Experimental Entanglement Activation from Discord in a Programmable Quantum Measurement

Gerardo Adesso, Vincenzo D’Ambrosio, Eleonora Nagali, Marco Piani, and Fabio Sciarrino

Phys. Rev. Lett. 112, 140501 – Published 7 April 2014

Abstract

In quantum mechanics, observing is not a passive act. Consider a system of two quantum particles $A$ and $B$ : if a measurement apparatus $M$ is used to make an observation on $B$ , the overall state of the system $A B$ will typically be altered. When this happens, no matter which local measurement is performed, the two objects $A$ and $B$ are revealed to possess peculiar correlations known as quantum discord. Here, we demonstrate experimentally that the very act of local observation gives rise to an activation protocol which converts discord into distillable entanglement, a stronger and more useful form of quantum correlations, between the apparatus $M$ and the composite system $A B$ . We adopt a flexible two-photon setup to realize a three-qubit system ( $A$ , $B$ , $M$ ) with programmable degrees of initial correlations, measurement interaction, and characterization processes. Our experiment demonstrates the fundamental mechanism underpinning the ubiquitous act of observing the quantum world and establishes the potential of discord in entanglement generation.

Received 12 December 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.140501

Authors & Affiliations

Gerardo Adesso¹, Vincenzo D’Ambrosio², Eleonora Nagali², Marco Piani³, and Fabio Sciarrino²

¹School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
²Dipartimento di Fisica, Sapienza Universitá di Roma, Roma 00185, Italy
³Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada

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Vol. 112, Iss. 14 — 11 April 2014

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Figure 1
Activation protocol: design and experimental setup. (a) Circuit model for the activation protocol [8, 9, 37]. The initial discord of the state $χ_{A | B}$ is activated into distillable entanglement for the state $ρ_{A B | M}$ by a local variable operation ( $V_{B M}$ ) composed by a single qubit operation on $B$ ( $U_{B}$ ) and a c-not between $B$ and $M$ . (b) Experimental setup. Two polarization entangled photons are generated in a beta barium borate crystal (BBO) via spontaneous parametric down conversion [39]. The entangled state is changed in different Bell states by adopting birefringent wave plates (WPg). The $U_{B}$ is realized by two wave plates [40] while the c-not is realized by the polarizing beam splitter (PBS1) which couples polarization and path of photon $B M$ . To characterize the output state, we adopt wave plates WPa, WPb, and analysis stages ASc, ASd, and AS1. Finally, single-photon detectors ( ${D_{i}}^{A}$ , ${D_{j}}^{B M}$ ) measure photon coincidences. All the WPs are mounted on motorized stages controlled via computer. The inset displays the equivalent displaced Sagnac interferometric scheme adopted in the experiment [41, 42, 43].
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Figure 2
Activation protocol: experimental results. (a) Measurement bases for qubit $B$ defined by Bloch vectors $\pm \vec{n} (θ_{j}, ϕ_{k})$ (dots), where $θ$ , $ϕ$ are wave plates angles [40]; the Bloch sphere is overlayed with a density plot of the expected negativity of the output premeasurement state $N (ρ_{A B | M}^{(q, θ, ϕ)})$ for $q = 0$ . (b) Comparative results of the activation protocol. Each plot corresponds to a different value of $q$ , and within each panel, 28 different settings are varied for $U_{B}$ . Each blue point amounts to the entanglement $N (ρ_{A B | M}^{(q, θ_{j}, ϕ_{k})})$ of the corresponding premeasurement state reconstructed by tomography; the errors, evaluated from the Poissonian statistics of photon events, are below $10^{- 2}$ . In each plot, we include the lower bound $N_{low} (ρ_{A B | M}^{(q, θ, ϕ)})$ on the negativity derived in Eq. (B.5) of [44] (wireframe meshed surface), which remains positive for $q > 0$ confirming that we sampled enough settings for $U_{B}$ to certify the unavoidable entanglement creation from initial discord. The green translucent smooth surfaces correspond to theoretical expectations $N_{th} (ρ_{A B | M}^{(q, θ, ϕ)})$ [44].
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Figure 3
Activation protocol: quantitative verification. (a) The minimum output entanglement activated with the apparatus, measured by the negativity $\min_{(θ, ϕ)} N (ρ_{A B | M}^{(q, θ, ϕ)})$ , is verified to match the input discord $D (χ_{A | B}^{(q)})$ in the system, measured by the trace distance from the set of quantum-classical states. (b) Input bipartite entanglement activates into genuine tripartite entanglement [37]. Measured expectation values of two witness operators (negative values detect entanglement) [2, 38] are plotted; $W_{A | B}^{(2)}$ is a witness for bipartite entanglement in the initial state $χ_{A | B}^{(q)}$ , while $W_{A | B | M}^{(3)}$ is a witness for genuine tripartite Greenberger-Horne-Zeilinger–type entanglement among $A$ , $B$ , and $M$ in the premeasurement state $ρ_{A B | M}^{(q)}$ [44].
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