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Probing and Harnessing Entanglement, Noise, and Dissipation across Quantum Metrology and Computing

Su Direkci

Published Sep 30, 2026• 0 citations
Publisher

Abstract

Modern quantum systems have two facets: they are resources we would like to harness, and they contain physics we would like to probe. This thesis studies both through several case studies in quantum metrology and computing, unified by the interplay between entanglement, noise, and dissipation. We first probe entanglement in an optomechanical setting, where a mechanical oscillator is continuously driven and monitored by a light field. Assuming Gaussian dynamics and arbitrary, possibly non-Markovian noise, we derive necessary and sufficient conditions for entanglement. For a vacuum input, the entangling-disentangling transition is set by the environmental noise alone and is independent of the optomechanical coupling strength. Furthermore, frequency-dependent squeezing cannot entangle a system that is separable when driven by vacuum. In the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO), we find that the present level of classical noise, dominated by low-frequency seismic noise, makes significant stationary entanglement unlikely. We then turn to quantum frequency estimation and present two schemes. The first scheme harnesses entanglement as a metrological resource, approaching Heisenberg-limited precision up to a constant factor using blocks of Greenberger-Horne-Zeilinger (GHZ) states prepared with logarithmic-depth circuits and read out with local, adaptive measurements. The second scheme addresses the precision-bandwidth trade-off through a weak-measurement Ramsey protocol that recovers the classical precision limit over an extended dynamic range. Finally, we harness dissipation by introducing the 0-n Fock qubit, a noise-biased bosonic encoding stabilized by frequency-selective dissipation, with bit-flip errors exponentially suppressed in n (the highest Fock level). Used as a bias-preserving ancilla for cat-qubit architectures, it enables noise-biased controlled-X gates and low logical error rates with experimentally realistic parameters. Together, these results explore the regimes where entanglement and quantum advantage can survive noise, and show how measurement and dissipation can be engineered to protect them.

