Experimental test of the Greenberger–Horne–Zeilinger-type paradoxes in and beyond graph states

Abstract

The Greenberger–Horne–Zeilinger (GHZ) paradox is an exquisite no-go theorem that shows the sharp contradiction between classical theory and quantum mechanics by ruling out any local realistic description of quantum theory. The investigation of GHZ-type paradoxes has been carried out in a variety of systems and led to fruitful discoveries. However, its range of applicability still remains unknown and a unified construction is yet to be discovered. In this work, we present a unified construction of GHZ-type paradoxes for graph states, and show that the existence of GHZ-type paradox is not limited to graph states. The results have important applications in quantum state verification for graph states, entanglement detection, and construction of GHZ-type steering paradox for mixed states. We perform a photonic experiment to test the GHZ-type paradoxes via measuring the success probability of their corresponding perfect Hardy-type paradoxes, and demonstrate the proposed applications. Our work deepens the comprehension of quantum paradoxes in quantum foundations, and may have applications in a broad spectrum of quantum information tasks.

Blindly Verifying Unknown Entanglement without State Tomography

“…Similarly, we can prove the inequality (31) for any mixed biseparable state in Eq. ( 29) in terms of each bi-…”

“…The new network is easy for proving the universality of generated entangled states [25]. Thus Theorem 3 provides a blind witness of universal quantum computation resources without the state tomography beyond previous results [27][28][29][30][31].…”

“…Here, the inequality ( 33) is followed from the convexity of the function f (x) = |x|. The inequality ( 34) is from the inequality (31). The inequality ( 35) is obtained from the equality: |1−ρ…”

“…any adjacent two parties share some entangled states. These multipartite entangled states can be in whole verified by using Bell inequalities [26,27], entanglement witness [28], or GHZ-type paradoxes [29][30][31]. Instead, the goal here is to witness unknown cluster states generated by entangled states (1) and ( 12) under blind channels.…”

Greenberger-Horne-Zeilinger Nonlocality in Time

“…It reveals the quantum-nonlocality of time-separated measurements with nonprobabilistic argument and establishes that quantum mechanics is inconsistent with time-local realism. The GHZ experiment [7,8] works as follows. Consider three spatially separated spin-1/2 particles prepared in an entangled state…”