Systems and methods for providing secure quantum digital signatures. In one embodiment, a digital signature user creates a plurality of identical "public" keys having one or more bits and a corresponding quantum mechanical one-way function. Quantum digital signature recipients use a "swap test" to check the validity of a copy of the key, and compare the test results with others. The quantum digital signature user sends a signed message over any channel, including an insecure channel. The recipients evaluate the signed message, and quantify the number of incorrect keys. The message is deemed valid and original, or forged and/or tampered with, when the number of incorrect keys is less than a lower threshold, or exceeds an upper threshold, respectively. For an intermediate number of incorrect keys, the recipients determine message authenticity by comparing observations. Hardware useful for application of the method is disclosed.