Linear optics for direct observation of quantum violation of pigeonhole principle by joint weak measurement

Abstract

When three pigeons are in two pigeonholes, at least two of them should be in the same pigeonhole, which is called pigeonhole principle. Recently Aharonov el al have shown that the principle can be violated in a pre-postselected quantum system. This violation sheds light on a new aspect of quantum correlations, as both of the pre and postselected states are separable states. To prove this kind of quantum correlations, a measurement apparatus must be arranged in entanglement to perform a joint measurement on the quantum system. In this paper we discuss how to design the state of entangled meters to achieve such a measurement. We also propose an experimental setup composed of linear optics for direct observation of violation of pigeonhole principle.

The real and imaginary parts of a weak value appearing as back-actions via a post-selection

“…It is known that a joint weak value can be estimated from a correlation of pointers in the higher order on the measurement strength like G 2 [14,[53][54][55]. Be that as it may, to perform a joint weak measurement straightforwardly, entangled meter qubits are generally needed [15,56] as long as considering local operations, where 'local' means a signal qubit is interacted with only the corresponding meter qubit (not the other meter qubits).…”