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Register a new userFisher information of a squeezed-state interferometer with a finite photon-number resolution
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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 $5bar{n}$.
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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.
We report demonstrations of both quadrature squeezed vacuum and photon number difference squeezing generated in an integrated nanophotonic device. Squeezed light is generated via strongly driven spontaneous four-wave mixing below threshold in silicon nitride microring resonators. The generated light is characterized with both homodyne detection and direct measurements of photon statistics using photon number-resolving transition edge sensors. We measure $1.0(1)$~dB of broadband quadrature squeezing (${sim}4$~dB inferred on-chip) and $1.5(3)$~dB of photon number difference squeezing (${sim}7$~dB inferred on-chip). Nearly-single temporal mode operation is achieved, with measured raw unheralded second-order correlations $g^{(2)}$ as high as $1.95(1)$. Multi-photon events of over 10 photons are directly detected with rates exceeding any previous quantum optical demonstration using integrated nanophotonics. These results will have an enabling impact on scaling continuous variable quantum technology.
Quantum teleportation provides a disembodied way to transfer an unknown quantum state from one quantum system to another. However, all teleportation experiments to date are limited to cases where the target quantum system contains no prior quantum information. Here we propose a scheme for teleporting a quantum state to a quantum system with prior quantum information. By using an optical qubit-ququart entangling gate, we have experimentally demonstrated the new teleportation protocol -- teleporting a qubit to a photon preloaded with one qubit of quantum information. After the teleportation, the target photon contains two qubits of quantum information, one from the teleported qubit and the other from the pre-existing qubit. The teleportation fidelities range from $0.70$ to $0.92$, all above the classical limit of $2/3$. Our work sheds light on a new direction for quantum teleportation and demonstrates our ability to implement entangling operations beyond two-level quantum systems.
In recent proposals for achieving optical super-resolution, variants of the Quantum Fisher Information (QFI) quantify the attainable precision. We find that claims about a strong enhancement of the resolution resulting from coherence effects are questionable because they refer to very small subsets of the data without proper normalization. When the QFI is normalized, accounting for the strength of the signal, there is no advantage of coherent sources over incoherent ones. Our findings have a bearing on further studies of the achievable precision of optical instruments.
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.
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