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The Null Subject Parameter pp Cite as. To hunt with a bow is fashionable this year.

Definite/indefinite articles

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Boundaries, objects, and connections | Meaningness

Skip to main content. Advertisement Hide. Arbitrary Null Objects and Unselective Binding. Authors Authors and affiliations J. Control theory is concerned with the circumstances under which PRO may or must be bound or free. An assumption commonly held in the many versions of control theory that have been proposed is that whenever PRO fails to be controlled i.

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Consider in this respect the following French sentences which both contain an instance of arbitrary PRO: 1 a. This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Ashton, E. Google Scholar.

Bach, E. Chomsky, N. Clark, R. Epstein, S. Heim, I.

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S1 to S3. Our main source of error is phase fluctuations in the two interferometers. Therefore, we performed a separate measurement presented in Materials and Methods to characterize this error. The error bars in Fig. We can now obtain a value for the CNS of our process by weighting the data presented in Fig.

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The result is. The disagreement between this and our measured result is caused primarily by two effects. The remaining discrepancy comes from systematic errors, such as wave plate miscalibration, which effectively mean that the unitaries Alice and Bob implement differ slightly from their targets.

Still, given our measured result, we can conclude that our process is causally nonseparable by a margin of approximately 7 SDs. As mentioned above, the causal nonseparability as measured using a causal witness can be considered as a measurement of how much noise can be added to the process before it becomes causally separable.

The CNS exp we have discussed so far refers to a worst-case noise model 11 , wherein the desired process is replaced with the process that can do the most damage to its causal nonseparability with a probability. We studied the effect of the noise most relevant to our experiment, namely, dephasing the control qubit but not the system qubit. This noise is the strongest in our setup because the control qubit is encoded in a path degree of freedom, which must remain interferometrically stable [see the study of Branciard 29 for the formal definition of this noise model].

The experimental signature of this imbalance is a reduced visibility of the interferometer. We measured the CNS for several visibilities between 0. There is an offset between the experimental data and the theoretical prediction due to systematic errors. However, both theory and experiment follow the same trend. The plot shows the causal nonseparability of our experimentally implemented SWITCH because the visibility of the two interferometers is decreased from right to left. The experimental data linearly decreases with visibility just as theory dashed line predicts.

The gap between theory and experiment is attributed to systematic errors. The visibility x axis is a measure of the dephasing strength on the control qubit. Our experiment demonstrates how to perform a measurement inside a quantum SWITCH without destroying the superposition of causal orders. Consequently, the superposition of causal orders becomes incoherent. Our way around this is to break the measurement into two steps: First, the system coherently interacts with an ancilla through a unitary operation namely, the additional path modes introduced by the local operation in our experiment.

We demonstrated the causal nonseparability of our experimental apparatus by measuring a causal witness.

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With the ability to perform a measurement inside the SWITCH, we could increase the robustness of the causal witness to noise. Although some other experiments 30 — 33 have also studied the topic of causal relations in quantum mechanics, they focused on a different aspect. For example, in previous studies 30 , 31 , 33 , instead of creating a genuinely indefinite causal order, as in our work, the authors distinguished between different causal structures.

The incoherent mixture 30 and a quantum superposition 31 of different causal relations reported previously are both compatible with one party in the past and the other in the future. Thus, in our language, they correspond to causally ordered processes. Our work represents the first experimental realization of a quantum superposition of orders of nonunitary channels and the first measurement of a causal witness. We believe that this will be an important step toward the realization of quantum superpositions of the order of more elaborate processes.

Because it has been theoretically demonstrated that causally nonordered processes can give rise to a reduction in the query complexity of certain tasks 4 — 6 and lead to more efficient communication channels 7 , 8 , it is important to study new techniques to create more complex, causally nonordered processes.

We already see an advantage in our current work. Making a measurement inside the quantum SWITCH made our experiment more robust to noise and allowed us to demonstrate, by approximately 7 SDs, that our setup cannot be described by a causally ordered process.

The Sagnac loop was realized using a dual-wavelength polarizing beam splitter and two mirrors. The SPDC crystal was a mm-long periodically poled crystal potassium titanyl phosphate crystal.

The crystal was pumped by a The polarization of the laser was set to be horizontal. Polarizers in the signal and idler modes were used to ensure that the polarization was in a well-defined state. The down-converted photons were coupled into single-mode fibers. After passing through the experiment, we observed a coincidence rate between the herald detector and the four final-measurement detectors of pairs per second.

As discussed in the main text, to experimentally measure a causal witness, Alice and Bob need to implement a series of quantum channels on a polarization qubit inside the quantum SWITCH. Alice must perform a measure-and-reprepare channel, whereas Bob must implement a unitary channel.


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Alice measures in four different bases. Thus, she has 16 different measure-and-reprepare maps. Bob simply implements 10 different unitary operators third column of Table 1. In Table 2 , we show the specific wave plate angles we used for each operator. A list of all of the wave plate angles used to perform the operators listed in Table 1.

In our experiment, all combinations of these settings were used, which, together with our three input states, results in measurement settings. Because Alice makes a two-outcome measurement, and our final measurement has two outcomes, for each setting of Alice and Bob, there are four different outcomes. Experimentally, each outcome corresponds to a different SPD. For each setting, we collected approximately counts in total after 2 s of data acquisition. From these counts, we estimated the four corresponding output probabilities through the formula.

The total number of efficiency corrected counts, appearing in Eq.

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The efficiency factors in the above equations are defined as follows. Roughly speaking, to estimate the relative efficiencies, we must send the same number of photons between the detectors and compare the measured count rates. Plots of representative interference fringes already efficiency corrected for each interferometer are shown in Fig. By requiring the total counts out of each port to be constant, we can obtain a relative efficiency between the two ports in each interferometer.

In practice, we obtain the efficiency by plotting the counts out of one port versus the counts out of the other port. If the two efficiencies are equal, the slope of this line will be 1. However, because of different coupling and detector efficiencies, this is enforced by requiring. We set one efficiency of each pair to 1, because we were interested in the relative efficiency.

These plots, for both interferometers, are shown in Fig. A plot of the coincidences between the herald and the two detectors at the output of each interferometer as the interferometer phase is varied. Triggered coincidences detected in port 1 plotted against those detected in port 0 for both interferometers. To do this, we used the state preparation wave plate Fig. In each case, we scanned the phase.

Then, we can calculate the final efficiency as. This works because by using the wave plates and the polarizing beam splitter, we can send nearly all of the incident photons one way or the other. Using this procedure, we now have relative efficiencies between all of the detectors.