Abstract Fisher information is a central diagnostic in quantum readout, sensing, and open-system dynamics, but a positive Fisher derivative is not by itself a non-Markovianity witness. This paper does not introduce a new universal monotonicity measure. Instead, it establishes an encoding-aware diagnostic rule for deciding when Fisher growth can be interpreted as information backflow and when it should be read as ordinary parameter imprinting or measurement readability. The rule separates three operational layers: input-encoded optimized Fisher geometry, channel-parameter Fisher information, and fixed-readout Fisher information. For input-encoded parameters propagated by parameter-independent CP-divisible dynamics, optimized quantum Fisher information has the expected Lyapunov contraction interpretation; a revival is therefore a genuine backflow candidate. For channel-encoded parameters, Fisher information can grow even under a Markovian semigroup because the dynamics progressively writes the process parameter into the output state. A calibrated binary readout makes the measurement layer explicit. Dephasing, amplitude-damping, and two-qubit X-state examples then show the quantum-information payoff: Fisher readability, coherence, concurrence, and complementarity coincide in special calibrated sectors but separate in general. In particular, amplitude-damped X-state slices contain regions with vanishing concurrence but nonzero phase Fisher readability. The resulting criterion is an interpretation rule, not a replacement for established non-Markovianity witnesses: Fisher growth becomes causally meaningful only after the encoding, dynamical map, and readout layer have been fixed.
Abstract Fisher information is a central diagnostic in quantum readout, sensing, and open-system dynamics, but a positive Fisher derivative is not by itself a non-Markovianity witness. This paper does not introduce a new universal monotonicity measure. Instead, it establishes an encoding-aware diagnostic rule for deciding when Fisher growth can be interpreted as information backflow and when it should be read as ordinary parameter imprinting or measurement readability. The rule separates three operational layers: input-encoded optimized Fisher geometry, channel-parameter Fisher information, and fixed-readout Fisher information. For input-encoded parameters propagated by parameter-independent CP-divisible dynamics, optimized quantum Fisher information has the expected Lyapunov contraction interpretation; a revival is therefore a genuine backflow candidate. For channel-encoded parameters, Fisher information can grow even under a Markovian semigroup because the dynamics progressively writes the process parameter into the output state. A calibrated binary readout makes the measurement layer explicit. Dephasing, amplitude-damping, and two-qubit X-state examples then show the quantum-information payoff: Fisher readability, coherence, concurrence, and complementarity coincide in special calibrated sectors but separate in general. In particular, amplitude-damped X-state slices contain regions with vanishing concurrence but nonzero phase Fisher readability. The resulting criterion is an interpretation rule, not a replacement for established non-Markovianity witnesses: Fisher growth becomes causally meaningful only after the encoding, dynamical map, and readout layer have been fixed.
A non-isolated physical system typically loses information to its environment, and when such loss is irreversible the evolution is said to be Markovian. Non-Markovian effects are studied by monitoring how information quantifiers, such as the distance between physical states, evolve in time. Here we show that the Fisher information metric emerges as a natural object to study in this context; we fully characterize the relation between its contractivity properties and Markovianity, both from the mathematical and operational point of view. We prove, for classical dynamics, that Markovianity is equivalent to the monotonous contraction of the Fisher metric at all points of the set of states. At the same time, operational witnesses of non-Markovianity based on the dilation of the Fisher distance cannot, in general, detect all non-Markovian evolutions, unless specific physical postprocessing is applied to the dynamics. Finally, we show for the first time that non-Markovian dilations of Fisher distance between states at any time correspond to backflow of information about the initial state of the dynamics at time 0, via Bayesian retrodiction. All the presented results can be lifted to the case of quantum dynamics by considering the standard CP-divisibility framework.
Non-Markovian evolution in open quantum systems is often characterized in terms of the backflow of information from environment to system and is thus an important facet in investigating the performance and robustness of quantum information protocols. In this work, we explore non-Markovianity through the breakdown of monotonicity of a metrological figure of merit, called the quantum interferometric power, which is based on the minimal quantum Fisher information obtained by local unitary evolution of one part of the system, and can be interpreted as a quantifier of quantum correlations beyond entanglement. We investigate our proposed non-Markovianity indicator in two relevant examples. First, we consider the action of a single-party dephasing channel on a maximally entangled two-qubit state, by applying the Jamio\l{}kowski-Choi isomorphism. We observe that the proposed measure is consistent with established non-Markovianity quantifiers defined using other approaches based on dynamical divisibility, distinguishability, and breakdown of monotonicity for the quantum mutual information. Further, we consider the dynamics of two-qubit Werner states, under the action of a local, single-party amplitude damping channel, and observe that the nonmonotonic evolution of the quantum interferometric power is more robust than the corresponding one for entanglement in capturing the backflow of quantum information associated with the non-Markovian process. Implications for the role of non-Markovianity in quantum metrology and possible extensions to continuous variable systems are discussed.
