Encrypted quantum correlations: delayed choice of quantum statistics and other applications

Abstract

In a three-particle extension of Wheeler's delayed choice gedanken experiment, the quantum statistics of two particles is undetermined until a third particle is measured. As a function of the measurement result, the particles behave either as bosons or as fermions. The particles are distinguishable if no measurement is performed at all or when the measurement is performed in a rotated basis. The scheme is based on Greenberger-Horne-Zeilinger quantum correlations. It can be interpreted more generally as the encryption of maximally entangled states in a larger quantum superposition. The local quantum information is scrambled but can be decoded by the measurement result of a control particle. This can be extended to multiple particles and allows to develop quantum information protocols whose successful implementation depends on the collaboration of all parties.Keywords Delayed-choice experiment · Hong-Ou-Mandel effect · Entanglement · GHZ states · Quantum communication · Nonlocality · Quantum eraser · Heisenberg limit 1 IntroductionParticle-like or wave-like behavior of photons can be observed in an interferometer depending on how the measurement is performed [1,2]. Wheeler famously raised the question [3] of when does the photon "decide" whether it is going to behave as a wave or as a particle? His gedanken experiments, which today have become an experimental reality [4], lead to the conclusion that the properties of quantum objects are intrinsically undetermined until a measurement is performed. These ideas have been extended to two entangled photons, such that the quantum properties of one of them are conditioned on the measurement results of

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“…When Alice measures her qubit in the σ z basis, Bob attains the quantum conditional variance . GHZ states have the property 29 , where are eigenstates of σ x . This allows Alice to steer Bob’s system into GHZ states by measuring in the σ x basis, and we obtain …”

Entanglement of Local Hidden States

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