Quantum Cheshire cats and their elements of reality.

Quantum Cheshire cats represent the violation of the product rule in terms of weak values being either 0 or 1. We explore the generalized fatter quantum Cheshire cats living in the larger Hilbert spaces. Specifically, two even-dimensional quantum systems are exploited. As for the physical implications, given that no disturbance is made in the weak measurements, quantum Cheshire cats reveal an alternative way of defying EPR elements of reality. In addition, we discuss the inconsistency between the Wigner's friend problem and quantum Cheshire cats. • We explore the quantum Cheshire cats in the Hilbert space of even-dimensions. • The EPR elements of reality can be refuted by quantum Cheshire cats. • The inconsistency between quantum Cheshire cats and Wigner's friend is studied. [ABSTRACT FROM AUTHOR]