No-go result for quantum postselection measurements of rank-m degenerate subspace

We present a no-go result for postselection measurements where the conditional expectation value of a joint system-device observable under postselection is nothing else than the conventional expectation value. Such a no-go result relies on the rank-m degenerate of the joint observable, where m is the dimension of the device subspace. Remarkable, we show that the error and disturbance in quantum measurements obey the no-go result, which implies that the error-disturbance uncertainty is unaffected under postselection measurements.Comment: 6 pages, 0 figur

Quantum uncertainties in sequential measurements under prediction and retrodiction

In sequential measurements, we consider the prediction is as an inference of the subsequent observational data from the prior measurements, while the retrodiction is as an inference of the prior observational data from the subsequent measurements. We theoretically study the impact of the quantum backaction (QBA) in the sequential measurements on the inferred observational data from the prediction and retrodiction. The QBA of the prediction behaves like the disturbance caused by prior measurements affecting subsequent measurements, whereas the QBA of the retrodiction behaves through the disturbance caused by the subsequent measurements affecting the prior measurements. In particular, we consider the sequential measurements of two observables A and B, one after another, i.e., A first and B later, and then we theoretically formulate the quantum uncertainties in the value of these observables (for both prediction and retrodiction) as figures of merit for the disturbances. These results are illustrated in spin systems, where we present the dependence of the uncertainty in subsequent measurement on the prior measurement and vice versa. We further find a hint for beyond the stronger uncertainty relation. The work is finally extended to N-sequential measurements.Comment: 11 pages, 4 figure

Stochastic parameter-shift rule for quantum metrology with general Hamiltonians

Recently, quantum metrology with multiplicative Hamiltonians has been proposed in the variational quantum algorithms, from which the estimation precision can be adaptively optimized via the variational circuits. For systems with general Hamiltonians, however, still lack these variational schemes. In this work, we introduce a quantum-circuit-based approach for studying quantum metrology with general Hamiltonians. We introduce the stochastic parameter-shift rule for the derivatives of the evolved quantum state under the parameterized gates in the circuit, whereby the quantum Fisher information can be obtained. Here the parameters are those we wish to estimate. We find that under the family of the parameterized gates, our scheme can be executed in universal quantum computers. Moreover, in the examples of the magnetic field estimation, we show the consistency between the results obtained from the stochastic parameter-shift rule and the exact results while the standard parameter-shift rule slightly deviates from the exact ones. Our work sheds new light for studying quantum metrology with general Hamiltonians using quantum circuit algorithms.Comment: 9 pages, 3 figure

Tradeoffs in multiple-parameter postselection measurements

We analyze simultaneous estimations of multiple parameters in postselection measurements in terms of a tradeoff relation. A system, or a sensor, is characterized by a set of parameters, interacts with a measurement apparatus (MA), and then is postselected onto a final state. Measurements of the MA yield an estimation of the parameters. We first derive classical and quantum Cramer-Rao lower bounds and discuss the tradeoffs in the postselection measurements in general. Then, we discuss simultaneous measurements of phase and its fluctuation as an example. We found that the quantum Cramer-Rao bound can be attained and the quantum tradeoff can be saturated and thus all the parameters can, in principle, attain the ultimate precision simultaneously.Comment: 20 pages, 2 figure