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Register a new userUltimate phase estimation in a squeezed-state interferometer using photon counters with a finite number resolution
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Photon counting measurement has been regarded as the optimal measurement scheme for phase estimation in the squeezed-state interferometry, since the classical Fisher information equals to the quantum Fisher information and scales as $bar{n}^2$ for given input number of photons $bar{n}$. However, it requires photon-number-resolving detectors with a large enough resolution threshold. Here we show that a collection of $N$-photon detection events for $N$ up to the resolution threshold $sim bar{n}$ can result in the ultimate estimation precision beyond the shot-noise limit. An analytical formula has been derived to obtain the best scaling of the Fisher information.
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Squeezed-state interferometry plays an important role in quantum-enhanced optical phase estimation, as it allows the estimation precision to be improved up to the Heisenberg limit by using ideal photon-number-resolving detectors at the output ports. Here we show that for each individual $N$-photon component of the phase-matched coherent $otimes$ squeezed vacuum input state, the classical Fisher information always saturates the quantum Fisher information. Moreover, the total Fisher information is the sum of the contributions from each individual $N$-photon components, where the largest $N$ is limited by the finite number resolution of available photon counters. Based on this observation, we provide an approximate analytical formula that quantifies the amount of lost information due to the finite photon number resolution, e.g., given the mean photon number $bar{n}$ in the input state, over $96$ percent of the Heisenberg limit can be achieved with the number resolution larger than $5bar{n}$.
Quantum phase estimation protocols can provide a measuring method of phase shift with precision superior to standard quantum limit (SQL) due to the application of a nonclassical state of light. A squeezed vacuum state, whose variance in one quadrature is lower than the corresponding SQL, has been pointed out a sensitive resource for quantum phase estimation and the estimation accuracy is directly influenced by the properties of the squeezed state. Here we detailedly analyze the influence of the purity and squeezing level of the squeezed state on the accuracy of quantum phase estimation. The maximum precision that can be achieved for a squeezed thermal state is evaluated, and the experimental results are in agreement with the theoretical analyses. It is also found that the width of the phase estimation interval $Delta theta $ beyond SQL is correlated with the purity of the squeezed state.
The large available Hilbert space and high coherence of cavity resonators makes these systems an interesting resource for storing encoded quantum bits. To perform a quantum gate on this encoded information, however, complex nonlinear operations must be applied to the many levels of the oscillator simultaneously. In this work, we introduce the Selective Number-dependent Arbitrary Phase (SNAP) gate, which imparts a different phase to each Fock state component using an off-resonantly coupled qubit. We show that the SNAP gate allows control over the quantum phases by correcting the unwanted phase evolution due to the Kerr effect. Furthermore, by combining the SNAP gate with oscillator displacements, we create a one-photon Fock state with high fidelity. Using just these two controls, one can construct arbitrary unitary operations, offering a scalable route to performing logical manipulations on oscillator-encoded qubits.
When estimating the phase of a single mode, the quantum Fisher information for a pure probe state is proportional to the photon number variance of the probe state. In this work, we point out particular states that offer photon number distributions exhibiting a large variance, which would help to improve the local estimation precision. These theoretical examples are expected to stimulate the community to put more attention to those states that we found, and to work towards their experimental realization and usage in quantum metrology.
A superconducting qubit in the strong dispersive regime of a circuit quantum electrodynamics system is a powerful probe for microwave photons in a cavity mode. In this regime, a qubit spectrum is split into multiple peaks, with each peak corresponding to an individual photon number in the cavity (discrete ac Stark shift). Here, we measure the qubit spectrum in the cavity that is driven continuously with a squeezed vacuum field generated by a Josephson parametric amplifier. By fitting the qubit spectrum with a model which takes into account the finite qubit excitation power, the photon number distribution, which is dissimilar from the apparent peak area ratio in the spectrum, is determined. The photon number distribution shows the even-odd photon number oscillation and quantitatively fulfills Klyshkos criterion for the nonclassicality.
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