In the quantum Cheshire Cat effect, weak measurements on a pre- and post-selected ensemble attribute a particle to one region of an interferometer while one of its other properties (polarization, spin, charge, internal energy, magnetic moment) is attributed to a different region. The originating paper (Aharonov, Popescu, Rohrlich and Skrzypczyk, New J. Phys. 15, 113015 (2013)) closed by asking what physical consequences such disembodiment would have: how an electron with disembodied charge and mass affects a nearby electron, what gravitational field an atom with internal energy disembodied from its mass produces, what thermal equilibrium a system with two separated degrees of freedom reaches, whether more than two degrees of freedom can be separated, whether angular momentum can be imparted to one object while radiation pressure acts on another, whether the single-shot N-particle realization can escape its exponentially small 4−N4^{-N} post-selection probability, and whether the effect can be harnessed in precision measurement. Later literature has answered the extensibility question and substantially developed the transfer question; the open core is the dynamical and physical consequences of disembodiment for gravitation, thermodynamics, strongly interacting probes, scalable strong realizations, and concrete metrological protocols.

Background

A pre- and post-selected experiment is an ensemble of quantum systems prepared in a known initial state ∣ψ⟩|\psi\rangle and then accepted only if a final measurement finds a chosen state ∣ϕ⟩|\phi\rangle (the post-selection); properties of the system between the two measurements are inferred from weak measurements. A weak measurement couples a pointer to an observable so weakly that the system is barely disturbed, at the cost of large noise per single run; averaging over many repetitions of the weak measurement on the pre- and post-selected ensemble yields the weak value

⟨A⟩w=⟨ϕ∣A∣ψ⟩⟨ϕ∣ψ⟩,\langle A\rangle_w=\frac{\langle\phi|A|\psi\rangle}{\langle\phi|\psi\rangle},

which can lie far outside the eigenvalue range of AA (anomalous weak values) and, in the two-state vector formalism (the time-symmetric description of a system by both ∣ψ⟩|\psi\rangle and ∣ϕ⟩|\phi\rangle), acts as the effective value of AA for any system that interacts sufficiently weakly with the ensemble.

Aharonov, Popescu, Rohrlich and Skrzypczyk used this formalism to exhibit the quantum Cheshire Cat: in a Mach-Zehnder-type interferometer (a two-arm interferometer in which a beam splitter divides the particle's path into two arms and a second beam splitter recombines them) with a horizontally polarized photon pre-selected in a superposition of the two arms and post-selected on a suitable state, the weak values of the path projectors give ⟨ΠL⟩w=1\langle\Pi_L\rangle_w=1 and ⟨ΠR⟩w=0\langle\Pi_R\rangle_w=0, while the weak values of the polarization (circular-polarization) projectors give ⟨σz(L)⟩w=0\langle\sigma_z^{(L)}\rangle_w=0 and ⟨σz(R)⟩w=1\langle\sigma_z^{(R)}\rangle_w=1. The photon (the cat) is thus attributed to the left arm while its angular momentum (the grin) is attributed to the right arm, even though these weak attributions can be probed simultaneously because the corresponding weak couplings do not disturb each other. A complementary N-electron scheme pre-selects and post-selects NN electrons so that, when the post-selection succeeds (with probability 4−N4^{-N}), weak gravitational and magnetic probes find all the mass in one box and a magnetic field emanating from the other, with single-shot precision N\sqrt{N}; the authors describe this strong version as beyond current technology.

The effect has since been demonstrated experimentally with neutrons and photons, but its interpretation is contested: several groups argue the weak-value pattern is equally well explained as ordinary interference, contextuality, or coherence effects, while others maintain the disembodiment picture in an operational sense. The originators' Conclusions section posed the question of what physical consequences disembodiment has, explicitly asking: how an electron with disembodied charge and mass affects a nearby electron; what gravitational field an atom with internal energy disembodied from its mass produces; what thermal equilibrium a system with two separated degrees of freedom reaches; whether more than two degrees of freedom can all be separated from each other; whether photons can impart angular momentum to one object while their radiation pressure is felt by another; and whether the effect can remove unwanted disturbance in precision measurements, for example by confining charge far from the magnetic moment that a protocol actually uses. These questions share one objective: to establish whether weak-value disembodiment has operational significance beyond the readouts of weakly coupled pointers, in real interactions, gravitational fields, thermal contact, and metrology.

