Every generalized cat state achieves the ultimate scaling sensitivity in quantum metrology

Measurement devices could benefit from entangled correlations to yield a measurement sensitivity approaching the physical Heisenberg limit. Building upon previous magnetometric work using pseudo-entangled spin states in solution-state NMR, we present two conceptual advancements to better prepare and interpret the pseudo-entanglement resource as well as the use of a 13-spin cat state to measure the local magnetic field with a sensitivity beyond the standard quantum limit.

Jul 9, 20092 citations

Every generalized cat state achieves the ultimate scaling sensitivity in quantum metrology

Mamiko Tatsuta, Yuichiro Matsuzaki, Akira Shimizu

Published Feb 5, 2019• 0 citations

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Quantum metrology with generalized cat states

Mamiko Tatsuta, Yuichiro Matsuzaki, Akira Shimizu

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.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.

arXiv:1902.01551Physical Review ASep 13, 201922 citations

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

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.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.

Mar 23, 20200 citations

Characterization and generation of a standard-quantum-limit–beating catlike state through repetitive measurements

Mamiko Tatsuta, Yuichiro Matsuzaki, Hiroki Kuji +2 more

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 $q$ indicating macroscopic coherence and prove that any state with $q>1.5$ 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 $N$ 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.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 $q$ indicating macroscopic coherence and prove that any state with $q>1.5$ 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 $N$ 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.

arXiv:2407.06829Physical Review AJan 12, 20260 citations

Heisenberg limited quantum metrology under the effect of dephasing

Yuichiro Matsuzaki, Simon C. Benjamin, Shojun Nakayama +2 more

Quantum sensors have the potential to outperform their classical counterparts. For classical sensing, the uncertainty of the estimation of the target fields decreases $1/\sqrt{T}$ with measurement time $T$ . On the other hand, by using quantum resources, one can decrease the uncertainty with time to $1/T$ - the Heisenberg limit. However as quantum states are susceptible to dephasing, it has been not clear whether one can achieve the Heisenberg limit for a measurement time scaling longer than the coherence time of those states. Here, we propose a scheme that estimates the amplitude of globally applied fields with Heisenberg limited sensitivity in principle for an arbitrary time scale under the effect of dephasing. We use one way quantum computing based teleportation between qubits to prevent the correlation between the quantum state and its local environment from increasing, and have shown that such a teleportation protocol can suppress the local dephasing while the information from the target fields keeps growing. Our methods has the potential to realize a quantum sensor with a sensitivity far beyond that of any classical sensors.Quantum sensors have the potential to outperform their classical counterparts. For classical sensing, the uncertainty of the estimation of the target fields decreases $1/\sqrt{T}$ with measurement time $T$. On the other hand, by using quantum resources, one can decrease the uncertainty with time to $1/T$ - the Heisenberg limit. However as quantum states are susceptible to dephasing, it has been not clear whether one can achieve the Heisenberg limit for a measurement time scaling longer than the coherence time of those states. Here, we propose a scheme that estimates the amplitude of globally applied fields with Heisenberg limited sensitivity in principle for an arbitrary time scale under the effect of dephasing. We use one way quantum computing based teleportation between qubits to prevent the correlation between the quantum state and its local environment from increasing, and have shown that such a teleportation protocol can suppress the local dephasing while the information from the target fields keeps growing. Our methods has the potential to realize a quantum sensor with a sensitivity far beyond that of any classical sensors.

Aug 4, 20170 citations

Global Precision Limits in Critical Quantum Metrology: From Cramér-Rao to Ziv-Zakai

Neng Zeng, Tao Liu, Yu-Ran Zhang

Critical quantum metrology with equilibrium states predicts quantum-enhanced sensitivity only in the vicinity of criticality, where large prior information about the parameter is required. By employing quantum Ziv-Zakai bounds, we derive a limit on the mean-square error in critical quantum metrology. For second-order quantum phase transitions, we show that the precision predicted by the Cramér-Rao bound offers no substantial improvement over the prior standard deviation. Thus, the critical quantum sensor's precision can only achieve a constant gain compared to the prior standard deviation, even without performing any measurement. We elucidate the fundamental limitation on the achievable precision in critical quantum metrology in the context of local sensing, even without considering state-preparation costs or noise. Thus, the super-Heisenberg-limited sensitivity at criticality arises from precise prior knowledge rather than a genuine gain due to criticality. Our work provides a practical framework for assessing critical quantum metrology and a routine for studying quantum sensing with many-body systems.Critical quantum metrology with equilibrium states predicts quantum-enhanced sensitivity only in the vicinity of criticality, where large prior information about the parameter is required. By employing quantum Ziv-Zakai bounds, we derive a limit on the mean-square error in critical quantum metrology. For second-order quantum phase transitions, we show that the precision predicted by the Cramér-Rao bound offers no substantial improvement over the prior standard deviation. Thus, the critical quantum sensor's precision can only achieve a constant gain compared to the prior standard deviation, even without performing any measurement. We elucidate the fundamental limitation on the achievable precision in critical quantum metrology in the context of local sensing, even without considering state-preparation costs or noise. Thus, the super-Heisenberg-limited sensitivity at criticality arises from precise prior knowledge rather than a genuine gain due to criticality. Our work provides a practical framework for assessing critical quantum metrology and a routine for studying quantum sensing with many-body systems.

quant-pharXiv:2607.08431Jul 10, 20260 citations

Magnetic field sensors using large cat states beyond the standard quantum limit

Stephanie Simmons, Jonathan A. Jones, Steven D. Karlen +2 more

Jul 9, 20092 citations

q

indicating macroscopic coherence and prove that any state with

q>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

N

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.

Quantum sensors have the potential to outperform their classical counterparts. For classical sensing, the uncertainty of the estimation of the target fields decreases

1/\sqrt{T}

with measurement time

T

. On the other hand, by using quantum resources, one can decrease the uncertainty with time to

1/T

- the Heisenberg limit. However as quantum states are susceptible to dephasing, it has been not clear whether one can achieve the Heisenberg limit for a measurement time scaling longer than the coherence time of those states. Here, we propose a scheme that estimates the amplitude of globally applied fields with Heisenberg limited sensitivity in principle for an arbitrary time scale under the effect of dephasing. We use one way quantum computing based teleportation between qubits to prevent the correlation between the quantum state and its local environment from increasing, and have shown that such a teleportation protocol can suppress the local dephasing while the information from the target fields keeps growing. Our methods has the potential to realize a quantum sensor with a sensitivity far beyond that of any classical sensors.