DOI
10.7907/c2gy-xk87

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Modern quantum systems have two facets: they are resources we would like to harness, and they contain physics we would like to probe. This thesis studies both through several case studies in quantum metrology and computing, unified by the interplay between entanglement, noise, and dissipation. We first probe entanglement in an optomechanical setting, where a mechanical oscillator is continuously driven and monitored by a light field. Assuming Gaussian dynamics and arbitrary, possibly non-Markovian noise, we derive necessary and sufficient conditions for entanglement. For a vacuum input, the entangling-disentangling transition is set by the environmental noise alone and is independent of the optomechanical coupling strength. Furthermore, frequency-dependent squeezing cannot entangle a system that is separable when driven by vacuum. In the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO), we find that the present level of classical noise, dominated by low-frequency seismic noise, makes significant stationary entanglement unlikely. We then turn to quantum frequency estimation and present two schemes. The first scheme harnesses entanglement as a metrological resource, approaching Heisenberg-limited precision up to a constant factor using blocks of Greenberger-Horne-Zeilinger (GHZ) states prepared with logarithmic-depth circuits and read out with local, adaptive measurements. The second scheme addresses the precision-bandwidth trade-off through a weak-measurement Ramsey protocol that recovers the classical precision limit over an extended dynamic range. Finally, we harness dissipation by introducing the 0-n Fock qubit, a noise-biased bosonic encoding stabilized by frequency-selective dissipation, with bit-flip errors exponentially suppressed in n (the highest Fock level). Used as a bias-preserving ancilla for cat-qubit architectures, it enables noise-biased controlled-X gates and low logical error rates with experimentally realistic parameters. Together, these results explore the regimes where entanglement and quantum advantage can survive noise, and show how measurement and dissipation can be engineered to protect them.
Probing quantum entanglement with macroscopic objects allows us to test quantum mechanics in new regimes. One way to realize such behavior is to couple a macroscopic mechanical oscillator to a continuous light field via radiation pressure. In view of this, the system that is discussed comprises an optomechanical cavity driven by a coherent optical field in the unresolved sideband regime where we assume Gaussian states and dynamics. We develop a framework to quantify the amount of entanglement in the system numerically. Different from previous work, we treat non-Markovian noise and take into account both the continuous optical field and the cavity mode. We apply our framework to the case of the Advanced Laser Interferometer Gravitational-Wave Observatory and discuss the parameter regimes where entanglement exists, even in the presence of quantum and classical noises. Published by the American Physical Society 2024
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 metrology promises to surpass classical precision limits by leveraging quantum resources such as entanglement. Maximally entangled Greenberger-Horne-Zeilinger (GHZ) states are theoretically optimal probes for quantum metrology. However, they are fragile to environmental noise, severely limiting their practical utility. To overcome this limitation, we propose and experimentally realize a noise-adaptive quantum metrology scheme that autonomously identifies optimal probes without any prior information of the noise. This is achieved by combining a variational quantum circuit that optimizes available resources with an efficient strategy for evaluating the sensing performance. Using a seven-qubit nuclear spin sensor, we identify optimal probe states that achieve precision improvements up to 0.698 dB over GHZ states when sensing a fixed magnetic field. Furthermore, we show that the learned probe state exhibits cross-parameter robustness, maintaining superior performance over a broad range of magnetic field frequencies. The proposed scheme is model-free, hardware-efficient, and scalable, providing a practical route to noise-resilient quantum metrology on near-term quantum devices.
Quantum entanglement and coherence often allow for protocols that outperform classical ones in estimating a system’s parameter. When using infinite-dimensional probes (such as a bosonic mode), one could, in principle, obtain infinite precision in a finite time for both classical and quantum protocols, which makes it hard to quantify potential quantum advantage. However, such a situation is unphysical, as it would require infinite resources, so one needs to impose some additional constraint: typically the average energy employed by the probe is finite. Here we treat both energy and time as a resource, showing that, in the presence of noise, there is a nontrivial interplay between the average energy and the time devoted to the estimation. Our results are valid for the most general metrological schemes (e.g., adaptive schemes, which may involve entanglement with external ancillae or any kind of continuous measurement). We apply recently derived precision bounds for all parameters characterizing the paradigmatic case of a bosonic mode, subject to Lindbladian noise. We show how the time employed in the estimation should be partitioned in order to achieve the best possible precision. In most cases, the optimal performance may be obtained without the necessity of adaptivity or entanglement with ancilla. We compare results with classical strategies. Interestingly, for temperature estimation, applying a fast-prepare-and-measure protocol with Fock states provides better scaling with the number of photons than any classical strategy.
Noise-biased qubits have bit-flip errors that are exponentially suppressed relative to phase-flip errors, and offer a promising route toward fault-tolerant quantum computing. However, this bias can be compromised during gate operations with non-biased control qubits. To address this limitation, we propose a "0-n" Fock qubit architecture that maintains the noise bias by encoding information in the ground state and n-th excited state of a nonlinear multi-level system, such as a transmon. This encoding is achieved via a dissipative stabilization that acts as decay and gain for lower and upper intermediate levels, respectively. We first analytically demonstrate that bit-flip errors are exponentially suppressed with the number of levels. Then, we present a practical implementation using a multi-mode lossy filter to achieve the frequency-selective dissipation. Finally, we numerically demonstrate that bit-flip probabilities approaching 10−810^{-8}10−8 are achievable for controlled-X gates on cat qubits using the 0-n qubit as an ancilla with n≥9n \geq 9n≥9 (i.e. ten or more levels), for realistic experimental parameters. Building on this, we simulate syndrome extraction in a repetition code, achieving logical error rates in the megaquop regime with only a distance of d=9d=9d=9.
Quantum noise limits high-precision sensing, such as in gravitational wave detectors. Caves first proposed beating this shot-noise limit by injecting squeezed vacuum at the dark port of an interferometer. Frequency-dependent squeezing through a filter cavity now delivers broadband quantum noise reductions of up to 5.2 dB at Hanford and 6.1 dB at Livingston in the LIGO detectors' fourth observing run. Building on these advances, this thesis develops techniques for interferometric sensing under realistic loss and phase noise, spanning Gaussian state preparation, optomechanical readout and feedback control, and non-Gaussian state preparation. In Parts I and II, we work in the two-photon formalism, where states are Gaussian and dynamics are linear. In Part I, we present a waveguide squeezer as an alternative to the traditional bulk cavity-based source; it is single-pass, broadband, and compact, and its modularity opens a path to non-Gaussian state generation. We report the detection of squeezed light from waveguide sources at 1064 nm in the sub-MHz regime, and we phase-stabilize the squeezed vacuum with quantum noise locking. We also analyze the loss and phase-noise tolerance of Gaussian states. In Part II, we design a tabletop phase-sensitive optomechanical amplifier and analyze its performance in terms of cavity stability, control system, and noise budget. We then implement the locking scheme, including Pound-Drever-Hall locking of the cavity, and characterize the noise budget at the initial stage. We also propose using optomechanics for coherent feedback control, which could evade back-action and broaden the detection bandwidth of future gravitational wave detectors. In Part III, we turn to non-Gaussian states. Phase noise does not preserve Gaussianity, so the best input state under combined loss and phase noise need not be Gaussian. We numerically optimize the input state for displacement sensing over the (η,σϕ)(\eta, \sigma_\phi)(η,σϕ​) landscape, integrating the Lindblad master equation in a truncated Fock basis and computing the quantum Fisher information. Within the Gaussian sub-family, the optimizer returns a displaced squeezed state once phase noise is appreciable, rather than pure squeezed vacuum. Without the Gaussian restriction, the optimized states sort roughly into four classes (Fock-like, cubic-phase-like, discrete-rotational, and squeezed), each dominant in a different region of the parameter space. In the experimentally relevant region of 1% loss and 100 mrad phase noise, cat states outperform squeezed vacuum even with balanced homodyne readout, an improvement implementable in the near term. We also show that the non-Gaussian advantage persists at higher photon budgets, well above Nˉ=5\bar{N} = 5Nˉ=5. Together, these results show how state preparation, readout, and feedback choices trade off against realistic loss and phase noise, and identify the regimes where non-Gaussian states perform better.