Implementation of a two-state quantum bit commitment protocol in optical fibers
A. J. Almeida, Aleksandar Stojanović, Nikola Paunković, Ricardo Loura, Nelson Jesus Muga, N A Silva, Paulo Mateus, Paulo Sérgio de Brito André, Armando N. Pinto
Abstract We demonstrate experimentally the feasibility of a two-state quantum bit commitment protocol, which is both concealing and partially binding, assuming technological limitations. The security of this protocol is based on the lack of long-term stable quantum memories. We use a polarization-encoding scheme and optical fiber as a quantum channel. The measurement probability for the commitment is obtained and the optimal cheating strategy demonstrated. The average success rates for an honest player in the case where the measurements are performed using equal bases are 93.4%, when the rectilinear basis is measured, and 96.7%, when the diagonal basis is measured. The rates for the case when the measurements are performed in different bases are 52.9%, when the rectilinear basis is measured, and 55.4% when the diagonal basis is measured. The average success rates for the optimal cheating strategy are 80% and 73.8%, which are way below the success rates of an honest player. Using a strict numerical validity criterion, we show that, for these experimental values, the protocol is secure.
Abstract We demonstrate experimentally the feasibility of a two-state quantum bit commitment protocol, which is both concealing and partially binding, assuming technological limitations. The security of this protocol is based on the lack of long-term stable quantum memories. We use a polarization-encoding scheme and optical fiber as a quantum channel. The measurement probability for the commitment is obtained and the optimal cheating strategy demonstrated. The average success rates for an honest player in the case where the measurements are performed using equal bases are 93.4%, when the rectilinear basis is measured, and 96.7%, when the diagonal basis is measured. The rates for the case when the measurements are performed in different bases are 52.9%, when the rectilinear basis is measured, and 55.4% when the diagonal basis is measured. The average success rates for the optimal cheating strategy are 80% and 73.8%, which are way below the success rates of an honest player. Using a strict numerical validity criterion, we show that, for these experimental values, the protocol is secure.
We present a two-state practical quantum bit commitment protocol, the security of which is based on the current technological limitations, namely the nonexistence of either stable long-term quantum memories or nondemolition measurements. For an optical realization of the protocol, we model the errors, which occur due to the noise and equipment (source, fibers, and detectors) imperfections, accumulated during emission, transmission, and measurement of photons. The optical part is modeled as a combination of a depolarizing channel (white noise), unitary evolution (e.g., systematic rotation of the polarization axis of photons), and two other basis-dependent channels, namely the phase- and bit-flip channels. We analyze quantitatively the effects of noise using two common information-theoretic measures of probability distribution distinguishability: the fidelity and the relative entropy. In particular, we discuss the optimal cheating strategy and show that it is always advantageous for a cheating agent to add some amount of white noise---the particular effect not being present in standard quantum security protocols. We also analyze the protocol's security when the use of (im)perfect nondemolition measurements and noisy or bounded quantum memories is allowed. Finally, we discuss errors occurring due to a finite detector efficiency, dark counts, and imperfect single-photon sources, and we show that the effects are the same as those of standard quantum cryptography.
We study cheating strategies against a practical four-state quantum bit-commitment protocol [A. Danan and L. Vaidman, Quant. Info. Proc. 11, 769 (2012)] and its two-state variant [R. Loura et al., Phys. Rev. A 89, 052336 (2014)] when the underlying quantum channels are noisy and the cheating party is constrained to using single-qubit measurements only. We show that simply inferring the transmitted photons' states by using the Breidbart basis, optimal for ambiguous (minimum-error) state discrimination, does not directly produce an optimal cheating strategy for this bit-commitment protocol. We introduce a strategy, based on certain postmeasurement processes and show it to have better chances at cheating than the direct approach. We also study to what extent sending forged geographical coordinates helps a dishonest party in breaking the binding security requirement. Finally, we investigate the impact of imperfect single-photon sources in the protocols. Our study shows that, in terms of the resources used, the four-state protocol is advantageous over the two-state version. The analysis performed can be straightforwardly generalized to any finite-qubit measurement, with the same qualitative results.
