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マクロに異なる量子状態の重ね合わせを用いた量子計測

Mamiko Tatsuta

Published Mar 23, 2020• 0 citations
Publisher

Abstract

In this thesis, a general relationship between the sensitivity in quantum metrology and a superposition of macroscopically distinct states is shown.The goal of quantum metrology is to estimate a target parameter as precisely as possible by exploiting quantum systems.The uncertainty of the estimation is bound by the standard quantum limit for separable states, while quantum mechanics allows a better uncertainty that is bound by the Heisenberg limit.Both limits depend on the degrees of freedom N, e.g.number of spins, of the probe system, showing different scalings.How the uncertainty scales with N is an important factor for judging the utility of a given sensor.We show that all the generalized cat states, superposition of macroscopically distinct states characterized by an index named q, achieve the ultimate scaling when used in quantum metrology.Index q identifies superposition of macroscopically distinct states by extracting the quantum coherence between macroscopically distinct states.The index can be used for both pure and mixed states, and even a mixed state with a small purity can be identified as a generalized cat state.We show that in the ideal case where noise is absent, every generalized state achieves the Heisenberg scaling uncertainty.Furthermore, we consider a realistic independent dephasing that generally degrades the performance of a sensor and show that generalized cat states still beat the standard quantum limit, achieving the ultimate scaling available in the presence of such dephasing.As an example, we discuss a generalized cat state with an exponentially small purity.We propose a theoretical recipe to generate such a state from a thermal equilibrium state.We numerically examine how much the sensitivity will be if this generalized cat state is realized in a silicon substrate and show that the state is indeed advantageous compared to a separable state sensor.A realistic protocol to create the state using a superconducting flux qubit and nitrogen-vacancy ensembles in diamond is also analyzed, and we numerically observe the emergence of a metrologically useful state.Revealing that a wide variety of states can be metrologically useful, this work broadens the potential application of quantum metrology.

