Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2604.28137

Weak-to-Strong Measurement Transition with Thermal Instabilities: From Anomalous Amplification to Metrological Sensitivity

Marcos V. S. Lima, Carlos H. S. Vieira, Irismar G. da Paz, Pedro R. Dieguez, Lucas S. Marinho

quant-phSubmitted Apr 30, 2026• Announced May 1, 2026• 0 citations• Revised Aug 24, 2026 (v2)
v1 · Apr 30, 2026v2 · Aug 24, 2026
arXivHTMLPDF

Abstract

Quantum measurement is physically realized through a finite dynamical interaction between a system and a measuring apparatus, giving rise to a continuous transition from weak to strong regimes. While this crossover is well understood under ideal conditions, the combined role of thermal instabilities and pre- and post-selection open dynamics has not been systematically addressed. Here, we develop a generalized open-system framework to analyze the weak-to-strong measurement transition in the simultaneous presence of environmental decoherence and thermal noise. We model the probe as a thermal Gaussian state, explicitly incorporating temperature-dependent fluctuations in the measuring device, and include open-system evolution of the measured system prior to post-selection. By deriving the apparatus's final state, we show that the measurement statistics are modified in a nontrivial, highly sensitive manner by the temperature regime of the system's thermal instabilities, the probe's thermal properties, and the particular choice of pre- and post-selection. This approach allows us to characterize how thermal effects reshape the weak-value condition, the anomalous amplification, and the resulting metrological sensitivity, demonstrating the protocol's practical utility for precision measurements across the full measurement crossover.

Related papers

Transition between weak and strong measurements in the presence of post-selection

Shogo Hanashiro, Holger F. Hofmann

In the weak measurement regime, post-selection can result in the observation of anomalous weak values, seemingly contradicting the eigenvalue statistics observed when the measurement interaction is strong. Here, we investigate the dependence of meter statistics on measurement strength in a post-selected measurement. We find that the meter statistics in the intermediate regime between weak and strong measurements is nearly independent of measurement strength and show that, in this regime, the system performs a measurement of momentum on the meter. Our results show that post-selection is extremely sensitive to the action of the meter on the system, highlighting the difference between the weak measurement regime where this back-action is negligible and the average meter position is a valid measurement result, and the intermediate regime where the meter statistics should not be misinterpreted as a measurement outcome. The transition between weak values and eigenvalues is facilitated by a reversal of the roles of the system and the meter, where the post-selection acts as a readout of information about the meter. The intermediate measurement regime thus reveals that the apparent contradictions between anomalous weak values and eigenvalues originate from the non-classical effects of back-action on the post-selected meter statistics.

quant-pharXiv:2609.04812•Sep 7, 2026•0 citations

Observation of the weak-to-strong transition of quantum measurement in trapped ions

Yiming Pan, Jie Zhang, Eliahu Cohen +3 more

Quantum measurement remains puzzling through the mist of their stormy history from the early birth of quantum mechanics to state-of-the-art quantum technologies. Here, we report the observation of measurement transition from weak to strong in a single trapped $40Ca^+$ ion system. By realizing a cat state of the ion's vibrational motion by pre- and post-selecting its internal electronic state, we observed the transition from weak value asymptotics to expectation value asymptotics. More precisely, the weak-to-strong measurement transition is characterized by a universal transition factor $\exp(-\Gamma^2/2)$, where $\Gamma$ is a dimensionless coupling parameter related to the system-apparatus interaction. This transition, which continuously connects Aharonov's weak measurement and von Neumann' strong projective measurement, is capable of opening new experimental possibilities for testing quantum foundations, as well as novel applications for computation in trapped ions and other physical systems.

•Oct 24, 2019•1 citation

Weak measurement amplification based on thermal noise effect

Gang Li, Tao Wang, He‐Shan Song

Abstract Most studies for postselected weak measurement focus on using the pure Gaussian state as a pointer, which can only give an amplification limit reaching the level of the ground state fluctuation. When the pointer is initialized in a thermal state, we find that the amplification limit after the postselection can reach the level of thermal fluctuation, indicating that the amplification effect achieving the level of thermal fluctuation is also increased with the temperature growth, and also that the amplification mechanism is different from that with pure Gaussian-state pointer. To illustrate these results, we propose two schemes to implement room temperature amplification of the mechanical oscillator’s displacement caused by a single photon in the optomechanical system. The two schemes both enhance the mechanical oscillator’s original displacement by nearly seven orders of magnitude, attaining sensitivity to displacements of ∼0.26 nm. Such amplification effect can be used to observe the impact of a single photon on a room temperature mechanical oscillator, which is hard to detect in traditional measurement.

