Interference experiment, anomalous weak value, and Leggett-Garg test of macrorealism

Pan, A. K.

doi:10.1103/physreva.102.032206

Cited by 30 publications

(14 citation statements)

References 73 publications

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“…Hence, LHS = exp(−im π 8 ). Hence we can write a two state solution for time multiples of π/8, as |α, t θ = e −it θ /2 (cos(t θ /2) |α + i sin(t θ /2) |−α ) (57) where t θ = m π 8 .…”

Section: Discussionmentioning

confidence: 99%

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

Thenabadu,

Reid

2021

Preprint

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We propose delayed choice experiments carried out with macroscopic qubits, realised as macroscopically-distinct coherent states |α and | − α . Quantum superpositions of |α and | − α are created via a unitary interaction U (θ) based on a nonlinear Hamiltonian, in analogy with polarising beam splitters used in photonic experiments. Macroscopic delayed-choice experiments give a compelling reason to develop interpretations not allowing macroscopic retrocausality (MrC). We therefore consider weak macroscopic realism (wMR), which specifies a hidden variable λ θ to determine the macroscopic qubit value (analogous to 'which-way' information), independent of any future measurement setting φ. 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 λ θ without specification of the state at the level of order , where fringes manifest. We then demonstrate violations of a delayed-choice Leggett-Garg inequality, and of the dimension witness inequality applied to the Wheeler-Chaves-Lemos-Pienaar experiment, where measurements need only distinguish the macroscopic qubit states. This negates all two-dimensional non-retrocausal models, thereby suggesting MrC. However, one can interpret consistently with wMR, thus avoiding conclusions of MrC, by noting extra dimensions, and by noting that the violations require further unitary dynamics U for each system. The violations are then explained as failure of deterministic macroscopic realism (dMR), which specifies validity of λ θ prior to the dynamics U (θ) determining the measurement setting θ. Finally, although there is consistency with wMR for macroscopic observations, we demonstrate Einstein-Podolsky-Rosen-type paradoxes at a microscopic level, based on fringe distributions.

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Section: Discussionmentioning

confidence: 99%

“…We comment that violations of Leggett-Garg inequalities have been predicted and tested for a range of superposition states (e.g. [46][47][48][49][50][51][52][53][54][55][56][57]) and alternative procedures exist to justify NIM.…”

Section: B Leggett-garg Inequality and Violationsmentioning

confidence: 99%

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

Thenabadu,

Reid

2021

Preprint

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“…This perspective has been analyzed in some detail in Ref. [27] (See also [28][29][30][31]). For the LG2s, the interference terms are proportional to the difference between Q i and Q M i , where the latter denotes the average of Q i in the presence of an earlier measurement that has been summed out.…”

Section: Three-timementioning

confidence: 99%

Detecting violations of macrorealism when the original Leggett-Garg inequalities are satisfied

Majidy,

Halliwell,

Laflamme

2021

Preprint

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Macroscopic realism (MR) is the notion that a time-evolving system possesses definite properties, irrespective of past or future measurements. Quantum mechanical theories can, however, produce violations of MR. Most research to date has focused on a single set of conditions for MR, the Leggett-Garg inequalities (LGIs), and on a single data set, the "standard data set", which consists of single-time averages and second-order correlators of a dichotomic variable Q for three times. However, if such conditions are all satisfied, then where is the quantum behaviour? In this paper, we provide an answer to this question by considering expanded data sets obtained from finer-grained measurements and MR conditions on those sets. We consider three different situations in which there are violations of MR that go undetected by the standard LGIs. First, we explore higher-order LGIs on a data set involving third-and fourth-order correlators, using a spin-1/2 and spin-1 system. Second, we explore the pentagon inequalities (PIs) and a data set consisting of all possible averages and second-order correlators for measurements of Q at five times. Third, we explore the LGIs for a trichotomic variable and measurements made with a trichotomic operator to, again, identify violations for a spin-1 system beyond those seen with a single dichotomic variable. We also explore the regimes in which combinations of two and three-time LGIs can be satisfied and violated in a spin-1 system, extending recent work. We discuss the possible experimental implementation of all the above results.

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“…There have also been some recent macroscopic non-classicality tests based on interferometric experiments, with quantum interference observed in C 60 and C 70 molecules [18,19], and in large organic molecules of masses up to 6910 amu [20]. These are not specifically LG tests, but proposals have been made to adapt them for this purpose [21,22].…”

Section: Introductionmentioning

confidence: 99%

Leggett-Garg tests for macrorealism in the quantum harmonic oscillator and more general bound systems

Mawby,

Halliwell

2021

Preprint

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Macrorealism (MR) is the world-view that at all moments of time, a system is definitely in one of the observable states available to it, irrespective of past or future measurements. The Leggett-Garg (LG) inequalities were introduced to test MR and therefore assess for the presence of macroscopic quantum coherence. Since such effects could plausibly be found in various types of macroscopic oscillators, we consider the application of the LG approach to the one-dimensional quantum harmonic oscillator and more general bound systems, using a single dichotomic variable Q given by the sign of the oscillator position. We present a simple method to calculate the temporal correlation functions appearing in the LG inequalities for any bound system for which the eigenspectrum is (exactly or numerically) known. We then apply this result to the quantum harmonic oscillator for a variety of experimentally accessible states, namely energy eigenstates, and superpositions thereof. For the subspace of states spanned by only the ground state and first excited state, we readily find substantial regions of parameter space in which the two and threetime LG inequalities can each be independently violated or satisfied. Similar results are found for four-time LG inequalities. We find that the violations persist (although are reduced) when the sign function defining Q is smeared to reflect experimental imprecision. We also find that LG violations diminish for higher energy eigenstates, showing the expected classicalization. With a Q defined using a more general type of position coarse graining, we find two-time LG violations even in the ground state, a simple example of a feature recently noted by Bose et al. [Phys. Rev. Lett. 120, 210402 (2018)]. We also show that two-time LG violations in a gaussian state are also readily found if the dichotomic variable at one of the times is taken to be the parity operator. To demonstrate the versatility of the technique we developed, we also calculate temporal correlators for the Morse potential, and present a brief analysis of the LG inequalities in this system, where we find significant violations for the first excited state.

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Interference experiment, anomalous weak value, and Leggett-Garg test of macrorealism

Cited by 30 publications

References 73 publications

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

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

Detecting violations of macrorealism when the original Leggett-Garg inequalities are satisfied

Leggett-Garg tests for macrorealism in the quantum harmonic oscillator and more general bound systems

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