No Fine theorem for macrorealism: Limitations of the Leggett-Garg inequality
arXiv:1509.00348 · doi:10.1103/PhysRevLett.116.150401
Abstract
Tests of local realism and macrorealism have historically been discussed in very similar terms: Leggett-Garg inequalities follow Bell inequalities as necessary conditions for classical behavior. Here, we compare the probability polytopes spanned by all measurable probability distributions for both scenarios and show that their structure differs strongly between spatially and temporally separated measurements. We arrive at the conclusion that, in contrast to tests of local realism where Bell inequalities form a necessary and sufficient set of conditions, no set of inequalities can ever be necessary and sufficient for a macrorealistic description. Fine's famous proof that Bell inequalities are necessary and sufficient for the existence of a local realistic model, therefore cannot be transferred to macrorealism. A recently proposed condition, no-signaling in time, fulfills this criterion, and we show why it is better suited for future experimental tests and theoretical studies of macrorealism. Our work thereby identifies a major difference between the mathematical structures of local realism and macrorealism.
6 pages, published version, comments welcome
References in corpus (8)
- Ideal negative measurements in quantum walks disprove theories based on classical trajectories
- Opening up the Quantum Three-Box Problem with Undetectable Measurements
- Necessary and sufficient conditions for macroscopic realism from quantum mechanics
- The Leggett-Garg Inequalities and No-Signalling in Time: A Quasi-Probability Approach
- A scattering quantum circuit for measuring Bell's time inequality: a nuclear magnetic resonance demonstration using maximally mixed states
- Leggett-Garg inequalities and the geometry of the cut polytope
- Hardy's paradox and violation of a state-independent Bell inequality in time
- Modeling Leggett-Garg-inequality violation
Cited by in corpus (75)
- Violation of the Leggett-Garg Inequality in Neutrino Oscillations
- A strict experimental test of macroscopic realism in a superconducting flux qubit
- Incompatible measurements in quantum information science
- Coherence and non-classicality of quantum Markov processes
- Leggett-Garg test of superconducting qubit addressing the clumsiness loophole
- Operational Characterization of Divisibility of Dynamical Maps
- Comparing Conditions for Macrorealism: Leggett-Garg Inequalities vs No-Signaling in Time
- Leggett-Garg macrorealism and the quantum nondisturbance conditions
- Optimal experimental demonstration of error-tolerant quantum witnesses
- Structure of temporal correlations of a qubit
- Assessing the quantumness of a damped two-level system
- Probing various formulations of macrorealism for unsharp quantum measurements
- Interference experiment, anomalous weak value and Leggett-Garg test of macrorealism
- Exploration of an augmented set of Leggett-Garg inequalities using a noninvasive continuous-in-time velocity measurement
- Enhanced violations of Leggett-Garg inequalities in an experimental three-level system
- Leggett-Garg Macrorealism and temporal correlations
- Ambiguous measurements, signalling and violations of Leggett-Garg inequalities
- Memory cost of temporal correlations
- Inequivalent Leggett-Garg inequalities
- Leggett-Garg tests for macrorealism: interference experiments and the simple harmonic oscillator
- Leggett-Garg tests of macrorealism: checks for non-invasiveness and generalizations to higher-order correlators
- A quasi-probability for the arrival time problem with links to backflow and the Leggett-Garg inequalities
- Genuine temporal correlations can certify the quantum dimension
- Quantifying quantum invasiveness
- Loophole free interferometric test of macrorealism using heralded single photons
- Subtleties of witnessing quantum coherence in non-isolated systems
- A Stronger Theorem Against Macro-realism
- Single-photon quantum contextuality on a chip
- Quantum violation of variants of LGIs upto algebraic maximum for qubit system
- Leggett-Garg tests of macro-realism for multi-particle systems including double-well Bose-Einstein condensates
- Violations of a Leggett-Garg inequality without signalling for a photonic qutrit probed with ambiguous measurements
- Fine's Theorem for Leggett-Garg tests with an arbitrary number of measurement times
- No-signaling-in-time as a condition for macrorealism: the case of neutrino oscillations
- Testing macroscopic local realism using cat-states and Bell inequalities in time
- Self-testing of binary Pauli measurements requiring neither entanglement nor any dimensional restriction
- Necessary and sufficient conditions for macrorealism using two and three-time Leggett-Garg inequalities
- Conditions for Macrorealism for Systems Described by Many-Valued Variables
- Influence of equilibrium and nonequilibrium environments on macroscopic realism through the Leggett-Garg inequalities
- Experimental Control of the Degree of Non-Classicality via Quantum Coherence
- Ticking-clock performance enhanced by nonclassical temporal correlations
- Simulating extremal temporal correlations
- Towards a Spectroscopic Protocol for Unambiguous Detection of Quantum Coherence in Excitonic Energy Transport
- Optical experiment to test negative probability in context of quantum-measurement selection
- Catalysis always degrades external quantum correlations
- Deccoherent Histories and Measurement of Temporal Correlation Functions for Leggett-Garg Inequalities
- Leggett-Garg violations for continuous variable systems with gaussian states
- Quantumness and speedup limit of a qubit under transition frequency modulation
- Structure of dimension-bounded temporal correlations
- Semi-device-independently characterizing quantum temporal correlations
- Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
- Connecting measurement invasiveness to optimal metrological scenarios
- Violating the Leggett-Garg inequalities with classical light
- Constraints on Macroscopic Realism Without Assuming Non-Invasive Measurability
- Test of a hypothesis of realism in quantum theory using a bayesian approach
- An unconditional experimental test of Nonclassicality
- Tests of macrorealism in meson oscillation physics
- Tsirelson inequalities: Detecting cheating and quantumness in a single framework
- The operational reality of quantum nonlocality
- Leggett-Garg test of macrorealism using indefinite causal order of measurements
- Investigating nonclassicality in nonlinear electronic spectroscopy
- Entanglement-breaking channels are a quantum memory resource
- Tailoring the quantumness of a driven qubit
- Lüders bounds of Leggett-Garg inequalities, - symmetric evolution and arrow-of-time
- Retrievability of information in quantum and realistic hidden variable theories
- Leggett-Garg inequalities for multitime processes
- Signaling between time steps does not allow for nonlocality beyond hidden nonlocality
- Quantum violations of Lüders bound Leggett-Garg inequalities for quantum channel
- Classical Invasive Description of Informationally-Complete Quantum Processes
- Operational quasiprobabilities for continuous variables
- Light polarization measurements in tests of macrorealism
- Hidden nonmacrorealism: reviving the Leggett-Garg inequality with stochastic operations
- Leggett-Garg inequalities with deformed Pegg-Barnett phase observables
- Shared randomness allows violation of macroscopic realism using a single measurement
- Probability vector representation of the Schrödinger equation and Leggett-Garg-type experiments
- Quantum Non-Demolition Measurements and Leggett-Garg inequality