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Abstract
We present a simple protocol for certifying graph states in quantum networks using stabiliser measurements. The certification statements can easily be applied to different protocols using graph states. We see, for example, how it can be used for measurement based verified quantum computation, certified sampling of random unitaries, quantum metrology and sharing quantum secrets over untrusted channels.
Highlights
Graph states are a family of multipartite quantum states, defined in one to one correspondence with a simple graph [1]
Many methods exist for testing graph states varying in the trust that must be assumed and the kind of statements that are made
A successful test for us is one that always accepts an ideal source and outputs the ideal source state and, if it accepts, the state is not too far from the ideal state. We see how it can be used for certification for various quantum network tasks, in particular for delegated computation, generation of randomness, quantum metrology and quantum secret sharing
Summary
Graph states are a family of multipartite quantum states, defined in one to one correspondence with a simple graph [1] They are incredibly useful resources across quantum information, acting as the key entanglement resource for error correction [2], measurement based quantum computation [3], quantum secret sharing [4] and more [1]. A successful test for us is one that always accepts an ideal source and outputs the ideal source state (completeness) and, if it accepts, the state is not too far from the ideal state (soundness—see below for technical definitions) With this in hand, we see how it can be used for certification for various quantum network tasks, in particular for delegated computation, generation of randomness, quantum metrology and quantum secret sharing. We conclude with discussions on variants of the protocol, some possible further applications and comments on the scaling of the security parameter
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