## 1 Introduction  
Quantum cryptography has achieved great success in many fields such as key distribution [1], but there are still other cryptographic problems that remain unconquered. Bit commitment (BC) [2] is known to be an essential building block for coin tossing [1], oblivious transfer [3, 4], and even more complicated multi-party secure computation protocols [5]. Unfortunately, since 1996, people started to realize that unconditionally secure quantum BC (QBC) is hard to achieve. The cheating strategy against the QBC protocol in ref. [2] was first proposed in ref. [6]. Shortly after, it was further asserted that all QBC protocols are not unconditionally secure in principle [7, 8]. Later, refs. [9, 10, 11, 12, 13, 14] reviewed the original no-go proof, with some examples of insecure protocols given in refs. [9, 13]. Ref. [11] also extended the proof to cover ideal quantum coin tossing (QCT). More examples on how to break some promising BC protocols at that time were provided too [15, 16]. Refs. [17, 18, 19, 20] proved the impossibility of some types of BC with a slightly different security criterion. Refs. [21, 22, 23, 24, 25] gave quantitative studies on the security bounds of QBC, with ref. [22] focused on the protocol in ref. [1], while refs. [23, 24] focused on another class of protocols. A very lengthy proof was first presented in the [PERSON] picture [26], then shortened and rephrased in the [PERSON] picture [27]. The validity of the no-go result was also studied in a world subject to superselection rules [28, 29, 30] or an epistemic local hidden variable theory [31]; for QBC associated with secret parameters [32, 33] or secret probability distributions [34]; or when the participants are restricted to use Gaussian states and operations only [35]. Refs. [36, 37] attempted to deduce the impossibility of QBC from the no-masking theorem. Ref. [38] studied the security of BC under the relativistic setting. Other efforts include refs. [39, 40, 41, 42, 43, 44], which tried to proved the no-go theorem with alternative approaches. These results, known as the Mayers-Lo-Chau (MLC) no-go theorem, were widely accepted de-spitesome attempts towards secure QBC (e.g., the references in refs. [45, 46, 47, 48, 49, 50, 51]), and were considered as a serious drawback on the potential of quantum cryptography.  
Nevertheless, the cheating strategy in all these no-go proofs is based on the Hughston-Jozsa-Wootters (HJW) theorem [52], a.k.a. the Uhlmann theorem [53; 54]. Recently, it was found that, in infinite-dimensional systems, there exists a specific form of quantum states to which the HJW theorem does not apply [55]. Based on this finding, we proposed a QBC protocol and proved theoretically that it remains secure against the cheating strategy in the no-go proofs [56]. Therefore, implementing the protocol in practice will be of great significance, as it can re-open the venue to many useful multi-party secure computation protocols that were once closed by the MLC no-go theorem.  
As pointed out in ref. [56], since the protocol requires infinite-dimensional systems, the implementation may be very hard if we want to use physical systems with an infinite number of energy levels, because it may imply an infinitely high energy. To circumvent the problem, here, we use the arrival time of photons as a trick, so that infinite-dimensional systems can be realized using simple optical devices. Consequently, the QBC protocol in ref. [56] can be implemented with a Mach-Zehnder (MZ) interferometer, which is within the capability of currently available technology.