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Quantum Tasks in Relativistic Spacetime

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In this talk I will set out two new contributions to the study of operational tasks in a relativistic quantum setting. First, I will present a generalisation of the task known as ‘summoning,’ in which an unknown quantum state is supplied to an agent and must be returned at a specified point when a corresponding call is made. I will show that when this task is generalised to allow for more than one call to be made, an apparent paradox arises: the extra freedom makes it strictly harder to complete the task. Second, I will describe a quantum generalisation of the classic cryptographic task known as ‘zero-knowledge-proving.’ I will show that there exists no perfectly secure quantum relativistic protocol for this task, and I will then set out a protocol which is conjectured to be close to optimal in security for this task. These results have practical applications for distributed quantum computing and cryptography and also interesting implications for our understanding of relativistic quantum information and its localisation in spacetime.