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arXiv:2601.00259

Dynamical onset of quasiprobability negativity in quantum many-body systems

Rohit Kumar Shukla, Amikam Levy

quant-phSubmitted Jan 1, 2026• Announced Jan 2, 2026• 0 citations• Revised Aug 20, 2026 (v2)
v1 · Jan 1, 2026v2 · Aug 20, 2026
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Abstract

Time-dependent quasiprobability distributions provide a quasiprobabilistic description of sequential measurement statistics generated by quantum dynamics, and can reveal nonclassical features with no classical probabilistic counterpart. Yet the dynamical emergence of their negativity in many-body systems remains largely unexplored. We introduce the \emph{first-time negativity} (FTN) of the Margenau-Hill quasiprobability as a dynamical indicator of when local measurement sequences in an interacting quantum system begin to exhibit genuinely nonclassical behavior. Using the Ising chain, we show that FTN discriminates clearly between interaction-dominated and field-dominated regimes, is systematically reshaped by temperature, and responds sensitively to the breaking of integrability. For spatially separated measurements, FTN appears abruptly near the interaction-field crossover, while measurements at opposite boundaries exhibit a distinct weak-field branch whose onset time grows with chain length and is consistent with ballistic propagation across the system. We further compare the numerical onset of negativity with a recently proposed quantum speed limit (QSL) for quasiprobabilities, which provides a geometric benchmark for the observed dynamics. Our results identify FTN as a practical and experimentally accessible probe of the real-time onset of quasiprobability negativity and contextual sequential measurement statistics, directly suited to current platforms capable of sequential weak and strong measurements.

