Digital signatures are frequently used in data transfer to prevent impersonation, repudiation and message tampering. Currently used classical digital signature schemes rely on public key encryption techniques, where the complexity of so-called ‘one-way’ mathematical functions is used to provide security over sufficiently long timescales. No mathematical proofs are known for the long-term security of such techniques. Quantum digital signatures offer a means of sending a message, which cannot be forged or repudiated, with security verified by information-theoretical limits and quantum mechanics. Here we demonstrate an experimental system, which distributes quantum signatures from one sender to two receivers and enables message sending ensured against forging and repudiation. Additionally, we analyse the security of the system in some typical scenarios. Our system is based on the interference of phase-encoded coherent states of light and our implementation utilizes polarization maintaining optical fibre and photons with a wavelength of 850 nm.