Necessary and sufficient conditions for macrorealism using two and three-time Leggett-Garg inequalities
arXiv:1811.10408 · doi:10.1088/1742-6596/1275/1/012008
Abstract
The Leggett-Garg (LG) inequalities were introduced, as a temporal parallel of the Bell inequalities, to test macroscopic realism -- the view that a macroscopic system evolving in time possesses definite properties which can be determined without disturbing the future or past state. The original LG inequalities are only a necessary condition for macrorealism, and are therefore not a decisive test. We argue, for the case of measurements of a single dichotomic variable Q, that when the original four three-time LG inequalities are augmented with a set of twelve two-time inequalities also of the LG form, Fine's theorem applies and these augmented conditions are then both necessary and sufficient. A comparison is carried out with the alternative necessary and sufficient conditions for macrorealism based on no-signaling in time conditions which ensure that all probabilities for Q at one and two times are independent of whether earlier or intermediate measurements are made. We argue that the two tests differ in their implementation of the key requirement of non-invasive measurability so are testing different notions of macrorealism, and these notions are elucidated.
arXiv comment12 pages. Latex. To appear in proceedings of the conference, Decoherence, Information, Complexity, Entropy (DICE), Castiglioncello, Italy, September 2018, edited by T.Elze et al. arXiv admin note: substantial text overlap with arXiv:1704.01485
References in corpus (15)
- Witnessing Quantum Coherence: from solid-state to biological systems
- Violation of the Leggett-Garg inequality with weak measurements of photons
- Violation of a Leggett-Garg inequality with ideal non-invasive measurements
- Condition for macroscopic realism beyond the Leggett-Garg inequalities
- No Fine theorem for macrorealism: Limitations of the Leggett-Garg inequality
- Addressing the clumsiness loophole in a Leggett-Garg test of macrorealism
- Necessary and sufficient conditions for macroscopic realism from quantum mechanics
- The Leggett-Garg Inequalities and No-Signalling in Time: A Quasi-Probability Approach
- Maximum violations of the quantum-witness equality
- Wigner's form of the Leggett-Garg inequality, No-Signalling in Time, and Unsharp Measurements
- Leggett--Garg inequality violations with a large ensemble of qubits
- Dynamics of a qubit as a classical stochastic process with time-correlated noise: minimal measurement invasiveness
- Two Proofs of Fine's Theorem
- Negative Probabilities, Fine's Theorem and Linear Positivity
- Ambiguous measurements, signalling and violations of Leggett-Garg inequalities
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