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11+7 pages, 3+4 figures

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Time-dependent quasiprobability distributions provide a quasiprobabilistic description of sequential measurement statistics generated by quantum dynamics, and can reveal nonclassical features with no classical probabilistic counterpart. Yet the dynamical emergence of their negativity in many-body systems remains largely unexplored. We introduce the \emph{first-time negativity} (FTN) of the Margenau-Hill quasiprobability as a dynamical indicator of when local measurement sequences in an interacting quantum system begin to exhibit genuinely nonclassical behavior. Using the Ising chain, we show that FTN discriminates clearly between interaction-dominated and field-dominated regimes, is systematically reshaped by temperature, and responds sensitively to the breaking of integrability. For spatially separated measurements, FTN appears abruptly near the interaction-field crossover, while measurements at opposite boundaries exhibit a distinct weak-field branch whose onset time grows with chain length and is consistent with ballistic propagation across the system. We further compare the numerical onset of negativity with a recently proposed quantum speed limit (QSL) for quasiprobabilities, which provides a geometric benchmark for the observed dynamics. Our results identify FTN as a practical and experimentally accessible probe of the real-time onset of quasiprobability negativity and contextual sequential measurement statistics, directly suited to current platforms capable of sequential weak and strong measurements.
Abstract Time-dependent quasiprobability distributions provide a quasiprobabilistic description of sequential measurement statistics generated by quantum dynamics, and can reveal nonclassical features with no classical probabilistic counterpart. Yet the dynamical emergence of their negativity in many-body systems remains largely unexplored. We introduce the first-time negativity (FTN) of the Margenau–Hill quasiprobability as a dynamical indicator of when local measurement sequences in an interacting quantum system begin to exhibit genuinely nonclassical behavior. Using the Ising chain, we show that FTN discriminates clearly between interaction-dominated and field-dominated regimes, is systematically reshaped by temperature, and responds sensitively to the breaking of integrability. For spatially separated measurements, FTN appears abruptly near the interaction-field crossover, while measurements at opposite boundaries exhibit a distinct weak-field branch whose onset time grows with chain length and is consistent with ballistic propagation across the system. We further compare the numerical onset of negativity with a recently proposed quantum speed limit for quasiprobabilities, which provides a geometric benchmark for the observed dynamics. Our results identify FTN as a practical and experimentally accessible probe of the real-time onset of quasiprobability negativity and contextual sequential measurement statistics, directly suited to current platforms capable of sequential weak and strong measurements.
Quasiprobability distributions offer a useful way of describing nonclassical features of quantum systems through their departure from classical probability theory. In this work, we investigate the quantification of nonclassicality associated with the Margenau--Hill quasiprobability (MHQ) distribution using its moments, without requiring reconstruction of the full distribution. First we introduce the logarithmic MHQ negativity as a quantifier of nonclassicality, and then derive a hierarchy of rigorous lower bounds in terms of low-order moments. Within the resulting hierarchy, the fourth-moment bound is the strongest among the bounds based on even moments. For qubits, we further derive a tight upper bound on the exact MHQ negativity and identify the corresponding extremal state. We also obtain an optimal positivity threshold based on the fourth moment for arbitrary pairs of qubit observables. Finally, we show that the relevant moments admit exact multicopy representations, providing a route to their estimation using interferometry or classical shadow techniques. Our results establish a moment-based framework for extracting quantitative information about MHQ negativity from a finite set of low-order observables.
We derive a quantum extension of the thermodynamic uncertainty relation where dynamical fluctuations are quantified by the Terletsky-Margenau-Hill quasiprobability, a quantum generalization of the classical joint probability. The obtained inequality plays a complementary role to existing quantum thermodynamic uncertainty relations, focusing on observables' change rather than exchange of charges through jumps and respecting initial coherence. Quasiprobabilities show anomalous behaviors that are forbidden in classical systems, such as negativity; we reveal that negativity or a nonclassically enhanced escape rate is necessary to increase an output-to-dissipation ratio beyond classical limitations and show that the requirements are basis independent and stronger than quantum coherence. To illustrate these statements, we employ a model that can exhibit a dissipationless heat current, which would be prohibited in classical systems; we construct a state that has much coherence but does not lead to a dissipationless current due to the absence of anomalous behaviors in quasiprobabilities.
Quantum nondemolition measurements define a noninvasive protocol to extract information from a monitored quantum system. This protocol exploits an additional quantum system that is sequentially coupled to the system and eventually measured to reconstruct temporal correlations developed by the system. In reference to a given measurement observable, the protocol's outcomes are well described by a quasiprobability distribution, which can be negative. In this paper, we prove that the presence of negative regions in this distribution defined at three times is a necessary and sufficient condition for the violation of macrorealism. This approach falls within the category of sequential noninvasive measurability and automatically satisfies all no-signaling-in-time conditions at multiple times by design. We show that reconstructing the negativity is a much stronger condition than the violation of the Leggett-Garg inequalities, commonly used for the same task, as they may be satisfied even if the macrorealism is violated. Quantum nondemolition measurements provide a clear and operational tool to identify violations of macrorealism directly. Thus, our result could also be applied to the study of the quantum-to-classical transition and in all those fields where quantumness certification is desirable.
Abstract We discuss and experimentally demonstrate the role of quantum coherence in a sequence of two measurements collected at different times using weak measurements. For this purpose, we have realized a weak-sequential measurement protocol with photonic qubits, where the first measurement is carried out as a positive operator-valued measure, whereas the second one is a projective operation. We determine the quasiprobability distributions associated to this procedure using both the commensurate and the Margenau-Hill quasiprobabilities. By tuning the weak measurements, we obtain a quasidistribution that may or may not exhibit negative parts, depending on the suitability of a contextual model for describing the experiment. Our results show how quasidistributions may find application in inspecting quantum monitoring, when part of the initial quantum coherence needs to be preserved.
Negative probability values have been widely employed as an indicator of the nonclassicality of quantum systems. Known as a quasiprobability distribution, they are regarded as a useful tool that provides significant insight into the underlying fundamentals of quantum theory when compared to the classical statistics. However, in this approach, an operational interpretation of these negative values with respect to the definition of probability-the relative frequency of occurred event-is missing. An alternative approach is therefore considered where the quasiprobability operationally reveals the negativity of measured quantities. We here present an experimental realization of the operational quasiprobability, which consists of sequential measurements in time. To this end, we implement two sets of polarization measurements of single photons. We find that the measured negativity can be interpreted in the context of selecting measurements, and it reflects the nonclassical nature of photons. Our results suggest a new operational way to unravel the nonclassicality of photons in the context of measurement selection.