arXiv:1507.00850•Journal of Physics B Atomic Molecular and Optical Physics•Jan 20, 2020•1 citation

Anomalous Weak Values Without Post-Selection

Alastair A. Abbott, Ralph Silva, Julian Wechs +2 more

A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an ``anomalous weak value'', is generally believed to be possible only when a non-trivial post-selection is performed, i.e., when only a particular subset of the data is considered. Here we show, however, that this is not the case in general: in scenarios in which several weak measurements are sequentially performed, an anomalous weak value can be obtained without post-selection, i.e., without discarding any data. We discuss several questions that this raises about the subtle relation between weak values and pointer positions for sequential weak measurements. Finally, we consider some implications of our results for the problem of distinguishing different causal structures.

arXiv:1805.09364•Quantum•Oct 14, 2019•13 citations

Optimal pre- and post-selections of weak measurements for precision parameter estimation

Xiong Liu, Xiaodong Qiu, Linguo Xie +4 more

Weak measurements, which offer a significant signal enhancement with pre- and post-selections, have proven to be powerful for precision metrology. However, the measured precision of the parameter of interest is always limited by the post-selection-induced probe loss, especially in the presence of technical noise. In this paper, we investigate the optimal pre- and post-selections of weak measurements for precision metrology in the presence of technical noise. While weak measurements apply more generally, we experimentally measure the spin splitting induced by the spin Hall effect of light (SHEL) to approach this issue. The highest measured precision of the spin splitting can be obtained with the post-selected state in the nonlinear intermediate regime. Surprisingly, the pre- and post-selections for the largest weak-value amplification are incapable of estimation of the spin splitting, since the amplified shift is independent of the spin splitting. Our results are not restricted to the SHEL and could be applied to other parameter estimations with weak measurements.

Journal of Applied Physics•May 28, 2017•5 citations

Precision metrology of weak measurement with thermal state pointer

Gang Li, Libo Chen, Tao Wang +2 more

Quantum metrology is being gradually studied for weak measurement systems. For weak measurement systems with thermal state pointer, we find that in the displacement space corresponding to imaginary weak values, the maximal QFI after successful postselection can attain the level of thermal fluctuations, without surpassing total QFI, and that QFI which increases with increasing temperature can constantly improve the measurement precision. These results are much better than that of weak measurement with pure state (i.e., Gaussian state) pointer. On the other hand, in Kerr nonlinear interaction systems with weak measurement, and by using thermal state pointer, we obtain in the phase space successful postselection and postselected measurements both achieve the Heisenberg limit of quantum metrology, and show weak measurement with thermal states only obtain classical Fisher information (CFI) which increases with increasing temperature and achieves classical enhanced scaling of N^2. Moreover, weak measurement with thermal states has an advantage over that with coherent states or mixed states of the light because generating these states with more large uncertainty are limited under the current technology, but thermal states with more large uncertainly are very easy to achieve with increasing temperature in nature, regardless of thermal states of the light or the matter.

