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arXiv:quant-ph/0610196 · Physical Review A

Information-disturbance trade-off in quantum-state discrimination

Francesco Buscemi, Massimiliano Federico Sacchi

Published Nov 14, 2006• 32 citations
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Abstract

When discriminating between two pure quantum states, there exists a quantitative trade-off between the information retrieved by the measurement and the disturbance caused on the unknown state. We derive the optimal trade-off and provide the corresponding quantum measurement. Such an optimal measurement smoothly interpolates between the two limiting cases of maximal information extraction and no measurement at all.

DOI
10.1103/physreva.74.052320

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When discriminating between two pure quantum states, there exists a quantitative trade-off between the information retrieved by the measurement and the disturbance caused on the unknown state. We derive the optimal trade-off and provide the corresponding quantum measurement. Such an optimal measurement smoothly interpolates between the two limiting cases of maximal information extraction and no measurement at all.
When an observer wants to identify a quantum state, which is known to be one of a given set of nonorthogonal states, the act of observation causes a disturbance to that state. We investigate the trade-off between the information gain and that disturbance. This issue has important applications in quantum cryptography. The optimal detection method, for a given tolerated disturbance, is explicitly found in the case of two equiprobable nonorthogonal pure states. \textcopyright{} 1996 The American Physical Society.
Quantum measurement unavoidably disturbs the state of a quantum system if any information about the system is extracted. Recently, the concept of reversing quantum measurement has been introduced and has attracted much attention. Numerous efforts have thus been devoted to understanding the fundamental relation of the amount of information obtained by measurement to either state disturbance or reversibility. Here, we experimentally prove the trade-off relations in quantum measurement with respect to both state disturbance and reversibility. By demonstrating the quantitative bound of the trade-off relations, we realize an optimal measurement for estimating quantum systems with minimum disturbance and maximum reversibility. Our results offer fundamental insights on quantum measurement and practical guidelines for implementing various quantum information protocols.
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 (MESs), 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 MESs. 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.
While an information-disturbance trade-off in quantum measurement has been at the core of foundational quantum physics and constitutes a basis of secure quantum information processing, recently verified reversibility of a quantum measurement requires to refine it toward a complete version of information trade-off in quantum measurement. Here we experimentally demonstrate a trade-off relation among all information contents, i.e., information gain, disturbance, and reversibility in quantum measurement. By exploring quantum measurements applied on a photonic qutrit, we observe that the information of a quantum state is split into three distinct parts accounting for the extracted, disturbed, and reversible information. We verify that such different parts of information are in trade-off relations not only pairwise but also triplewise all at once, and find that the triplewise relation is tighter than any of the pairwise relations. Finally, we realize optimal quantum measurements that inherently preserve quantum information without loss of information, which offer wider applications in measurement-based quantum information processing.