Bit commitment is an essential primitive in quantum cryptography. It is the basic building block of many cryptographic protocols in which it provides security over distrustful parties. This paper proposes a secured quantum two-bit commitment protocol for any two classical bits. The protocol contains two parties - a committer and a receiver - who share both quantum and classical communication channels. The main phases of this protocol are commitment and revealing phases where the concealing and binding conditions are proved in order to accept the commitment message. The proposed framework utilizes different security layers to hide specific quantum states in a superposition alongside trivial one qubit operations. The secured unitary transformations are applied by the two parties to meet the concealing and binding conditions. To verify the success of the proposed protocol, the measured output of the two parties are compared. The protocol operates under the assumption that the two parties might cheat and the possible existence of an eavesdropper.
In classical cryptography, the bit commitment scheme is one of the most important primitives. We review the state of the art of bit commitment protocols, emphasizing its main achievements and applications. Next, we present a practical quantum bit commitment scheme, whose security relies on current technological limitations, such as the lack of long-term stable quantum memories. We demonstrate the feasibility of our practical quantum bit commitment protocol and that it can be securely implemented with nowadays technology.
This thesis begins by proposing the implementation of a probabilistic photon source based on the stimulated four-wave mixing (FWM) process. This source was implemented experimentally and characterized in terms of its statistical distribution. Next, the impact of the stimulated FWM process in a co-propagating quantum signal was studied experimentally. Finally, the violation of Clauser-Horne-Shimony-Holt (CHSH) inequality was experimentally verified using polarization-entangled photon pairs, which were obtained from the spontaneous FWM process in a Sagnac loop. The experimental evolution of the quantum-bit error rate (QBER) in a system without control of polarization, using this degree of freedom to encode information, was studied. It was found out that the QBER increases with the length of the transmission fiber. It was also verified that the increase in the QBER was due to the random rotation of photon’s polarization. A model for the rigorous estimation of the QBER was derived and developed an automatic method to compensate the random rotations of polarization. The method was validated numerically and experimentally, in a transmission system with 40km, showing that it can compensate for the rotations that photons suffer during propagation in optical fibers. Finally, a quantum bit commitment (QBC) protocol between two untrusted entities was implemented. The encoding was performed using two nonorthogonal states of polarization (SOPs). As quantum channel between the two entities, it was first assumed that the transmitter and the receiver were side by side, and after that, they were separated by 8 km and finally, that they were 16km from each other. The implementation of the protocol was performed with a success rate in measurements exceeding 93%, well above the theoretical security limit of 85%. The best strategy for deceiving the commitment was also implemented, and its security experimentally confirmed with a confidence of 7 standard deviations.
Bit commitment protocols whose security is based on the laws of quantum mechanics alone are generally held to be impossible. We give a strengthened and explicit proof of this result. We extend its scope to a much larger variety of protocols, which may have an arbitrary number of rounds, in which both classical and quantum information is exchanged, and which may include aborts and resets. Moreover, we do not consider the receiver to be bound to a fixed ``honest'' strategy, so that ``anonymous state protocols,'' which were recently suggested as a possible way to beat the known no-go results, are also covered. We show that any concealing protocol allows the sender to find a cheating strategy, which is universal in the sense that it works against any strategy of the receiver. Moreover, if the concealing property holds only approximately, the cheat goes undetected with a high probability, which we explicitly estimate. The proof uses an explicit formalization of general two-party protocols, which is applicable to more general situations, and an estimate about the continuity of the Stinespring dilation of a general quantum channel. The result also provides a natural characterization of protocols that fall outside the standard setting of unlimited available technology and thus may allow secure bit commitment. We present such a protocol whose security, perhaps surprisingly, relies on decoherence in the receiver's laboratory.