The action of qubit channels on projective measurements on a qubit state is used to establish an equivalence between channels and properties of generalized measurements characterized by bias and sharpness parameters. This can be interpreted as shifting the description of measurement dynamics from the Schrodinger to the Heisenberg picture. In particular, unital (non-unital) quantum channels are shown to induce unbiased (biased) measurements. The Markovian channels are found to be equivalent to measurements for which sharpness is a monotonically decreasing function of time. These results are illustrated by considering various noise channels. Further, the effect of bias and sharpness parameters on the energy cost of a measurement and its interplay with the non-Markovian dynamics is also discussed.The action of qubit channels on projective measurements on a qubit state is used to establish an equivalence between channels and properties of generalized measurements characterized by bias and sharpness parameters. This can be interpreted as shifting the description of measurement dynamics from the Schrodinger to the Heisenberg picture. In particular, unital (non-unital) quantum channels are shown to induce unbiased (biased) measurements. The Markovian channels are found to be equivalent to measurements for which sharpness is a monotonically decreasing function of time. These results are illustrated by considering various noise channels. Further, the effect of bias and sharpness parameters on the energy cost of a measurement and its interplay with the non-Markovian dynamics is also discussed.

Mar 1, 20211 citation

Maximal coherence of quantum measurement and the resource theory of sharpness

Kyunghyun Baek, Yonggi Jo, Hyunchul Nha

A resource theory of quantum measurement can be addressed in terms of quantum coherence and measurement sharpness, respectively. The former analyzes the off-diagonal structure of POVM elements in a predetermined basis while the latter analyzes the deviation from trivial, state-independent, measurements. We establish a direct connection between the two resource theories by identifying measurement sharpness as the maximal coherence that is achievable under all possible unitary changes of the reference basis. For a broad class of POVMs whose elements share a common eigenbasis, we show that the maximal distance-based coherence of measurement coincides exactly with the corresponding distance-based sharpness monotone. We further extend this equivalence, with element-additive distances, to POVMs whose elements admit a common mutually unbiased basis structure. These results provide a measurement-theoretic analogue of the maximal-coherence \& purity correspondence for quantum states. We also show that the maximal coherence of measurement is faithful with respect to trivial measurements and is monotonic under fuzzifying operations for dichotomic measurements, as well as under mixed-unitary and unitarily covariant preprocessing channels. Finally, we illustrate the operational meaning and limitations of the equivalence through qubit POVMs, single-photon phase sensing, and noisy photon-number resolving detection. In particular, the maximal Fisher information in a Mach-Zehnder interferometer is shown to be determined by the squared maximal coherence of the measurement, while in an imperfect photon-number resolving detector the maximal coherence behaves as a proper sharpness monotone, unlike conventional PVM-based unsharpness measures.A resource theory of quantum measurement can be addressed in terms of quantum coherence and measurement sharpness, respectively. The former analyzes the off-diagonal structure of POVM elements in a predetermined basis while the latter analyzes the deviation from trivial, state-independent, measurements. We establish a direct connection between the two resource theories by identifying measurement sharpness as the maximal coherence that is achievable under all possible unitary changes of the reference basis. For a broad class of POVMs whose elements share a common eigenbasis, we show that the maximal distance-based coherence of measurement coincides exactly with the corresponding distance-based sharpness monotone. We further extend this equivalence, with element-additive distances, to POVMs whose elements admit a common mutually unbiased basis structure. These results provide a measurement-theoretic analogue of the maximal-coherence \& purity correspondence for quantum states. We also show that the maximal coherence of measurement is faithful with respect to trivial measurements and is monotonic under fuzzifying operations for dichotomic measurements, as well as under mixed-unitary and unitarily covariant preprocessing channels. Finally, we illustrate the operational meaning and limitations of the equivalence through qubit POVMs, single-photon phase sensing, and noisy photon-number resolving detection. In particular, the maximal Fisher information in a Mach-Zehnder interferometer is shown to be determined by the squared maximal coherence of the measurement, while in an imperfect photon-number resolving detector the maximal coherence behaves as a proper sharpness monotone, unlike conventional PVM-based unsharpness measures.

