Single-Particle Interference Can Witness ipartite Entanglement Torsten Scholak 1 3 Florian Mintert 2 3 Cord. Müller 1 1 2 3 March 13, 2008
Introduction Proposal Quantum Optics Scenario Motivation Definitions Motivation double slit experiment 1 source detector 2 perfect visibility perfect knowledge * atoms provide information about photon path? photon gathers information about atoms cf. U. Eichmann, Phys. Rev. Lett. 70, 2359(1993)
Introduction Proposal Quantum Optics Scenario Motivation Definitions What Information Can e Gained by Scattering a Probe? 1 source ϱ t detector 2 correlations? distinguish between classical and quantum correlations? witness entanglement
Introduction Proposal Quantum Optics Scenario Motivation Definitions Entanglement Witnesses an observable W is an entanglement witness: { 0, for all separable states ϱ t W =tr{ϱ t W } < 0, for at least one entangled state negative outcome: ϱ t entangled! look for characteristic sign changes! entangled W =0 separable cf. P. Horodecki, Phys. Lett. 232, 33(1997)
Probe-Target Interaction preparation probe target ϱ = ϱ p ϱ t 1 2
Probe-Target Interaction preparation probe target ϱ = ϱ p ϱ t 1 2 T = e iφ T + e iφ T φ = φ φ interaction ϱ = T ( ) T
Probe-Target Interaction preparation probe target ϱ = ϱ p ϱ t 1 2 T = e iφ T + e iφ T φ = φ φ interaction measurement ϱ = T ( ) projector P probe P = T PT + T PT }{{} I 0 0, no witness T ] + [e iφ T PT + e iφ T PT }{{} δi (φ) I 0, witness?
Central Result: Connection of Pattern and Witness designated entanglement witness: reading off interference contribution at φ =0 measuring exp. value of observable on the target system δi (0) = T PT + T PT =tr t { ϱ t M }
Central Result: Connection of Pattern and Witness designated entanglement witness: reading off interference contribution at φ =0 measuring exp. value of observable on the target system ( )} δi (0) = tr p&t {(ϱ p ϱ t ) T PT + T PT =tr t {ϱ t M }
Central Result: Connection of Pattern and Witness designated entanglement witness: reading off interference contribution at φ =0 measuring exp. value of observable on the target system { [ )] δi (0) = tr t ϱ t tr p ϱ p (T } { PT + T PT =tr t ϱ t M }
Central Result: Connection of Pattern and Witness designated entanglement witness: reading off interference contribution at φ =0 measuring exp. value of observable on the target system { [ )] δi (0) = tr t ϱ t tr p ϱ p (T } { PT + T PT =tr t ϱ t M }
Central Result: Connection of Pattern and Witness designated entanglement witness: reading off interference contribution at φ =0 measuring exp. value of observable on the target system { [ )] δi (0) = tr t ϱ t tr p ϱ p (T } { PT + T PT =tr t ϱ t M } criterion: I 0+δI > 0: δi (0) 0 φ no detection < 0 : ϱ t entangled!
Introduction Proposal Quantum Optics Scenario Quantum Optics Realization of W k single probe photon elastic single scattering 2atomscarrytarget qubit pair unpolarized incident beam, no polarizer (P = 1) k 1 2 for detection at right angles to incidence ( k k ): M =2(1 2 Ψ Ψ ) witnesses the singlet state Ψ = 1 2 (,, ) works for all entangled states Ψ with Ψ Ψ 2 > 1 2
Discussion Introduction Proposal Quantum Optics Scenario single-particle interference is sensitive for entanglement mapping of a two-particle observable to a single-particle observable proof-of-concept model found in quantum optics arxiv:0710.0825: 2 1 1 1 Φ 2 2
Introduction Proposal Quantum Optics Scenario Thank You for Your ttention!