Free-Space Quantum Signatures Using Heterodyne Measurements

Abstract

Digital signatures guarantee the authorship of electronic communications. Currently used "classical" signature schemes rely on unproven computational assumptions for security, while quantum signatures rely only on the laws of quantum mechanics to sign a classical message. Previous quantum signature schemes have used unambiguous quantum measurements. Such measurements, however, sometimes give no result, reducing the efficiency of the protocol. Here, we instead use heterodyne detection, which always gives a result, although there is always some uncertainty. We experimentally demonstrate feasibility in a real environment by distributing signature states through a noisy 1.6 km free-space channel. Our results show that continuous-variable heterodyne detection improves the signature rate for this type of scheme and therefore represents an interesting direction in the search for practical quantum signature schemes. For transmission values ranging from 100% to 10%, but otherwise assuming an ideal implementation with no other imperfections, the signature length is shorter by a factor of 2 to 10. As compared with previous relevant experimental realizations, the signature length in this implementation is several orders of magnitude shorter. DOI: 10.1103/PhysRevLett.117.100503 Digital signatures [1] are ubiquitous in electronic communication, used in, for example, Email and digital banking. They guarantee the provenance, integrity, and transferability of messages. Currently used classical digital signature schemes, however, rely on unproven computational assumptions [2], and may become insecure especially if quantum computers can be built [3]. Quantum digital signatures (QDSs) [4][5][6][7][8][9][10], on the other hand, give information-theoretic security [7], loosely speaking based on the fact that nonorthogonal quantum states cannot be perfectly distinguished from each other.The first quantum signature schemes assumed tamperproof, "authenticated" quantum communication links. Intuitively, this could be accomplished using parameter estimation techniques similar to those used in quantum key distribution (QKD). How to achieve this was explicitly shown only recently [10,11]. In addition, recent quantum signature schemes [6,9], including our protocol, do not require long-term quantum memory. Importantly, this means that quantum signatures can be implemented with current technology, essentially similar to QKD setups. "Classical" signature schemes with information-theoretic security also exist [12][13][14], but rely on secret shared keys, which could be accomplished using QKD. Quantum signature schemes may have some advantages over schemes relying on shared keys generated using QKD. In particular, the quantum bit error threshold for a signature scheme is in practice less strict than for distilling a secret shared key [11]. In addition, the required postprocessing is less demanding. Exactly what signature schemes are the most efficient, however, remains an open problem.Note that most QDS protocols, including this one, use quantu...

Experimental demonstration of quantum digital signatures over 43 dB channel loss using differential phase shift quantum key distribution

“…Hence, except with probability ε , the protocol will not abort unnecessarily and dishonest parties will not be able to forge, repudiate, or create non-transferable messages. Successful operation has been shown over a combination of installed optical fiber and additional channel loss corresponding to 134.2 ± 3.8 km of installed optical fiber at two security levels, ε  = 10 −4 , as used in many previous demonstrations of QDS 11, 14, 16, 17 and ε  = 10 −10 , as commonly used in QKD systems. The performance of this system is enhanced compared to that reported previously over 90 km of installed optical fiber 20 in that it can now sign approximately 5 bits per second at 90 km for an ε of 10 −4 , as opposed to 2 bits per second previously, and 2 bits per second at an ε of 10 −10 , as opposed to 1.…”

“…An experimental demonstration 16 using a variation of this scheme was able to successfully transmit signatures over 2 km of optical fiber in a laboratory environment. The first demonstration of QDS over a free-space link was conducted over 1.6 km in an urban environment 17 using a continuous-variable free-space QKD implementation 18, 19 as the underlying system. The first experimental demonstration of QDS over installed optical fiber 20 was only conducted over one optical fiber transmission channel at a fixed distance of 90 km.…”

Continuous-variable quantum digital signatures over insecure channels

“…For example, if Bob measures b ∈ C with Re (b) > 0 and Im (b) > 0 then he will "eliminate" states | − α and | − iα since these are the least likely of Alice's sent states to generate this outcome. Recipients Bob and Charlie each now possess an "eliminated signature" [7,8,11] of length L containing a record of which states were eliminated at each position in the sequence. Since measurements are performed immediately on receipt of the states, no quantum memory is required [7].…”

“…The protocol fails if it allows a forging or repudiation attack, or if it aborts even when all parties are honest. The proofs of robustness and security against repudiation from [11] can be directly applied to our new protocol. For completeness we reproduce the key results in Eqs.…”

Passive state preparation in continuous-variable quantum key distribution

“…More recently, this passive state preparation scheme has been extended to measurement-device-independent CV QKD [23]. It could also be applied in other CV quantum communication protocols, such as quantum secret sharing [24] and quantum digital signature [25].…”