Technical Comments

Response to Comment on "Quantum State Transfer Between Matter and Light"

Science  19 Aug 2005:
Vol. 309, Issue 5738, pp. 1187
DOI: 10.1126/science.1111237

The comment by van Enk and Kimble (1) does not challenge the principal result of our study (2)—that we achieved quantum state transfer from an atomic qubit to a photonic qubit. They also do not challenge our quantitative measurement of that transfer (2). We used the ratio of certain measured coincidence counts as the experimental value of the overlap |〈ψIi〉|2 between the intended state of the atomic qubit |ψI〉 and the measured state of the photonic qubit |ψi〉. Our measured values for this quantity in two orthogonal measurement bases were F0 = 0.88 ± 0.03 and F45 = 0.75 ± 0.02. As in the quantum teleportation experiment reported by Zeilinger and co-workers (3), the fact that these values were greater than 2/3 confirms the quantum character of the state transfer.

Instead, van Enk and Kimble make three assertions about our study: (i) that we claimed to have measured maximally entangled states; (ii) that our method of analysis does not establish the presence of entangled states; and (iii) that all our experimental results can be explained using unentangled states.

The first assertion is simply incorrect—and, we suspect, stems from a conflation of our introductory theoretical remarks with our actual experimental results. The theoretical introduction to our paper (2) focused on an ideal situation in which there is no decoherence or noise of any kind. This material was essentially a restatement of the theory of Duan et al. (4) and was cited as such in our paper. Among the idealized equations, equation 1 in (2) described a fundamental atom-photon state; equation 4 in (2) described a maximally entangled state of two atomic ensembles; and equation 6 in (2) described a maximally entangled two-photon state. This theoretical part apparently served as the basis for van Enk and Kimble to state that we claimed to have produced a maximally entangled state between an atomic ensemble and a photon, and to have produced maximal entanglement between two atomic ensembles, and that we would have produced a maximally entangled two-photon state between the two signal and idler photons if a fiber were used.

In the experimental part of (2) that followed this theoretical treatment, we presented experimental evidence supporting the realization for a nonideal system of a protocol based on equations 1 to 6 in (2). We clearly enumerated the various inefficiencies inherent in our experiment, which prevent the realization of the ideal pure states described by those equations, and the subsequent impact of those inefficiencies on the fidelity of the quantum state transfer. For example, we noted, “As in any real experiment, various imperfections prevent the read-out of the quantum memory (idler photon) from being identical to the state that we intended to write into the memory” (2).

As stated explicitly in our paper, our observations pertain to mixed joint states of the signal and idler photons, necessarily described by density operators (2). We used the ideal states simply to define the experimental protocol. We deduced that this protocol, although not working ideally, does indeed violate classical thresholds. Our method of data analysis—identical to the one used by Bouwmeester et al. (3)—was not questioned by van Enk and Kimble.

The second assertion of van Enk and Kimble (1)—that our method of analysis does not establish the presence of entangled states—is based on a complete dismissal of our calculation of entanglement fidelity, which involved postselection of two-photon coincidence events. We do not understand their complaint; our calculation followed a standard procedure used in every experiment (using either parametric down-conversion or atomic cascades), to our knowledge, that has studied two-photon entanglement. Nevertheless, we will take this opportunity to remind the reader why our procedures are correct.

As a check on the method we employed in (2), we used an alternative method of data analysis to confirm the presence of entanglement. This was adapted from the work of Blinov et al. (5), who deduced photon-ion entanglement from a calculation of a quantity called “entanglement fidelity.” Our measured value of entanglement fidelity, Fsi = 0.67 ± 0.02 > 1/2, confirms entanglement (although not maximal entanglement, as discussed above). van Enk and Kimble (1) deny the veracity of this check, arguing, first, that “no analysis is given (for the entanglement between atomic ensembles)”; second, that the method of Blinov et al. is inapplicable to deduce entanglement between the signal photon and the idler photon because of the large vacuum component in the wave function; and, third, that the two data sets shown in figures 2 and 3 in (2) are not independent.

The first argument does not apply to our work; our study did not claim to have measured entanglement between atomic ensembles. The second argument is addressed directly in the groundbreaking study of Duan et al. (4) that inspired our work. That study analyzed the role of the vacuum component in the context of quantum networking and concluded that the vacuum is not part of the logical Hilbert space but is discarded by the postselection of coincidence events. Duan et al. specifically noted that “the vacuum components...are removed from the confirmation of the detector clicks, and thus have no influence on the fidelity of all the application schemes” (4). The conclusion of Duan et al. regarding the vacuum component is independent of how much vacuum is present in the quantum state of interest. In both our experiments (2, 6) and those of Blinov et al. (5, 7), exclusion of the vacuum component was performed by postselection of data based on coincident detection (8). The third argument of van Enk and Kimble (1) regarding our method of entanglement (that the two data sets we show are not independent) is technically correct but irrelevant (8).

The final major assertion of van Enk and Kimble (1), that our results can all be explained using unentangled states, is proven neither in the comment itself (1) nor in its supporting online material. Their treatment of this issue begins with a discussion of the quantum state of two atomic ensembles. None of these results pertain to our study (2), however, because, as already noted, we did not attempt to characterize this state. van Enk and Kimble then turn to the quantum state of a photon and two atomic ensembles. We cannot refute their claim that an unentangled state describes our measurements, because they never explicitly provide a state to analyze. Instead, they repeat their claim that the state of equation 1 in (2) contains only “small amounts of entanglement” owing to the large vacuum component. This appears to be another denial of the analysis of Duan et al. (4) regarding the role of the vacuum. They make the same claim regarding our proposed entangled state between the signal photon and the idler photon without ever proposing a candidate unentangled state.

We conclude that the statements of van Enk and Kimble in (1) do not in any way affect the results of our work. In our study (2), we have carefully realized part of the proposal of Duan et al. (4). Our claims are consistent with the theoretical proposal and with our experimental data. We have achieved the quantum state transfer between matter and light that will be a crucial element of long-distance quantum networking (8).

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