Problem Statement

For a pre- and post-selected ensemble exhibiting the quantum Cheshire Cat effect — in which weak values attribute a particle's position to one region of an interferometer and one of its other properties (charge, mass, internal energy, magnetic moment, polarization, spin) to a different region — determine the physical consequences of the disembodiment for systems that are not merely weakly coupled pointers, and determine whether and how a practically realizable strong version of the effect can be established. Specifically: (1) What interaction does an electron whose charge and mass are attributed (in the weak-value sense) to different regions exert on a nearby electron or other probe that couples to charge or mass? (2) What gravitational field is produced by an atom whose internal energy is disembodied from its mass, and how could such a field be measured? (3) What thermal equilibrium, and what heat exchange, is reached by a system whose two degrees of freedom (for example mass and internal energy) have been spatially separated by pre- and post-selection and then brought into thermal contact with reservoirs? (4) Can the high-precision, single-shot N-particle realization be achieved without the exponentially small 4−N4^{-N} post-selection probability, and if so, by what experimental route can one balance success probability, signal size, and technological constraints? (5) Can Cheshire-Cat separations be turned into concrete metrological protocols, for example separating a magnetic moment from charge so that unwanted charge-induced disturbance is confined far from the region where the magnetic moment is measured, and, if so, what performance gains do such protocols deliver? The five parts above are the question, each separately meaningful; because the interpretation of weak-value disembodiment is itself contested, they are to be settled in terms of what weakly and strongly coupled probes, fields, and reservoirs actually register, and in terms of whether and how pre- and post-selection changes what other physical systems, including gravitational probes, experience.