quant-pharXiv:2607.05847Jul 8, 20260 citations

Measurement sharpness and disturbance tradeoff

Nayere Saberian, Seyed Javad Akhtarshenas, Fereshte Shahbeigi

Obtaining information from a quantum system through a measurement typically disturbs its state. The postmeasurement states for a given measurement, however, are not unique and highly rely on the chosen measurement model, complicating the puzzle of information disturbance. Two distinct questions are then in order. First, what is the minimum disturbance a measurement may induce? Second, when a fixed disturbance occurs, how informative is the possible measurement in the best-case scenario? Here we propose various approaches to tackle these questions and provide explicit solutions for the set of unbiased binary qubit measurements and postmeasurement state spaces that are equivalent to the image of a unital qubit channel. In particular, we show there are different tradeoff relations between the sharpness of this measurement and the average fidelity of the premeasurement and postmeasurement state spaces as well as the sharpness and quantum resources preserved in the postmeasurement states in terms of coherence and discordlike correlation once the measurement is applied locally.Obtaining information from a quantum system through a measurement typically disturbs its state. The postmeasurement states for a given measurement, however, are not unique and highly rely on the chosen measurement model, complicating the puzzle of information disturbance. Two distinct questions are then in order. First, what is the minimum disturbance a measurement may induce? Second, when a fixed disturbance occurs, how informative is the possible measurement in the best-case scenario? Here we propose various approaches to tackle these questions and provide explicit solutions for the set of unbiased binary qubit measurements and postmeasurement state spaces that are equivalent to the image of a unital qubit channel. In particular, we show there are different tradeoff relations between the sharpness of this measurement and the average fidelity of the premeasurement and postmeasurement state spaces as well as the sharpness and quantum resources preserved in the postmeasurement states in terms of coherence and discordlike correlation once the measurement is applied locally.

arXiv:2308.04133Physical Review AJan 2, 20246 citations

Relationship between subjecting the qubit to dynamical decoupling and to a sequence of projective measurements

Fattah Sakuldee, Łukasz Cywiński

We consider a qubit coupled to another system (its environment) and discuss the relationship between the effects of subjecting the qubit to either a dynamical decoupling sequence of unitary operations or a sequence of projective measurements. We give a formal statement concerning the equivalence of a sequence of coherent operations on a qubit, precisely operations from a minimal set ${{\mathbb{1}}_{Q},{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}}$, and a sequence of projective measurements of observable ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$. Using it we show that when the qubit is subjected to $n$ such successive projective measurements at certain times, the expectation value of the last measurement can be expressed as a linear combination of expectation values of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$ observed after subjecting the qubit to dynamical decoupling sequences of $\ensuremath{\pi}$ pulses, with $k\ensuremath{\le}n$ of them applied at subsets of these times. Performing a sequence of measurements on the qubit gives then access to the same properties of the environment and qubit-environment coupling that are affecting the coherence observed in a dynamical decoupling experiment. Analyzing the latter has been widely used to characterize the environmental dynamics (perform so-called noise spectroscopy), so our result shows how the results obtained with dynamical-decoupling-based protocols are related to those that can be obtained just by performing multiple measurements on the qubit. We also discuss in more detail the application of the general result to the case of the qubit undergoing pure dephasing and outline possible extensions to higher-dimensional systems (a qudit or multiple qubits).We consider a qubit coupled to another system (its environment) and discuss the relationship between the effects of subjecting the qubit to either a dynamical decoupling sequence of unitary operations or a sequence of projective measurements. We give a formal statement concerning the equivalence of a sequence of coherent operations on a qubit, precisely operations from a minimal set ${{\mathbb{1}}_{Q},{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}}$, and a sequence of projective measurements of observable ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$. Using it we show that when the qubit is subjected to $n$ such successive projective measurements at certain times, the expectation value of the last measurement can be expressed as a linear combination of expectation values of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$ observed after subjecting the qubit to dynamical decoupling sequences of $\ensuremath{\pi}$ pulses, with $k\ensuremath{\le}n$ of them applied at subsets of these times. Performing a sequence of measurements on the qubit gives then access to the same properties of the environment and qubit-environment coupling that are affecting the coherence observed in a dynamical decoupling experiment. Analyzing the latter has been widely used to characterize the environmental dynamics (perform so-called noise spectroscopy), so our result shows how the results obtained with dynamical-decoupling-based protocols are related to those that can be obtained just by performing multiple measurements on the qubit. We also discuss in more detail the application of the general result to the case of the qubit undergoing pure dephasing and outline possible extensions to higher-dimensional systems (a qudit or multiple qubits).

