Can you sign a quantum state?

Understand

Cryptography with quantum states exhibits a number of surprising and counterintuitive features.

• In a 2002 work, Barnum et al.
• argue that these features imply that digital signatures for quantum states are impossible (Barnum et al., FOCS 2002).
• In this work, we ask: can all forms of signing quantum data, even in a possibly weak sense, be completely ruled out? We give two results which shed significant light on this basic question.