References

  1. Yakir Aharonov, Sandu Popescu, Daniel Rohrlich, Paul Skrzypczyk, 'Quantum Cheshire Cats', New J. Phys. 15, 113015 (2013), DOI 10.1088/1367-2630/15/11/113015, https://doi.org/10.1088/1367-2630/15/11/113015 (source paper; full text available as arXiv:1202.0631v2)
  2. Chang-Ling Zou, Xu-Bo Zou, F.-W. Sun, Guang-Can Guo, 'Disembodiment of Physical Properties by Pre- and Post-Selections', arXiv:1203.4384 (2012), https://arxiv.org/abs/1203.4384
  3. Yelena Guryanova, Nicolas Brunner, Sandu Popescu, 'The Complete Quantum Cheshire Cat', arXiv:1203.4215 (2012), https://arxiv.org/abs/1203.4215
  4. Antonio Di Lorenzo, 'Hunting for the Quantum Cheshire Cat', arXiv:1205.3755 (2012), https://arxiv.org/abs/1205.3755
  5. Tobias Denkmayr, Hermann Geppert, Stephan Sponar, Hartmut Lemmel, Alexandre Matzkin, Jeff Tollaksen, Yuji Hasegawa, 'Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment', Nat. Commun. 5, 4492 (2014), DOI 10.1038/ncomms5492, https://doi.org/10.1038/ncomms5492
  6. Raul Corrêa, Marcelo França Santos, C. H. Monken, Pablo L. Saldanha, "'Quantum Cheshire Cat' as simple quantum interference", New J. Phys. 17, 053042 (2015), DOI 10.1088/1367-2630/17/5/053042, https://doi.org/10.1088/1367-2630/17/5/053042
  7. W. M. Stuckey, Michael Silberstein, Timothy McDevitt, 'Concerning Quadratic Interaction in the Quantum Cheshire Cat Experiment', arXiv:1410.1522 (2014), https://arxiv.org/abs/1410.1522
  8. Yakir Aharonov, Eliahu Cohen, Sandu Popescu, 'A Current of the Cheshire Cat's Smile: Dynamical Analysis of Weak Values', arXiv:1510.03087 (2015), https://arxiv.org/abs/1510.03087
  9. Kristel Michielsen, Thomas Lippert, Hans De Raedt, 'Discrete-event simulation unmasks the quantum Cheshire Cat', J. Comput. Theor. Nanosci. 14, 2268-2283 (2017), arXiv:1707.04230, https://arxiv.org/abs/1707.04230
  10. Q. Duprey, S. Kanjilal, U. Sinha, D. Home, A. Matzkin, 'The Quantum Cheshire Cat effect: Theoretical basis and observational implications', Ann. Phys. 391, 1-15 (2018), DOI 10.1016/j.aop.2018.01.011, https://doi.org/10.1016/j.aop.2018.01.011
  11. Debmalya Das, Arun Kumar Pati, 'Can two quantum Cheshire cats exchange grins?', New J. Phys. 22, 063032 (2020), DOI 10.1088/1367-2630/ab8e5a, https://doi.org/10.1088/1367-2630/ab8e5a
  12. Alok Kumar Pan, 'Disembodiment of arbitrary number of properties in quantum Cheshire cat experiment', Eur. Phys. J. D 74, 151 (2020), DOI 10.1140/epjd/e2020-10246-9, https://doi.org/10.1140/epjd/e2020-10246-9
  13. Pratyusha Chowdhury, Arun Kumar Pati, Jing-Ling Chen, 'Wave and particle properties can be spatially separated in a quantum entity', Photonics Research 9, 1379 (2021), arXiv:2009.00545, https://arxiv.org/abs/2009.00545
  14. Yosep Kim, Dong-Gil Im, Yong-Su Kim, Sang-Wook Han, Sung Moon, Yoon-Ho Kim, Young-Wook Cho, 'Observing the "quantum Cheshire cat" effect with noninvasive weak measurement', npj Quantum Inf. 7, 13 (2021), DOI 10.1038/s41534-020-00350-6, https://doi.org/10.1038/s41534-020-00350-6
  15. Yakir Aharonov, Eliahu Cohen, Sandu Popescu, 'A dynamical quantum Cheshire Cat effect and implications for counterfactual communication', Nat. Commun. 12, 4770 (2021), DOI 10.1038/s41467-021-24933-9, https://doi.org/10.1038/s41467-021-24933-9
  16. Ahana Ghoshal, Soham Sau, Debmalya Das, Ujjwal Sen, 'Isolating noise and amplifying the signal using weak quantum measurement and postselection', Phys. Rev. A 107, 052214 (2023), DOI 10.1103/PhysRevA.107.052214, https://doi.org/10.1103/PhysRevA.107.052214 (preprint posted as 'Isolating noise and amplifying signal with quantum Cheshire cat', arXiv:2203.00254, https://arxiv.org/abs/2203.00254)
  17. Jonte R. Hance, Ming Ji, Holger F. Hofmann, 'Contextuality, Coherences, and Quantum Cheshire Cats', New J. Phys. 25, 113028 (2023), DOI 10.1088/1367-2630/ad0bd4, https://doi.org/10.1088/1367-2630/ad0bd4
  18. Richard Wagner, Wenzel Kersten, Hartmut Lemmel, Stephan Sponar, Yuji Hasegawa, 'Quantum causality emerging in a delayed-choice quantum Cheshire Cat experiment with neutrons', Sci. Rep. 13, 3865 (2023), DOI 10.1038/s41598-023-29970-6, https://doi.org/10.1038/s41598-023-29970-6
  19. Armin Danner, Niels Geerits, Hartmut Lemmel, Richard Wagner, Stephan Sponar, Yuji Hasegawa, 'Three-Path Quantum Cheshire Cat Observed in Neutron Interferometry', arXiv:2303.18092 (2023), https://arxiv.org/abs/2303.18092
  20. Jia-Kun Li, Kai Sun, Yan Wang, Ze-Yan Hao, Zheng-Hao Liu, Jie Zhou, XingYan Fan, Jing-Ling Chen, Jin-Shi Xu, Chuan-Feng Li, Guang-Can Guo, 'Experimental demonstration of separating the wave-particle duality of a single photon with the quantum Cheshire cat', Light Sci. Appl. 12, 18 (2023), DOI 10.1038/s41377-022-01063-5, https://doi.org/10.1038/s41377-022-01063-5 (preprint arXiv:2303.05187, https://arxiv.org/abs/2303.05187)
  21. Yakir Aharonov, Daniel Collins, Sandu Popescu, 'Angular momentum flow without anything carrying it', Phys. Rev. A 110, L030201 (2024), DOI 10.1103/PhysRevA.110.L030201, https://doi.org/10.1103/PhysRevA.110.L030201
  22. Jonte R. Hance, James Ladyman, John Rarity, 'Is the dynamical quantum Cheshire cat detectable?', New J. Phys. 26, 073038 (2024), DOI 10.1088/1367-2630/ad6476, https://doi.org/10.1088/1367-2630/ad6476
  23. Mordecai Waegell, Jeff Tollaksen, Yakir Aharonov, 'Separating a particle's mass from its momentum', Quantum 8, 1536 (2024), DOI 10.22331/q-2024-11-26-1536, https://doi.org/10.22331/q-2024-11-26-1536
  24. Partha Ghose, Sudip Patra, 'Context and Complementarity: Formalizing Bohr's Vision through Many-Valued Contextual Logic', arXiv:2505.09333 (2025), https://arxiv.org/abs/2505.09333
  25. Monika Richter, Bartosz Dziewit, Jerzy Dajka, 'The Quantum Cheshire Cat Effect in the Presence of Decoherence', Adv. Math. Phys. 2018, 7060586 (2018), DOI 10.1155/2018/7060586, https://doi.org/10.1155/2018/7060586
  26. Jerzy Dajka, 'Scattering-Like Control of the Cheshire Cat Effect in Open Quantum Systems', Quantum Rep. 2 (1), 1-11 (2019), DOI 10.3390/quantum2010001, https://doi.org/10.3390/quantum2010001