Experimental delayed-choice entanglement swapping

Journal name:
Nature Physics
Volume:
8,
Pages:
479–484
Year published:
DOI:
doi:10.1038/nphys2294
Received
Accepted
Published online
Corrected online

Abstract

Motivated by the question of which kind of physical interactions and processes are needed for the production of quantum entanglement, Peres has put forward the radical idea of delayed-choice entanglement swapping. There, entanglement can be ‘produced a posteriori, after the entangled particles have been measured and may no longer exist’. Here, we report the realization of Peres’s gedanken experiment. Using four photons, we can actively delay the choice of measurement—implemented through a high-speed tunable bipartite-state analyser and a quantum random-number generator—on two of the photons into the time-like future of the registration of the other two photons. This effectively projects the two already registered photons onto one of two mutually exclusive quantum states in which the photons are either entangled (quantum correlations) or separable (classical correlations). This can also be viewed as ‘quantum steering into the past’.

At a glance

Figures

  1. The concept of delayed-choice entanglement swapping.
    Figure 1: The concept of delayed-choice entanglement swapping.

    Two entangled pairs—photons 1 and 2 and photons 3 and 4—are produced in the state in the EPR sources I and II, respectively. At first, Alice and Bob perform polarization measurements on photons 1 and 4, choosing freely the polarization analysis basis among three mutually unbiased bases (horizontal/vertical: |Hright fence/|V right fence,right-circular/left-circular: |Rright fence/|Lright fence,plus/minus:|+right fence/|−right fence), and record the outcomes. Photons 2 and 3 are sent to Victor, who then subjects them to either an entangled-state measurement or a separable-state measurement (SSM), projecting them randomly onto one of two possible Bell states (|φ+right fence23 or |φright fence23) or one of two separable states (|HHright fence23 or |V V right fence23). Victor records the outcome and keeps it to himself. This procedure projects photons 1 and 4 onto a corresponding entangled (|φ+right fence14 or |φright fence14) or separable state (|V V right fence14 or |HHright fence14), respectively. According to Victor’s choice and his results, Alice and Bob can sort their already recorded data into subsets and can verify that each subset behaves as if it consisted of either entangled or separable pairs of distant photons, which have neither communicated nor interacted in the past.

  2. Experimental set-up.
    Figure 2: Experimental set-up.

    A pulsed ultraviolet laser beam with a central wavelength of 404nm, a pulse duration of 180fs and a repetition rate of 80MHz successively passes through two BBO crystals to generate two polarization-entangled photon pairs (photons 1 and 2 and photons 3 and 4) through type-II spontaneous parametric down-conversion39, 45. Single-mode fibres and interference filters (IF) are used to clean their spatial and spectral modes. We use the interference filters with 1nm (3nm) bandwidth centred around 808nm for photons 2 and 3 (photons 1 and 4). Photons 1 and 4 are directly subject to the polarization measurements performed by Alice and Bob (green blocks). Photons 2 and 3 are each delayed with a 104m single-mode fibre and then coherently overlapped on the tunable BiSA (purple block). The single-mode fibre coupler of photon 2 is mounted on step motors and used to compensate the time delay for the interference at the tunable BiSA. An active phase-stabilization system is employed to compensate the phase noise in the tunable BiSA, which is composed of an auxiliary power-stabilized diode laser, a photon detector (PD) and a ring piezo-transducer controlled by an analogue proportional-integral-derivative (PID) regulator. Two pairs of cross-oriented BBO crystals (BBOs3 and BBOs4) are placed in each arm of the Mach–Zehnder interferometer (with input and output beam splitters BS 1 and BS 2) to compensate the unwanted birefringence. On each spatial mode, we employ the combination of a half-wave plate (λ/2), a quarter-wave plate (λ/4) and a polarizing beam splitter (PBS) for measuring the pair-wise correlations between different photons in different polarization bases. Photons are detected by using single-photon counting modules (SPCM). The fourfold coincidence count rate is about 0.016Hz. See Supplementary Information for details.

  3. Experimental results.
    Figure 3: Experimental results.

    Correlation function between photons 1 and 4 for the three mutually unbiased bases (|Hright fence/|V right fence,|Rright fence/|Lright fence,|+right fence/|−right fence). a,b, Victor subjects photons 2 and 3 to either a BSM (a) or an SSM (b). These results are obtained from coincidence counts of photons 1 and 4, conditioned on the coincidence of same polarization and different spatial output modes of photons 2 and 3 (b′′ and c′′ in Fig. 2). a, When Victor performs a BSM and finds photons 2 and 3 in the state , entanglement is swapped to photons 1 and 4. This is confirmed by all three correlation functions being of equal magnitude (within statistical error) and their absolute sum exceeding 1. b, When Victor performs an SSM and finds photons 2 and 3 in either the state |HHright fence23 or |V V right fence23, entanglement is not swapped. This is confirmed by only the correlation function in the |Hright fence/|V right fence basis being significant whereas the others vanish. The experimentally obtained correlation functions of photons 1 and 4 in the (|Hright fence/|V right fence,|Rright fence/|Lright fence,|+right fence/|−right fence) bases are 0.511±0.089, 0.603±0.071, −0.611±0.074 respectively for case a and 0.632±0.059, 0.01±0.072, −0.045±0.070 respectively for case b. Whereas entangled states can show maximal correlations in all three bases (the magnitude of all correlation functions equals 1 ideally), separable states can be maximally correlated (ideal correlation function 1) only in one basis, the others being 0. The uncertainties represent plus/minus one standard deviation deduced from propagated Poissonian statistics.

Change history

Corrected online 26 April 2012
In the version of this Article originally published online, the definition of the witness operator given in the paragraph after equation (4) was incorrect. This error has been corrected in all versions of the Article.

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Author information

Affiliations

  1. Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria

    • Xiao-song Ma,
    • Stefan Zotter,
    • Johannes Kofler,
    • Rupert Ursin,
    • Thomas Jennewein,
    • Časlav Brukner &
    • Anton Zeilinger
  2. Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria

    • Xiao-song Ma &
    • Anton Zeilinger
  3. Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria

    • Časlav Brukner &
    • Anton Zeilinger
  4. Present addresses: Center for Medical Physics and Biomedical Engineering, Medical University of Vienna, Waehringer Guertel 18-20, A-1090 Vienna, Austria (S.Z.); Max Planck Institute of Quantum Optics, Hans-Kopfermann-Str. 1, 85748 Garching/Munich, Germany (J.K.); Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, 200 University Ave W., Waterloo, Ontario, Canada N2L3G1 (T.J.)

    • Stefan Zotter,
    • Johannes Kofler &
    • Thomas Jennewein

Contributions

X-s.M. designed and carried out the experiment and analysed data. S.Z. provided experimental assistance. J.K. provided the theoretical analysis and analysed data. R.U. provided experimental and conceptual assistance. T.J. conceived the research, planned and performed the experiment and analysed data. Č.B. provided theoretical suggestions and analysis. A.Z. conceived the research, designed the experiment and supervised the project. All authors wrote the manuscript.

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The authors declare no competing financial interests.

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