arXiv:1907.05165Physical Review AApr 23, 202014 citations

Optimal parameter estimation of Pauli channels

László Ruppert, Dániel Virosztek, Katalin Hangos

The optimal measurement configuration, i.e. the optimal input quantum state and measurement in the form of a positive operator-valued measure with two elements, is investigated in this paper for qubit and generalized Pauli channels. The channel directions are defined as the contracting directions of the channel with an arbitrary fixed basis of Pauli matrices. In the qubit Pauli channel case with known channel directions it is shown that the optimal configuration that maximizes the Fisher information of the estimated parameters consists of three von Neumann measurements together with pure input states directed to the appropriate channel directions. Extensions of these results for generalized Pauli channels are also given. Furthermore, a computationally efficient estimation method is proposed for estimating the channel directions in the qubit Pauli channel case. The efficiency of this method is illustrated by simulations: it is shown that its variance is of order 1/ N , where N is the number of used measurements.The optimal measurement configuration, i.e. the optimal input quantum state and measurement in the form of a positive operator-valued measure with two elements, is investigated in this paper for qubit and generalized Pauli channels. The channel directions are defined as the contracting directions of the channel with an arbitrary fixed basis of Pauli matrices. In the qubit Pauli channel case with known channel directions it is shown that the optimal configuration that maximizes the Fisher information of the estimated parameters consists of three von Neumann measurements together with pure input states directed to the appropriate channel directions. Extensions of these results for generalized Pauli channels are also given. Furthermore, a computationally efficient estimation method is proposed for estimating the channel directions in the qubit Pauli channel case. The efficiency of this method is illustrated by simulations: it is shown that its variance is of order 1/ N , where N is the number of used measurements.

arXiv:1511.06662Journal of Physics A Mathematical and TheoreticalJun 14, 201217 citations

Optimal parameter estimation of Pauli channels

László Ruppert, D, Virosztek, Katalin Mária Hangos

The optimal measurement configuration, i.e. the optimal input quantum state and measurement in the form of a positive operator-valued measure with two elements, is investigated in this paper for qubit and generalized Pauli channels. The channel directions are defined as the contracting directions of the channel with an arbitrary fixed basis of Pauli matrices. In the qubit Pauli channel case with known channel directions it is shown that the optimal configuration that maximizes the Fisher information of the estimated parameters consists of three von Neumann measurements together with pure input states directed to the appropriate channel directions. Extensions of these results for generalized Pauli channels are also given. Furthermore, a computationally efficient estimation method is proposed for estimating the channel directions in the qubit Pauli channel case. The efficiency of this method is illustrated by simulations: it is shown that its variance is of order 1/N, where N is the number of used measurements.The optimal measurement configuration, i.e. the optimal input quantum state and measurement in the form of a positive operator-valued measure with two elements, is investigated in this paper for qubit and generalized Pauli channels. The channel directions are defined as the contracting directions of the channel with an arbitrary fixed basis of Pauli matrices. In the qubit Pauli channel case with known channel directions it is shown that the optimal configuration that maximizes the Fisher information of the estimated parameters consists of three von Neumann measurements together with pure input states directed to the appropriate channel directions. Extensions of these results for generalized Pauli channels are also given. Furthermore, a computationally efficient estimation method is proposed for estimating the channel directions in the qubit Pauli channel case. The efficiency of this method is illustrated by simulations: it is shown that its variance is of order 1/N, where N is the number of used measurements.

Jan 1, 20128 citations

n

such successive projective measurements at certain times, the expectation value of the last measurement can be expressed as a linear combination of expectation values of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$ observed after subjecting the qubit to dynamical decoupling sequences of $\ensuremath{\pi}$ pulses, with $k\ensuremath{\le}n$ of them applied at subsets of these times. Performing a sequence of measurements on the qubit gives then access to the same properties of the environment and qubit-environment coupling that are affecting the coherence observed in a dynamical decoupling experiment. Analyzing the latter has been widely used to characterize the environmental dynamics (perform so-called noise spectroscopy), so our result shows how the results obtained with dynamical-decoupling-based protocols are related to those that can be obtained just by performing multiple measurements on the qubit. We also discuss in more detail the application of the general result to the case of the qubit undergoing pure dephasing and outline possible extensions to higher-dimensional systems (a qudit or multiple qubits).