-Clauser-Horne-Shimony-Holt inequality is derived that tests $\ensuremath{\delta}$-LR, and a quantitative proposal given for experiments based on polarization entanglement. In the proposal, $\ensuremath{\delta}$ is the magnitude of the quantum noise scaled by an adjustable coherent amplitude $\ensuremath{\alpha}$ that can also be considered part of the measurement apparatus. Thus, $\ensuremath{\delta}$ is large in an absolute sense, but scales inversely with the square root of the system size, which is proportional to ${|\ensuremath{\alpha}|}^{2}$. We discuss how the proposed experiment gives a realization of a type of Schr\"odinger-cat experiment without problems of decoherence.
Macroscopic Realism (MR) says that a macroscopic system is always determinately in one or other of the macroscopically distinguishable states available to it. The Leggett-Garg (LG) inequality was derived to allow experimental test of whether or not this doctrine is true; it is also often thought of as a temporal version of a Bell-inequality. Despite recent interest in the inequality, controversy remains regarding what would be shown by its violation. Here we resolve this controversy, which arises due to an insufficiently general and model-independent approach to the question so far. We argue that LG's initial characterisation of MR does not pick out a particularly natural realist position, so we articulate an operationally well-defined and well-motivated position in its place. We show that much weaker conditions than LG's are sufficient to derive the inequality: in the first instance, its violation only demonstrates that certain measurements fail to be non-disturbing at the operational level. We articulate three distinct species of MR-ist position, and argue that it is only the first of these which can be refuted by LG inequality violation. This first position is an attractive one, so ruling it out remains of interest, however. A crucial role is played in LG's argument by the assumption of noninvasive measurability. We show that this notion is ambiguous between the weaker notion of disturbance at the operational level, and the stronger notion of invasiveness at the ontic level of properties of the system. Ontic noninvasiveness would be required to rule out MR per se but this property is not entailed by MR, and its presence cannot be established in a model-independent way. It follows that despite the formal parallels, Bell's and LG's inequalities are not methodologically on a par. We close with some reflections on the implications of our analysis for the pedagogy of quantum superposition.
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.