4,741 research outputs found
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
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