DOI
10.15083/0002004692

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In this thesis, a general relationship between the sensitivity in quantum metrology and a superposition of macroscopically distinct states is shown.The goal of quantum metrology is to estimate a target parameter as precisely as possible by exploiting quantum systems.The uncertainty of the estimation is bound by the standard quantum limit for separable states, while quantum mechanics allows a better uncertainty that is bound by the Heisenberg limit.Both limits depend on the degrees of freedom N, e.g.number of spins, of the probe system, showing different scalings.How the uncertainty scales with N is an important factor for judging the utility of a given sensor.We show that all the generalized cat states, superposition of macroscopically distinct states characterized by an index named q, achieve the ultimate scaling when used in quantum metrology.Index q identifies superposition of macroscopically distinct states by extracting the quantum coherence between macroscopically distinct states.The index can be used for both pure and mixed states, and even a mixed state with a small purity can be identified as a generalized cat state.We show that in the ideal case where noise is absent, every generalized state achieves the Heisenberg scaling uncertainty.Furthermore, we consider a realistic independent dephasing that generally degrades the performance of a sensor and show that generalized cat states still beat the standard quantum limit, achieving the ultimate scaling available in the presence of such dephasing.As an example, we discuss a generalized cat state with an exponentially small purity.We propose a theoretical recipe to generate such a state from a thermal equilibrium state.We numerically examine how much the sensitivity will be if this generalized cat state is realized in a silicon substrate and show that the state is indeed advantageous compared to a separable state sensor.A realistic protocol to create the state using a superconducting flux qubit and nitrogen-vacancy ensembles in diamond is also analyzed, and we numerically observe the emergence of a metrologically useful state.Revealing that a wide variety of states can be metrologically useful, this work broadens the potential application of quantum metrology.
We show a general relationship between a superposition of macroscopically distinct states and sensitivity in quantum metrology. Generalized cat states are defined by using an index which extracts the coherence between macroscopically distinct states, and a wide variety of states, including a classical mixture of an exponentially large number of states, has been identified as the generalized cat state with this criterion. We find that, if we use the generalized cat states for magnetic field sensing without noise, we achieve the Heisenberg limited sensitivity. Moreover, we even show that sensitivity of generalized cat states achieves the ultimate scaling sensitivity beyond the standard quantum limit under the effect of dephasing. As an example, we investigate the sensitivity of a generalized cat state that is attainable through a single global manipulation on a thermal equilibrium state and find an improvement of a few orders of magnitude from the previous sensors. Clarifying a wide class that includes such a peculiar state as metrologically useful, our results significantly broaden the potential of quantum metrology.
We show a general relationship between a superposition of macroscopically distinct states and sensitivity in quantum metrology. Generalized cat states are defined by using an index which extracts the coherence between macroscopically distinct states, and a wide variety of states, including a classical mixture of an exponentially large number of states, has been identified as the generalized cat state with this criterion. We find that if we use the generalized cat states for magnetic field sensing without noise, the sensitivity achieves the Heisenberg scaling. More importantly, we even show that sensitivity of generalized cat states achieves the ultimate scaling sensitivity beyond the standard quantum limit under the effect of dephasing. As an example, we investigate the sensitivity of a generalized cat state that is attainable through a single global manipulation on a thermal equilibrium state and find an improvement of a few orders of magnitude from the previous sensors. Clarifying a wide class that includes such a peculiar state as metrologically useful, our results significantly broaden the potential of quantum metrology.
Sensitivity in metrology without entanglement is limited by the standard quantum limit (SQL). Recent studies have found that the Heisenberg-limited scaling, the ultimate sensitivity in quantum metrology, can be achieved by generalized cat states, which are characterized by an index that indicates coherence among macroscopically distinct states and are associated with additive observables. Although generalized cat states include diverse states, encompassing classical mixtures of exponentially large numbers of states, the preparation of large generalized cat states has not been demonstrated yet. Here we characterize SQL-beating catlike states using the index qqq indicating macroscopic coherence and prove that any state with q>1.5q>1.5q>1.5 has a potential to surpass the SQL when used as a sensor. We propose a protocol to generate them through repetitive measurements on a quantum spin system of NNN spins, which we call a spin ensemble. Starting from a thermal equilibrium state of the spin ensemble, we demonstrate that we can increase the coherence among the spin ensemble via repetitive weak measurements of its total magnetization, which is indirectly measured through an ancillary qubit collectively coupled to the ensemble. Notably, our method for creating the SQL-beating catlike states requires no dynamical control over the spin ensemble. As a potential experimental realization, we discuss a hybrid system composed of a superconducting flux qubit and donor spins in silicon. Our results pave the way for the realization of entanglement-enhanced quantum metrology in state-of-the-art technology.
Making use of coherence and entanglement as metrological quantum resources allows us to improve the measurement precision from the shot-noise or quantum limit to the Heisenberg limit. Quantum metrology then relies on the availability of quantum engineered systems that involve controllable quantum degrees of freedom which are sensitive to the measured quantity. Sensors operating in the qubit mode and exploiting their coherence in a phase-sensitive measurement have been shown to approach the Heisenberg scaling in precision. Here, we show that this result can be further improved by operating the quantum sensor in the qudit mode, i.e., by exploiting ddd rather than two levels. Specifically, we describe the metrological algorithm for using a superconducting transmon device operating in a qutrit mode as a magnetometer. The algorithm is based on the base-3 semiquantum Fourier transformation and enhances the quantum theoretical performance of the sensor by a factor of 2. Even more, the practical gain of our qutrit implementation is found in a reduction of the number of iteration steps of the quantum Fourier transformation by the factor $ln(2)/ln(3)\ensuremath{\approx}0.63$ compared to the qubit mode. We show that a two-tone capacitively coupled radio-frequency signal is sufficient for implementation of the algorithm.
The Heisenberg limit is the superior precision available by entanglement sensors. However, entanglementis fragile against dephasing, and there is no known quantum metrology protocol that can achieve Heisenberg limited sensitivity with the presence of independent dephasing. Here, we show that the Heisenberg limit is attainable under the effect of independent dephasing under conditions where the probe qubits decohere due to both target fields and local environments. To detect the target fields, we exploit the entanglement properties to decay much faster than the classical states due to collective noise while most of the previous schemes use a coherent phase shift from the target fields. Actually, if the temporally fluctuating target fields behave as Markovian collective dephasing, we can estimate the collective dephasing rate with a sensitivity at the Heisenberg limit under the effect of independent dephasing. Our work opens the possibility for robust Heisenberg-limited metrology.
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the estimation error. Here we derive a formula for rigorously evaluating an upper bound for the estimation error in a general setting of quantum metrology with arbitrary finite data sets. Unlike in the standard approach, where lower bounds for the error are evaluated in an ideal setting with almost infinite data, our method rigorously guarantees the estimation precision in realistic settings with finite data. We also prove that our upper bound shows the Heisenberg limit scaling whenever the linearized uncertainty, which is a popular benchmark in the standard approach, shows it. As an example, we apply our result to a Ramsey interferometer, and numerically show that the upper bound can exhibit the quantum enhancement of precision for finite data.