Conclusive quantum steering with superconducting transition-edge sensors

Abstract

Quantum steering allows two parties to verify shared entanglement even if one measurement device is untrusted. A conclusive demonstration of steering through the violation of a steering inequality is of considerable fundamental interest and opens up applications in quantum communication. To date, all experimental tests with single-photon states have relied on post selection, allowing untrusted devices to cheat by hiding unfavourable events in losses. Here we close this 'detection loophole' by combining a highly efficient source of entangled photon pairs with superconducting transition-edge sensors. We achieve an unprecedented ∼62% conditional detection efficiency of entangled photons and violate a steering inequality with the minimal number of measurement settings by 48 s.d.s. Our results provide a clear path to practical applications of steering and to a photonic loophole-free Bell test.

Figure 1. Conceptual depiction of quantum steering.

Alice and Bob receive particles from a black box (the source, S) and want to establish whether these are entangled. From a prearranged set, they each choose measurements to be performed on their respective particles. Bob's measurement implementation is trusted, but this need not be the case for Alice's; her measurement device is also treated as a black box from which she gets either a 'conclusive', A_i=±1, or a 'non-conclusive' outcome, A_i=0. To demonstrate entanglement, Alice and Bob need to show that she can steer his state by her choice of measurement. They can do so through the violation of a steering inequality: whenever Bob's apparatus detects a particle, Alice needs to provide her measurement result. If the recorded correlations of their measurement results surpass the bound imposed by the steering inequality, Alice and Bob have conclusively proven the entanglement of their particles.

Figure 2. Experimental scheme.

Polarization-entangled two-photon states are generated in a periodically poled 10 mm KTiOPO₄ (ppKTP) crystal inside a polarization Sagnac loop. The continuous wave, grating-stabilized 410-nm pump laser (LD) is focussed into this crystal with an aspheric lens (L1, f=4.0 mm) and its polarization is set with a fibre polarization controller (PC) and a half-wave plate (HWP), controlling the entangled output state. Bob filters his output photon with a long-pass glass filter (LP) and a 3-nm band-pass filter (BP), before collecting it with an aspheric lens (L2, f=18.4 mm) into a single-mode fibre. He performs his measurement in an external fibre bridge, with a combination of a quarter-wave plate (QWP), HWP, a polarizing beam displacer (BD) and multi-mode-fibre-coupled single-photon avalanche diodes (SPADs). To minimize loss, Alice performs her measurement directly at the source using a QWP, HWP and a polarizing beamsplitter (PBS), followed by a LP filter and fibre collection with focussing optics identical to Bob's, finally detecting her photons with highly efficient superconducting transition-edge sensors (TESs).

Figure 3. Experimental violation of a steering inequality.

(a) Probability distributions P(A_i=a, B_j=b) for the S₃ measurements , Ŷ and Ẑ calculated by normalizing the registered coincident events for each measurement setting to the total count numbers. The green and blue bars represent correlations that indicate the quality of the shared entangled state. The orange bars represent events that Alice failed to detect. Error bars are too small to be seen on this scale. For S₂, we used the data obtained from the measurements of and Ŷ. (b) Theoretical visibility required to violate steering inequalities for N=3 (red dashed line) and N=2 (black line) for a given efficiency η. Our measurement clearly violates this bound, with an averaged visibility of V=0.9678±0.0005 at a mean heralding efficiency of η=0.6175±0.0008 for the N=3 measurements (red) and V=0.9601±0.0006, η=0.6169±0.0008 for N=2 (black). All error bars (1 s.d.) were calculated assuming Poissonian photon-counting statistics. The correction to the analytic bound of inequality (3) due to measurement imprecision (calculated in the Methods section) is shown by the dash-dotted red line for S₃ and the dashed black line for S₂.