Quantum de Finetti theorem under fully-one-way adaptive measurements

Abstract

We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multi-fold product states. The approximation is measured by distinguishability under fully one-way LOCC (local operations and classical communication) measurements. Our result strengthens Brandão and Harrow's de Finetti theorem where a kind of partially one-way LOCC measurements was used for measuring the approximation, with essentially the same error bound. As main applications, we show (i) a quasipolynomial-time algorithm which detects multipartite entanglement with amount larger than an arbitrarily small constant (measured with a variant of the relative entropy of entanglement), and (ii) a proof that in quantum Merlin-Arthur proof systems, polynomially many provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations.

arXiv commentV2: minor changes. V3: new title, more discussions added, presentation improved. V4: minor changes, close to published version

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• Estimating operator norms using covering nets
• Divide-and-conquer verification method for noisy intermediate-scale quantum computation
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• Stabilization against collapse of 2D attractive Bose-Einstein condensates with repulsive, three-body interactions
• Locally-Measured Rényi Divergences
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• Experimental Verification of Entangled States in the Adversarial Scenario