Trade-off between Information Gain and Disturbance in Local Discrimination of Entangled Quantum States

• URL: http://arxiv.org/abs/2308.16032v2
• Date: Thu, 21 Nov 2024 10:54:38 GMT
• Title: Trade-off between Information Gain and Disturbance in Local Discrimination of Entangled Quantum States
• Authors: Youngrong Lim, Minki Hhan, Hyukjoon Kwon,
• Abstract summary: We establish an information gain-disturbance trade-off relation in local state discrimination. We show that the trade-off can be circumvented when local operations are aided by pre-shared entanglement. We propose an entanglement certification protocol that is robust against depolarizing noise and generalize it to multipartite scenarios in a quantum network.
• Score: 4.843959205337007
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• Abstract: We establish an information gain-disturbance trade-off relation in local state discrimination. Our result demonstrates a fundamental limitation of local strategy to discriminate entangled quantum states without disturbance, which becomes more difficult as the entanglement of the states to be discriminated increases. For a set of maximally entangled states, the capability of local strategy is tightly suppressed, as random guessing without measurements saturates the bound provided by the trade-off relation. We also show that the trade-off can be circumvented when local operations are aided by pre-shared entanglement. To simultaneously achieve correct guessing of state and non-disturbance, an entirely different strategy from conventional state discrimination should be adopted to lower the cost of pre-shared entanglement. We explicitly propose an adaptive and non-destructive strategy based on the stabilizer formalism, which shows a strict advantage over conventional teleportation-based approaches in pre-shared entanglement cost for discriminating a set of maximally entangled states. As an application of the trade-off relation, we propose an entanglement certification protocol that is robust against depolarizing noise and generalize it to multipartite scenarios in a quantum network.

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