arXiv:1508.05705•Aug 24, 2015•0 citations
Quantum measurement is physically realized through a finite dynamical interaction between a system and a measuring apparatus, giving rise to a continuous transition from weak to strong regimes. While this crossover is well understood under ideal conditions, the combined role of thermal instabilities and pre- and post-selection open dynamics has not been systematically addressed. Here, we develop a generalized open-system framework to analyze the weak-to-strong measurement transition in the simultaneous presence of environmental decoherence and thermal noise. We model the probe as a thermal Gaussian state, explicitly incorporating temperature-dependent fluctuations in the measuring device, and include open-system evolution of the measured system prior to post-selection. By deriving the apparatus's final state, we show that the measurement statistics are modified in a nontrivial, highly sensitive manner by the temperature regime of the system's thermal instabilities, the probe's thermal properties, and the particular choice of pre- and post-selection. This approach allows us to characterize how thermal effects reshape the weak-value condition, the anomalous amplification, and the resulting metrological sensitivity, demonstrating the protocol's practical utility for precision measurements across the full measurement crossover.
In the weak measurement regime, post-selection can result in the observation of anomalous weak values, seemingly contradicting the eigenvalue statistics observed when the measurement interaction is strong. Here, we investigate the dependence of meter statistics on measurement strength in a post-selected measurement. We find that the meter statistics in the intermediate regime between weak and strong measurements is nearly independent of measurement strength and show that, in this regime, the system performs a measurement of momentum on the meter. Our results show that post-selection is extremely sensitive to the action of the meter on the system, highlighting the difference between the weak measurement regime where this back-action is negligible and the average meter position is a valid measurement result, and the intermediate regime where the meter statistics should not be misinterpreted as a measurement outcome. The transition between weak values and eigenvalues is facilitated by a reversal of the roles of the system and the meter, where the post-selection acts as a readout of information about the meter. The intermediate measurement regime thus reveals that the apparent contradictions between anomalous weak values and eigenvalues originate from the non-classical effects of back-action on the post-selected meter statistics.
Quantum measurement remains puzzling through the mist of their stormy history from the early birth of quantum mechanics to state-of-the-art quantum technologies. Here, we report the observation of measurement transition from weak to strong in a single trapped 40Ca+40Ca^+40Ca+ ion system. By realizing a cat state of the ion's vibrational motion by pre- and post-selecting its internal electronic state, we observed the transition from weak value asymptotics to expectation value asymptotics. More precisely, the weak-to-strong measurement transition is characterized by a universal transition factor exp⁡(−Γ2/2)\exp(-\Gamma^2/2)exp(−Γ2/2), where Γ\GammaΓ is a dimensionless coupling parameter related to the system-apparatus interaction. This transition, which continuously connects Aharonov's weak measurement and von Neumann' strong projective measurement, is capable of opening new experimental possibilities for testing quantum foundations, as well as novel applications for computation in trapped ions and other physical systems.
Abstract Most studies for postselected weak measurement focus on using the pure Gaussian state as a pointer, which can only give an amplification limit reaching the level of the ground state fluctuation. When the pointer is initialized in a thermal state, we find that the amplification limit after the postselection can reach the level of thermal fluctuation, indicating that the amplification effect achieving the level of thermal fluctuation is also increased with the temperature growth, and also that the amplification mechanism is different from that with pure Gaussian-state pointer. To illustrate these results, we propose two schemes to implement room temperature amplification of the mechanical oscillator’s displacement caused by a single photon in the optomechanical system. The two schemes both enhance the mechanical oscillator’s original displacement by nearly seven orders of magnitude, attaining sensitivity to displacements of ∼0.26 nm. Such amplification effect can be used to observe the impact of a single photon on a room temperature mechanical oscillator, which is hard to detect in traditional measurement.
A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an ``anomalous weak value'', is generally believed to be possible only when a non-trivial post-selection is performed, i.e., when only a particular subset of the data is considered. Here we show, however, that this is not the case in general: in scenarios in which several weak measurements are sequentially performed, an anomalous weak value can be obtained without post-selection, i.e., without discarding any data. We discuss several questions that this raises about the subtle relation between weak values and pointer positions for sequential weak measurements. Finally, we consider some implications of our results for the problem of distinguishing different causal structures.
Weak measurements, which offer a significant signal enhancement with pre- and post-selections, have proven to be powerful for precision metrology. However, the measured precision of the parameter of interest is always limited by the post-selection-induced probe loss, especially in the presence of technical noise. In this paper, we investigate the optimal pre- and post-selections of weak measurements for precision metrology in the presence of technical noise. While weak measurements apply more generally, we experimentally measure the spin splitting induced by the spin Hall effect of light (SHEL) to approach this issue. The highest measured precision of the spin splitting can be obtained with the post-selected state in the nonlinear intermediate regime. Surprisingly, the pre- and post-selections for the largest weak-value amplification are incapable of estimation of the spin splitting, since the amplified shift is independent of the spin splitting. Our results are not restricted to the SHEL and could be applied to other parameter estimations with weak measurements.
Quantum metrology is being gradually studied for weak measurement systems. For weak measurement systems with thermal state pointer, we find that in the displacement space corresponding to imaginary weak values, the maximal QFI after successful postselection can attain the level of thermal fluctuations, without surpassing total QFI, and that QFI which increases with increasing temperature can constantly improve the measurement precision. These results are much better than that of weak measurement with pure state (i.e., Gaussian state) pointer. On the other hand, in Kerr nonlinear interaction systems with weak measurement, and by using thermal state pointer, we obtain in the phase space successful postselection and postselected measurements both achieve the Heisenberg limit of quantum metrology, and show weak measurement with thermal states only obtain classical Fisher information (CFI) which increases with increasing temperature and achieves classical enhanced scaling of N^2. Moreover, weak measurement with thermal states has an advantage over that with coherent states or mixed states of the light because generating these states with more large uncertainty are limited under the current technology, but thermal states with more large uncertainly are very easy to achieve with increasing temperature in nature, regardless of thermal states of the light or the matter.