Research ArticlePHYSICS

Experimentally reducing the quantum measurement back action in work distributions by a collective measurement

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Science Advances  01 Mar 2019:
Vol. 5, no. 3, eaav4944
DOI: 10.1126/sciadv.aav4944
  • Fig. 1 Experimental setup for both CM and TPM schemes.

    The setup is divided into three modules: state preparation (A), CM (B), and TPM (C). Module A can generate an arbitrary one-copy polarization-encoded state |Φ〉 or a two-copy polarization path–encoded state |Φ〉⊗2 of a single photon. Module B implements the CM on |Φ〉⊗2. The rotation angle of two β–half-wave plates (HWPs) is adjustable for different unitary processes U(θ) with cos22β = 2sin2θ. The rotation angles of the other four HWPs are fixed as follows: H5, 22.5°; H6, 45°; H8, 67.5°; H9, 45°. Module C implements the TPM schemes on |Φ〉, and the rotation angle of the two γ-HWPs is adjustable and can implement different U(θ) with θ = 2γ. SPD, single-photon detector; FC, fiber coupler; BD, beam displacer; M, mirror; BBO, β-barium borate; IF, interference filter.

  • Fig. 2 Transition probabilities for the initial state |+〉 and the unitary U(π/4) from experimental data.

    Experimental results for the transition probabilities of the CM and TPM measurements correspond to the red and blue cylinders, respectively. (A) The factual transition U(π/4) takes an initial maximally coherent state |+〉 to an incoherent pure state |0〉, and the quantum states are shown by Bloch representation. (B) The transition probabilities for the CM are Embedded Image, and the results of the TPM are Embedded Image. The theoretical fitting values are shown by black-edged transparent cylinders.

  • Fig. 3 Measurement back action (obtained from experimental data) for various coherent processes.

    Experimental results for the measurement back action, quantified by the fidelity between measured and unmeasured final energy distributions, of the TPM (blue) and CM (red) schemes. The results are obtained by fixing the initial state to a maximally coherent state |+〉 and for various unitary processes U(θ) with θ between 0° and 45°, mapping a fixed input to a class of pure states, as shown in (A). The fidelity in (B) is plotted against the cohering power of U(θ).

  • Fig. 4 Measurement back action (obtained from experimental data) for different initial states.

    Experimental results for the fidelity between the measured and unmeasured final energy distributions, for both the TPM (blue) and CM (red) schemes. The results are obtained for input states of the form Embedded Image for various values of p0 between 0 and 1, and p0 + p1 = 1. The unitary is fixed to U(π/6) with a cohering power of Embedded Image, mapping a class of pure states to another class of pure states, as shown in (A). The experimental results in (B) agree well with theoretical predictions.

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Theoretical aspects
    • Section S2. Experimental aspects
    • Table S1. Experimental data for different coherent processes.
    • Table S2. Experimental data for states with various initial coherence.

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