Abstract Quantum Fisher information quantifies the sensitivity encoded in a parameter-dependent quantum state, whereas the performance of a practical sensor is limited by the information that survives the physical channel and can be extracted by the available receiver. We introduce an accessible Fisher-information framework based on a physically admissible family of measurements and use it to separate state-level sensitivity, channel degradation, and receiver limitations. The framework is applied to Ramsey and NOON interferometry, squeezed-state displacement sensing, two-level thermometry, and multiparameter qubit sensing. We show that resource normalization, finite visibility, readout errors, measurement rank, shot allocation, calibration uncertainty, and nuisance parameters can substantially modify the experimentally available advantage. For squeezed-state sensing, homodyne-axis misalignment produces a finite optimal squeezing, while bounded calibration uncertainty leads to a robust operating rule. In the pure-loss model considered here, attenuation reduces the attainable information without shifting this optimum. The results provide practical design rules that connect quantum-enhanced state preparation with realistic measurement constraints and experimentally extractable sensing performance.
We introduce a quantum Fisher information based measurement-induced nonlocality (QFI-MIN), which quantifies the maximal statistical distinguishability induced by locally invariant unitary dynamics. The proposed measure inherits desirable properties including positivity, local unitary invariance, monotonicity under local operations, and immunity to the local ancilla problem. Analytical expressions are obtained for pure states, arbitrary two-qubit states, and two-qubit X states, revealing a direct connection with entanglement for pure systems. We further establish clear operational interpretations of QFI-MIN in quantum parameter estimation, local channel discrimination, and correlation-assisted communication. Its behavior under amplitude damping, depolarizing, and generalized amplitude damping channels demonstrates robustness against environmental noise. The proposed framework provides a physically consistent and operationally meaningful quantifier of quantum correlations, linking nonlocality, quantum metrology, and quantum information processing
Protected and peripheral Liouvillian modes identify which components of an open quantum system can survive, but they do not determine whether those components are readable by a specified detector, syndrome channel, or feedback record. This preprint introduces a readout-rate operator for finite-dimensional semistable quantum dynamics. The operator isolates the coefficient of the linear large-window growth of the finite-time readout Gramian and provides a detector-relative criterion for persistent readout visibility. For semisimple neutral spectrum, the readout-rate operator is expressed in terms of the Riesz projectors onto the neutral frequency blocks and the experimentally specified readout map. Thus the Liouvillian spectrum identifies persistent coordinates, whereas the readout-rate operator identifies the subset of those coordinates that produces a persistent measurement record. Under additive Gaussian readout noise, the same operator becomes the classical Fisher-information-rate matrix for estimating the persistent coordinate from the specified record. The construction is intended as a diagnostic and design principle for decoherence-free subspaces, quantum memories, syndrome records, feedback architectures, and stable auxiliary transduction paths in open quantum systems. It is detector-relative and does not claim optimization over all possible quantum measurements. The main theorem applies to finite-dimensional semistable generators with semisimple neutral spectrum. Keywords: open quantum systems; semistable Liouvillian dynamics; quantum readout; observability Gramian; decoherence-free subspaces; Fisher information; quantum feedback; syndrome extraction; Riesz projectors.
This technical note introduces clockability as an operational criterion for assessing the validity of time-local descriptions in open quantum systems. While non-Markovian dynamics are commonly characterized through information backflow or violations of CP-divisibility, the structural conditions under which a temporal description remains operationally meaningful are rarely made explicit. This work reframes non-Markovianity not as a dynamical anomaly, but as a signal of local clockability breakdown: the failure of the environment to function as a stable register of persistent and locally accessible traces. Within this framework, CP-divisibility emerges as a sufficient condition for local clockability, whereas its violation marks the loss of applicability of time-local master equations rather than a failure of quantum dynamics itself. The note clarifies the relationship between divisibility-based and information-theoretic measures of non-Markovianity and motivates a hierarchical domain-of-validity analysis for temporal descriptions. No new physical mechanisms or mathematical formalisms are introduced. Instead, the work provides a diagnostic, information-theoretic perspective on when time-local representations (e.g., GKSL forms) are structurally justified, and when dynamical descriptions should be interpreted as non-local, history-dependent responses. This contribution is intended as a conceptual and methodological clarification relevant to quantum information theory, open quantum systems, and the operational foundations of time.