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arXiv:1110.6392 · Scientific Reports

Testing sequential quantum measurements: how can maximal knowledge be extracted?

Eleonora Nagali, Simone Felicetti, Pierre-Louis de Assis, Vincenzo D’Ambrosio, Radim Filip, Fabio Sciarrino

Published Jun 19, 2012• 25 citations
arXivHTMLPDF

Abstract

The extraction of information from a quantum system unavoidably implies a modification of the measured system itself. In this framework partial measurements can be carried out in order to extract only a portion of the information encoded in a quantum system, at the cost of inducing a limited amount of disturbance. Here we analyze experimentally the dynamics of sequential partial measurements carried out on a quantum system, focusing on the trade-off between the maximal information extractable and the disturbance. In particular we implement two sequential measurements observing that, by exploiting an adaptive strategy, is possible to find an optimal trade-off between the two quantities.

DOI
10.1038/srep00443

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The extraction of information from a quantum system unavoidably implies a modification of the measured system itself. In this framework partial measurements can be carried out in order to extract only a portion of the information encoded in a quantum system, at the cost of inducing a limited amount of disturbance. Here we analyze experimentally the dynamics of sequential partial measurements carried out on a quantum system, focusing on the trade-off between the maximal information extractable and the disturbance. In particular we implement two sequential measurements observing that, by exploiting an adaptive strategy, is possible to find an optimal trade-off between the two quantities.
The aim of the work is to investigate a non-demolishing measurement strategy which allows to maximize the amount of information extracted from an entangled quantum state, given a certain amount of induced decoherence on the whole system. The protocol can be applied to a single measurement step, as well as extended to a number N of sequential measurements. Furthermore we demonstrate that by implementing a sequence of non-demolishing measurement on the state, it is still possible to achieve a strategy which leads to an optimal trade off between knowledge and decoherence induced.
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.
We compare a trade-off between knowledge and decoherence for the incoherent and coherent partial sequential compatible measurements on single-qubit systems. The individual partial measurement nondestructively monitors basis states of the system by single-qubit meter. For the same decoherence caused by this unbiased measurement, the individual coherent measurement gives more knowledge than the incoherent one. For identical sequential coherent measurements, knowledge accumulated not additively increases more slowly than for the incoherent measurements. The overall knowledge can be accumulated using an adaptive measurement strategy on the meters if the single-qubit coherence of meters is kept. On the other hand, preservation of the mutual qubit coherence between the meters necessary for the collective measurement strategy is not required. A loss of single-qubit coherence degrades the coherent measurements back to the incoherent ones. Since the decoherence caused by the measurement process is a quadratic function of knowledge extracted by the individual measurement, Zeno-like behavior can be observed for repetitive weak compatible measurements. This unconditional universal effect does not depend on any dynamics of the qubit and it is a direct consequence of optimally controlled sequential evolution of quantum information.
One of the basic lessons of quantum theory is that one cannot obtain information on an unknown quantum state without disturbing it. Hence, by performing a certain measurement, we limit the other possible measurements that can be effectively implemented on the original input state. It has been recently shown by two of the authors of the present article [T. Heinosaari and T. Miyadera, Phys. Rev. A 91, 022110 (2015)] that one can implement sequentially any device, either channel or observable, which is compatible with the first measurement. In this work, we prove that this can be done, apart from some special cases, only when the succeeding device is implemented on a larger system than just the input system. This means that some part of the still available quantum information has been flown to the environment and cannot be gathered by accessing the input system only. We characterize the size of the post-measurement system by determining the class of measurements for the observable in question that allow the subsequent realization of any measurement process compatible with the said observable. We also study the class of measurements that allow the subsequent realization of any observable jointly measurable with the first one and show that these two classes coincide when the first observable is extreme.
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.