Multiphoton quantum metrology without pre-and post-selected measurements
Chenglong You, Thomas Gerrits, Peter Bierhorst, Adriana E. Lita, Scott Glancy, Narayan Bhusal, Jonathan P. Dowling, Emanuel H. Knill, Sae Woo Nam, Richard P. Mirin, Omar S. Magaña‐Loaiza
We demonstrate the first protocol for quantum-enhanced phase estimation without pre- and post-selected measurements. Our experiment, with an overall efficiency of 82%, utilizes two-mode squeezed vacuum states and photon-number-resolving detection to surpass the standard quantum limit.
The quantum statistical fluctuations of electromagnetic fields establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here, we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broad range of phases, with neither pre- nor post-selected measurements. This is achieved through the efficient design of a source of spontaneous parametric downconversion in combination with photon-number-resolving detection. The robustness of two-mode squeezed vacuum states against loss allows us to outperform schemes based on N00N states, in which the loss of a single photon is enough to remove all phase information from a quantum state. In contrast to other schemes that rely on N00N states or conditional measurements, the sensitivity of our technique could be improved through the generation and detection of high-order photon pairs. This unique feature of our protocol makes it scalable. Our work is important for quantum technologies that rely on multiphoton interference such as quantum imaging, boson sampling, and quantum networks.
The control of photons represents a pillar for our modern technological society. The emerging field of quantum photonics exploits quantum properties of light to dramatically improve the performance of protocols for metrology, communication and information processing. However, modern applications exploit very little of the enormous potential of the photon. Unfortunately, the challenges involved in the preparation and characterization of photonic states with multiple particles, impose practical limitations to realistic quantum technologies. In this talk, I will report on our recent results on the preparation, manipulation and characterization of quantum states with multiple photons. I will describe how the manipulation of the quantum electromagnetic fluctuations of a pair of vacuum states leads to a novel family of quantum-correlated multiphoton states with tunable mean photon numbers and degrees of correlations. Our technique relies on the use of conditional measurements to engineer the vacuum and consequently the excitation mode of the field through the simultaneous subtraction of photons from two-mode squeezed vacuum states. In addition, I will describe the potential of combing these states with photon number resolving measurements for quantum phase estimation. The last part of my talk will be devoted to discuss our recent technique that allowed us to utilize compressive sensing to demonstrate measurement of high-dimensional states, that describe telecom photon pairs in the spatial and spectral degrees of freedom, with 12 billions of elements using only a small fraction of measurements.
This thesis explores various protocols which can be applied to quantum metrology, such that precision of the measurement can beat the best classical approaches. We first demonstrate that ancilla-assisted schemes can improve phase estimation in the presence of noise, and we propose an experiment to demonstrate these effects. Given that the use of ancillae helps, it is no surprise that there are noisy channels for which the optimal strategy may depend on the noise level. We show that there is a non-trivial crossover between the ancilla-assisted strategy and the parallel-entangled strategy for Pauli noise channels and the amplitude damping channel. We see that under certain circumstances, the environment cannot access the parameter of interest. We then integrated techniques from quantum communication, to derive a general framework that renders quantum metrology protocols into cryptographic ones. Here the protocol is unconditionally secure if the trusted parties wish only to achieve the standard quantum limit. If Heisenberg-limited precision is to be achieved, they sacrifice some security, where adversaries can access information, but only at the risk of getting caught at it (cheat-sensitivity). In many scenarios, the quantum Fisher information is achieved for only one value of the phase. In a particular phase estimation scheme that measures the parity at the output of a Mach-Zehnder interferometer where the input is a two-mode squeezed vacuum, this problem is particularly imminent. We apply an adaptive technique to resolve this issue, showing that one can achieve precisions substantially below the shot noise limit. The key to a quadratically enhanced improvement in quantum metrology is entanglement. Finally, we demonstrate in a photonic system how high-dimensional entanglement can be certified, and provide an alternate interpretation of entanglement from an information-theoretic perspective.
Quantum-enhanced interferometers utilize non-classical states of light in order to surpass the limitations imposed by classical physics on phase measurement sensitivity and resolution. We review key scientific developments in this growing field of research and derive fundamental metrology concepts, namely the Cram\'{e}r-Rao bound and the Fisher information, which are used to analyze the metrological performance of quantum states of light. We propose a supersensitive quantum interferometry protocol that can be amplified to the macroscopic realm (i.e. the mean number of photons of the probe state can reach approximately 100,000 photons) using contemporary techniques of spontaneous parametric down conversion. The parity measurement on the output field asymptotically saturates the quantum Cram\'{e}r-Rao bound, which scales like the Heisenberg limit. We uncover the role of photon statistics on phase sensitivity and rule out the necessity of mode entanglement for quantum-enhanced interferometry. Based on these insights we outline a practical metrology technique (independent of mode entanglement) that measures a phase delay of a single-mode anti-squeezing operation. This scheme can also be scaled macroscopically using contemporary techniques and is shown to significantly surpass the shot-noise limit (SNL) in the presence of realistic losses. Finally, the physical resources that enable quantum-enhanced interferometry is studied by analyzing the quantum Fisher information (QFI) using the first quantization and the second quantization formalisms of quantum mechanics. It is shown that increasing the intra-mode correlations of an interferometer (as quantified by the second order Glauber coherence function) can be conducive to attaining a quantum advantage in phase estimation; whereas, introducing mode entanglement can reduce phase sensitivity. Using the first quantization description, we derive a formula for the QFI that shows explicitly how the Heisenberg scaling term depends on particle entanglement.
We theoretically investigate the quantum enhanced metrology using two-mode squeezed twin-Fock states and parity detection. Our results indicate that, for a given initial squeezing parameter, compared with the two-mode squeezed vacuum state, both phase sensitivity and resolution can be enhanced when the two-mode squeezed twin-Fock state is considered as an input state of a Mach–Zehnder interferometer. Within a constraint on the total photon number, although the two-mode squeezed vacuum state gives the better phase sensitivity when the phase shift φ to be estimated approaches to zero, the phase sensitivity offered by these non-Gaussian entangled Gaussian states is relatively stable with respect to the phase shift itself. When the phase shift slightly deviates from φ = 0, the phase sensitivity can be still enhanced by the two-mode squeezed twin-Fock state over a broad range of the total mean photon number where the phase uncertainty is still below the quantum standard noise limit. Finally, we numerically prove that the quantum Cramér–Rao bound can be approached with the parity detection.
We propose a self-guided quantum phase estimation protocol based on a squeezed vacuum state and a stochastic optimization algorithm. Our protocol dynamically aligns the measurement basis with the target phase, eliminating the need for prior knowledge of the squeezing parameter. We demonstrate that this approach successfully tracks the target phase across the entire [0, π) periodicity interval, achieving a measurement precision that surpasses the Standard Quantum Limit and approaches the Heisenberg Limit.