Quantum erasure with causally disconnected choice

Abstract

The counterintuitive features of quantum physics challenge many common-sense assumptions. In an interferometric quantum eraser experiment, one can actively choose whether or not to erase which-path information (a particle feature) of one quantum system and thus observe its wave feature via interference or not by performing a suitable measurement on a distant quantum system entangled with it. In all experiments performed to date, this choice took place either in the past or, in some delayed-choice arrangements, in the future of the interference. Thus, in principle, physical communications between choice and interference were not excluded. Here, we report a quantum eraser experiment in which, by enforcing Einstein locality, no such communication is possible. This is achieved by independent active choices, which are space-like separated from the interference. Our setup employs hybrid path-polarization entangled photon pairs, which are distributed over an optical fiber link of 55 m in one experiment, or over a free-space link of 144 km in another. No naive realistic picture is compatible with our results because whether a quantum could be seen as showing particle- or wave-like behavior would depend on a causally disconnected choice. It is therefore suggestive to abandon such pictures altogether.

Fig. 1.

Concept of our quantum eraser under Einstein locality conditions. Hybrid entangled photon-pair source, labeled as S, emits path-polarization entangled photon pairs. System photons are propagating through an interferometer (Right) and the environment photons are subject to polarization measurements (Left). Choices to acquire welcher-weg information or to obtain interference of the system photons are made under Einstein locality so that there are no causal influences between the system photons and the environment photons.

Fig. 2.

(A) Scheme of the Vienna experiment: In Lab 1, the source (S) emits polarization entangled photon pairs, each consisting of a system and an environment photon, via type-II spontaneous parametric down-conversion. Good spectral and spatial mode overlap is achieved by using interference filters with 1-nm bandwidth and by collecting the photons into single-mode fibers. The polarization entangled state is subsequently converted into a hybrid entangled state with a polarizing beam splitter (PBS1) and two fiber polarization controllers (FPC). Interferometric measurement of the system photon is performed with a single-mode fiber beam splitter (BS) with a path length of 2 m, where the relative phase between path a and path b is adjusted by moving PBS1’s position with a piezo-nanopositioner. The polarization projection setup of the environment photon consists of an electro-optic modulator (EOM) and another PBS (PBS2). Both photons are detected by silicon avalanche photodiodes (DET 1–4). The choice is made with a QRNG (44). (B) Space–time diagram. The choice-related events C_e and the polarization projection of the environment photon P_e are space-like separated from all events of the interferometric measurement of the system photon I_s. Additionally, the events C_e are also space-like separated from the emission of the entangled photon pair from the source E_se. Shaded areas are the past and the future light cones of events I_s. This ensures that Einstein locality is fulfilled. Details are provided in the main text and SI Text. BS, beam splitter; FPCs, fiber polarization controllers; PBS, polarized beam splitter.

Fig. 3.

Experimental results. (A and B) When measurement (i) is performed (EOM is off), the detection of the environment photon in the state reveals the welcher-weg information of the system photon, being confirmed by measuring the counts of DET 1 and DET 2 conditional on the detection of the environment photon in DET 4. (A) We obtain that the system photon propagates through path a and path b with probabilities 0.023(5) (cyan) and 0.978(5) (yellow), respectively. The integration time is about 120 s. As a consequence of revealing welcher-weg information, phase-insensitive counts are obtained. Mean value of the counts is indicated with a black line, as shown in B. (C and D) When measurement (ii) is performed (EOM on), detection of the environment photon in erases the welcher-weg information of the system photon. (C) Probabilities of the system photon propagating through path a and path b are 0.521(16) (cyan) and 0.478(16) (yellow), respectively. The integration time is about 120 s. Because welcher-weg information is irrevocably erased, two oppositely modulated sinusoidal interference fringes with average visibility 0.951(18) show up as a function of the position change of PBS1, as shown in D. Error bars: ±1 SD, given by Poissonian statistics.

Fig. 4.

Experimental test of the complementarity inequality under Einstein locality, manifested by a tradeoff of the welcher-weg information parameter and the interference visibility. We vary the polarization projection basis of the environment photon via adjusting the applied voltage of the EOM. Note that the leftmost and the rightmost data points correspond to Fig. 3 A and B and 3 C and D, respectively. The dotted line is the ideal curve from the saturation of inequality in Eq. 3. The solid line is the estimation from the actual experimental imperfections, which are measured independently. Error bars: ±1 SD, given by Poissonian statistics.

Fig. 5.

Satellite image of the Canary Islands of Tenerife and La Palma and overview of the experimental setup (Google Earth). The two laboratories are spatially separated by about 144 km. In La Palma, the source (S) emits polarization entangled photon pairs, which subsequently are converted to a hybrid entangled state with a PBS (PBS1) and a half-wave plate oriented at 45°. The interferometric measurement of the system photon is done with a free-space BS, where the relative phase between path a and path b is adjusted by moving PBS1’s position with a piezo-nanopositioner. The total path length of this interferometer is about 0.5 m. The projection setup consists of a quarter-wave plate (QWP), an EOM, and a PBS (PBS2), which together project the environment photon into either the H/V or ^+/− basis (with and ). Both the system photon and the environment photon are detected by silicon avalanche photodiodes (DET 1–4). A QRNG defines the choice for the experimental configuration fast and randomly. A delay card is used to adjust the relative time between the choice event and the other events. Independent data registration is performed by individual time-tagging units on both the system and environment photon sides. The time bases on both sides are established by global positioning system (GPS) receivers.