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Physical Review A

Coherent versus incoherent sequential quantum measurements

Radim Filip

Published Mar 18, 2011• 8 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.83.032311

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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.
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.
A pair of quantum observables diagonal in the same basis can be measured jointly, so some coherence is obviously needed for measurement incompatibility. It is equally clear that these quantum resources are not comparable for general observables. However, in the spirit of complementarity between path and superposition, one expects a precise measurement of the incoherent basis label to be incompatible with sufficiently coherent observables. Here we formalise this idea in a very general framework, involving pairs where one observable is incoherent (diagonal), and the coherence in the other is adjusted by damping via genuinely incoherent operations. An extreme case is a basis measurement mutually unbiased to the incoherent basis, leading to an interesting interplay between coherence and complementarity. In terms of measurement theory, we show that if coherence is insufficient to sustain incompatibility, the associated joint measurements have sequential implementations via incoherent instruments. This yields a concrete method for solving joint measurability problems, tractable even in large systems without resorting to numerical optimisation: we find analytical bounds for the coherence needed for incompatibility, in terms of a divergence measure characterising basis state distinguishability of incoherent observables. We verify the consistency of our theory by a quick proof of the known noise bound for the incompatibility of mutually unbiased bases, and then apply it to study emergent classicality in the spin-boson model of pure decoherence on an N-qubit open quantum system.
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.
A pair of quantum observables diagonal in the same ``incoherent'' basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to the diagonal elements of any observable jointly measurable with it, leading to a general criterion for the coherence needed for incompatibility. Specializing to the case where the second observable is incoherent (diagonal), we develop a concrete method for solving incompatibility problems, tractable even in large systems by analytical bounds, without resorting to numerical optimization. We verify the consistency of our method by a quick proof of the known noise bound for mutually unbiased bases, and apply it to study emergent classicality in the spin-boson model of an NNN-qubit open quantum system. Finally, we formulate our theory in an operational resource-theoretic setting involving ``genuinely incoherent operations'' used previously in the literature, and show that if the coherence is insufficient to sustain incompatibility, the associated joint measurements have sequential implementations via incoherent instruments.
The quantum Zeno effect is the suppression of Hamiltonian evolution by repeated observation, which pins the system to an eigenstate of the measurement observable. Using measurement alone, control of the state can be achieved if the observable is slowly varied, so that the state tracks the now time-dependent eigenstate. We demonstrate this using a circuit-QED readout technique that couples to a dynamically controllable observable of a qubit. Continuous monitoring of the measurement record allows us to detect an escape from the eigenstate, thus serving as a built-in form of error detection. We show this by postselecting on realizations with high fidelity with respect to the target state. Our dynamical measurement operator technique offers a new tool for numerous forms of quantum feedback protocols, including adaptive measurements and rapid state purification.
In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. The effect is conventionally controlled by the measurement frequency. Here we study the development of the Zeno regime as a function of the measurement strength for a continuous partial measurement. We show that the onset of the Zeno regime is marked by a cascade of transitions in the system dynamics as the measurement strength is increased. Some of these transitions are only apparent in the collective behavior of individual quantum trajectories and are invisible to the average dynamics. They include the appearance of a region of dynamically inaccessible states and of singularities in the steady-state probability distribution of states. These predicted dynamical features, which can be readily observed in current experiments, show the coexistence of fundamentally unpredictable quantum jumps with those continuously monitored and reverted in recent experiments.