Measurement of Geometric Phase for Mixed States Using Single Photon Interferometry

Abstract

Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for mixed input states. We report the first experiment to measure mixed-state geometric phases in optics, using a Mach-Zehnder interferometer, and polarization mixed states that are produced in two different ways: decohering pure states with birefringent elements; and producing a nonmaximally entangled state of two photons and tracing over one of them, a form of remote state preparation.

Experimental measurement of mixed state geometric phase by quantum interferometry using NMR

“…The geometric phase can be directly measured from the shift of the interference pattern. Mixed state geometric phase has been experimentally demonstrated by Du et al [12] using NMR and by Ericsson et al [13] using single photon interferometry. Du et al have experimentally demonstrated the mixed state geometric phase by measuring the relative phase change of an auxiliary spin.…”

Braiding transformation, entanglement swapping, and Berry phase in entanglement space

“…(i) Very recently, geometric phases for mixed states [20] have been observed in experiments by using NMR interferometry [21] as well as single photon interferometry [22]. Under a certain noisy environment, the states |χ ± (θ, ϕ) may become mixed states as…”

“…(22) can be expressed in terms of the concurrence of the states |χ ± (θ, ϕ) as γ ± = ∓π(1 − √ 1 − C 2 ), with C = | sin θ| being the concurrence. It is well-known that C is an invariant of entanglement for the entangled states |χ ± (θ, ϕ) , while Berry phase is related to some certain topological structures.…”

“…Berry phase for spin coherence states has been discussed in [19], where the corresponding result coincides with Eq. (22).…”

“…Let θ be timeindependent, when the parameter ϕ(t) evolves adiabatically from 0 to 2π, one obtains the Berry phases for χ±(θ, ϕ) as shown in Eq. (22). The relation between Berry phases and concurrence of the entangled states χ±(θ, ϕ) is γ± = ∓π(1 − √ 1 − C 2 ), where C = | sin θ| is the concurrence.…”