The Quantum Cheshire Cat (QCC) phenomenon was first proposed in a 2013 paper for the New Journal of Physics (ref.) The authors proposed that at quantum level, a particle's properties (e.g. polarization, momentum, spin etc etc ) can be entirely separated from the particle itself - even traveling along different physical paths, and existing at different times.

We have shown that Cheshire Cats have a place in quantum mechanics - physical properties can be disembodied from the objects they belong to in a pre- and post-selected experiment. Although here we have only presented one example in full detail, where a photon is disembodied from its polarization, it should be clear that this effect is quite general - we can separate, for example, the spin from the charge of an electron, or internal energy of an atom from the atom itself. Furthermore it is important to realize that it is not just pointers of well-prepared measuring devices that indicate that the properties are disembodied - any external system which interacts weakly with the pre- and post-selected system will react accordingly."

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This highly counter-intuitve phenomenon, if generally confirmed, would have extraordinary implications for the entire field of quantum mechanics. An analogy could be a macro-world object which has a 'colour' that can be completely separated from it.

Several research groups now assert that the effect has been experimentally demonstrated - several times, in different setups, at different research labs., and with different particles.

For an example of a recent paper, see : Quantum causality emerging in a delayed‑choice quantum Cheshire Cat experiment with neutrons, Scientific Reports 13:3865

The obtained results of the experiment confirm the fact that the location of the neutron and its spin can be interchanged actively for a suitable selected pairs of post-selections. This is presumed to be a consequence of quantum causality; the dynamical behavior of a quantum system is undefined until it is actually registered. Further investigations are required to answer the question, whether this dynamical consequence is attributed to the intrinsic indeterminacy of quantum mechanics or constitutes an influence of retro-causal origin."

Other research groups, however, robustly dispute the existence of the QCC effect :

Example [1]

[…] the limitations of the experiments performed to date imply that a loophole-free experimental demonstration of the QCC has not yet been achieved."

Source : Annals of Physics Volume 391, Pages 1-15

Example [2]

[…] we show that these results can be interpreted as simple quantum interference, with no separation between the quantum particle and its internal degree of freedom. We thus hope to clarify the phenomenon with this work, by removing these apparent paradoxes."

New J. Phys. 17 053042