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Physical Review A

Probabilistic minimal disturbance measurement of symmetrical qubit states

Radim Filip, Ladislav Mišta, F. De Martini, Marco Ricci, Fabio Sciarrino

Published Nov 8, 2006• 3 citations
Publisher

Abstract

We derive fidelity tradeoffs for probabilistic minimal disturbance measurements for certain discrete sets of symmetrical single qubit states. We propose and experimentally demonstrate a simple linear optical scheme saturating these tradeoffs in which the degree of disturbance is controlled only by measurement of a single ancillary photon.

DOI
10.1103/physreva.74.052312

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We derive fidelity tradeoffs for probabilistic minimal disturbance measurements for certain discrete sets of symmetrical single qubit states. We propose and experimentally demonstrate a simple linear optical scheme saturating these tradeoffs in which the degree of disturbance is controlled only by measurement of a single ancillary photon.
We demonstrate a linear optical device which performs optimal quantum measurement or minimum disturbance measurement on a single-photon polarization qubit with the help of an ancillary path qubit introduced to the same photon. We show theoretically and experimentally that this device satisfies the minimum disturbance measurement condition by investigating the relation between the information gain (estimation fidelity) and the state disturbance due to measurement (operation fidelity). Our implementation of minimal disturbance measurement is postselection-free in the sense that all detection events are counted toward evaluation of the estimation fidelity and the operation fidelity, i.e., there is no need for coincidence postselection of the detection events.
We propose and demonstrate a linear optical device which deterministically performs optimal quantum measurement or minimum disturbance measurement on a single-photon polarization qubit with the help of an ancillary path qubit introduced to the same photon. We show theoretically and experimentally that this device satisfies the minimum disturbance measurement condition by investigating the relation between the information gain (estimation fidelity) and the state disturbance due to measurement (operation fidelity). Our implementation of minimum disturbance measurement is postselection-free in the sense that all detection events are counted toward evaluation of the estimation fidelity and the operation fidelity, i.e., there is no need for coincidence postselection of the detection events.
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Quantum mechanics sets a bound between the quality of estimation from measurement of a single copy of a ddd-level system and the degree of disturbance of this system. We show that ideal quantum nondemolition (QND) measurement fed by a properly prepared ancilla saturates this bound. The ratio between the quality of estimation and the degree of disturbance can be continuously controlled by preparation of the ancilla. Further, we show that also nonideal QND measurement achieves this bound if a suitable measurement on the ancilla is performed. Finally, we propose a feasible scheme for such a measurement for optical two-level systems that is based on the controlled-NOT gate.