## 2 Results
### The Experimental Implementation  
Ref. [56] was devoted to the problem of whether unconditionally secure QBC is allowed in principle. Thus, it only provided a theoretical description of the protocol without considering the implementation. To realize the protocol, the most important point is to find a feasible implementation of the infinite-dimensional systems. Here, we propose a trick to implement the infinite-dimensional system in each round of the protocol using a single photon only. The experimental apparatus is illustrated in Figure 1. In each of the \(s\) rounds of step (i) of the protocol, [PERSON] sends a single photon either from the source \(S_{0}\) (for sending \(\psi_{i}^{0}\)) or \(S_{1}\) (for sending \(\psi_{i}^{1}\)), then splits it into two wave packets \(|x\rangle\) and \(|y\rangle\) by the 50:50 non-polarizing beam splitter \(BS_{A}\). \(|x\rangle\) is sent directly to [PERSON] via path \(X\) while \(|y\rangle\) is delayed by the storage ring \(SR_{A}\) (which introduces a delay time \(\tau\) chosen by [PERSON] secretly) before sending via path \(Y\). At [PERSON]'s site, \(|x\rangle\) is delayed by the storage rings \(SR_{x}\) and \(SR_{B}\)\(|y\rangle\) is delayed by the storage ring \(SR_{y}\), which is identical to \(SR_{x}\), so that they introduce the same amount of delay time, then meets \(|x\rangle\) at the 50:50 beam splitter \(BS_{B}\) and interferes. We can see that when the delay times caused by \(SR_{A}\) and \(SR_{B}\) are tuned to be equal, the complete apparatus forms a balanced MZ interferometer, so that \(\psi_{i}^{0}\) (\(\psi_{i}^{1}\)) will make the detector \(D_{0}\) (\(D_{1}\)) click with certainty in principle. Before running the protocol, [PERSON] should set up another set of devices at his own site as a reference, which is completely identical to that of [PERSON]'s. By sending photons using this reference set and monitoring his detectors \(D_{0}\) and \(D_{1}\), he can estimate the error rate \(\varepsilon\) of the whole system, i.e., the probability that the photon \(\psi_{i}^{0}\) (\(\psi_{i}^{1}\)) sent from the source \(S_{0}\) (\(S_{1}\)) will mistakenly make the detector \(D_{1}\) (\(D_{0}\)) click or simply get lost. For better performance, if the distance between [PERSON] and [PERSON] is very long, paths \(X\) and \(Y\) in Figure 1 should be implemented using optical fibers, instead of letting the photons travel through free space. Meanwhile, [PERSON] should also have optical fibers of the same length in his reference set and place them in an environment (e.g., temperature, humidity, etc.) similar to that of the optical fibers placed between [PERSON] and [PERSON] in the actual set. The purpose is to ensure that the error rate \(\varepsilon\) that [PERSON] learns from his reference set is very close to the one in the actual set. After obtaining \(\varepsilon\) all by himself, [PERSON] runs the following experimental protocol with [PERSON]. _Our experimental QBC protocol:_  
_The commit phase:_  
(i) _[PERSON] and [PERSON] agree on a maximum delay time \(\tau_{\max}\) and the sending times \(t_{j}\) (\(j=1,\ldots,s\)) with \(t_{1}<t_{2}<\cdots<t_{s}\) and \(\tau_{\max}<t_{j}-t_{j-1}\) (\(j=2,\ldots,s\)). Then, [PERSON] decides on the value of \(b\) (\(b=0\) or \(1\)) that she wants to commit, and for \(j=1\) to \(s\):_  
_[PERSON] randomly picks \(\tau_{j}\in[0,\tau_{\max}]\)and sets the delay time of her storing ring \(SR_{A}\) as \(\tau_{j}\). Then, she sends [PERSON] a photon \(\Psi_{j}\) from the source \(S_{b}\) at time \(t_{j}\);_  
_Note that, in each round, \(\tau_{j}\) is independently chosen, while \(b\) remains the same for all \(j\);_  
_The holding phase:_  
(ii) _[PERSON] stores the wave packets of each photon in \(SR_{x}\) and \(SR_{y}\) unmeasuredly;_  
_The unveil phase:_  
(iii) _[PERSON] announces the values of \(b\) and all \(\tau_{j}\) (\(j=1,\ldots,s\));_  
(iv) _For \(j=1\) to \(s\): [PERSON] sets the delay time of his storing ring \(SR_{B}\) as \(\tau_{j}\).