Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2611.04263

Information-Geometric Representation of Upper Bounds on Fluctuation Growth in Open Quantum Systems

Newshaw Bahreyni·Paul M. Alsing
View original source ↗Read source document ↗Export metadata ↓

Abstract

Building on our earlier results for closed quantum systems, we investigate the dynamical evolution of quantum fluctuations and their connections to Fisher information and the quantum operations describing open-system dynamics. Starting from a general expression for the time derivative of an observable's uncertainty, we derive an alternative upper bound on fluctuation growth in an open quantum system using the Cauchy-Schwarz inequality. The resulting bound separates contributions from the evolution of the quantum state and the explicit time dependence of the observable, reducing to a known result for closed-system dynamics. We then establish a connection between fluctuation dynamics and quantum Fisher information by decomposing the density operator and the symmetric logarithmic derivative (SLD) into coherent and incoherent contributions, which leads to a bound relating the evolution of observable uncertainty to the coherent and incoherent components of the Fisher information, providing an information-geometric interpretation of fluctuation growth. To connect fluctuation dynamics with quantum operations governing open-system evolutions, we derive the time evolution of the eigenvalues of the density operator in terms of Kraus operators. Using the infinitesimal-time relation between Kraus and Lindblad operators, we obtain a corresponding expression for the eigenvalue dynamics in terms of Lindblad operators. This formulation directly relates changes in the density operator eigenvalues to the quantum processes acting on the system. We then study the results using some examples. Our results provide a framework connecting observable fluctuation growth, Fisher information, and the Kraus and Lindblad descriptions of quantum evolution, offering a route toward understanding how specific quantum channels influence the information and fluctuations available in an evolving quantum system.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Newshaw Bahreyni, Paul M. Alsing. 2026-11-03. Information-Geometric Representation of Upper Bounds on Fluctuation Growth in Open Quantum Systems. https://arxiv.org/abs/2611.04263

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Everlasting secure key agreement from a quantum computational hybrid security model

We introduce the Quantum Computational Timelock (QCT) model, combining time-lock encryption with a quantitative noisy-quantum-storage assumption. Time-lock encryption gives Bob immediate access to the encoding seed and gives Eve the same final information as access to that seed only after a protected interval. Eve may then process her retained information without computational restriction. We state this delayed-access encryption assumption explicitly and construct MUB-QCT from a complete set of mutually unbiased bases in dimension $d$ and an affine pair-wise independent permutation family. For single-copy encoding, every seed-independent immediate measurement has trace-distance advantage at most $1/(2\sqrt{d+1})$ and mutual information at most $1/(d+1)$. Effective residual storage at diamond distance at most $δ$ from replacement adds at most $δ$ to the individual-attack distinguishing bound. Under i.i.d. individual attacks and entropy-preserving acceptance, we obtain an asymptotic key-rate bound and formulate final-key secrecy in composable trace distance. For $m$ independently randomized signals sharing one bit and seed, the optimal leakage under non-adaptive product measurements is $\min\{1,m/(d+1)\}$, allowing a linear-in-$d$ detection enhancement in that attack model. We also construct a seed-independent joint measurement that recovers the bit after disclosure with error at most $\varepsilon$ from $O(\log d+\log(1/\varepsilon))$ signals, retaining only classical information after measurement. This gives a quantitative separation between product and joint measurements. Bob uses two logical detection outcomes independently of $d$.

quant-ph↗
arXiv2026

Linear optics and the problem of Bell-like state discrimination

A linear optics-based scheme to implement various quantum information processing tasks is of paramount importance due to its ease of implementation and low noise. Many information-theoretic tasks depend on the successful discrimination of Bell states. A no-go theorem states that it is not possible to perfectly discriminate among the four Bell states when the measurement apparatus is restricted to linear optical elements. The success probability is only $50\%$. Using extra resources such as hyperentanglement, ancillary entanglement, and even a minimum amount of non-linearity, complete Bell-state discrimination can be achieved. The success probability for Bell-like state discrimination is only $25\%$. Bell-like states are non-maximally entangled two-qubit states that resemble Bell states in structure but have unequal Schmidt coefficients. We find that this can be boosted to $50\%$ using hyperentanglement, where extra ancillary degrees of freedom (DOF) of photons, such as polarization, momentum, or OAM, are also entangled along with the system DOF. This contrasts with Bell-state discrimination, where $100\%$ can be achieved. Furthermore, we find that using correlations in the photons' arrival times, all four Bell states can be distinguished with $100\%$ success probability, while for Bell-like state discrimination, it increases only to $37.5\%$ from $25\%$. We observe a similar contrast when using ancillary entangled photons. While the success probability for discriminating all four Bell states increases as $1-\frac{1}{2^N}$, where $N$ is the number of ancillary photon pairs, for Bell-like states, it depends on the state parameters and can be less than $25\%$ in some cases. Also, adding further ancillary photons decreases the success probability. We then show that using non-linear gadgets, namely SFG, $100\%$ success probability can be achieved even for Bell-like state discrimination.

quant-ph↗
arXiv2026

Memory-Augmented Hybrid Quantum Reservoir Computing

Reservoir computing (RC) is an effective method for predicting chaotic systems by using a high-dimensional dynamic reservoir with fixed internal weights, while keeping the learning phase linear, which simplifies training and reduces computational complexity compared to fully trained recurrent neural networks (RNNs). Quantum reservoir computing (QRC) uses the exponential growth of Hilbert spaces in quantum systems, allowing for greater information processing, memory capacity, and computational power. However, the original QRC proposal requires coherent injection of inputs multiple times, complicating practical implementation. We present a hybrid quantum-classical approach that implements memory through classical post-processing of quantum measurements. This approach avoids the need for multiple coherent input injections and is evaluated on benchmark tasks, including the chaotic Mackey-Glass time series prediction. We tested our model on two physical platforms: a fully connected Ising model and a Rydberg atom array. The optimized model demonstrates promising predictive capabilities, achieving a higher number of steps compared to previously reported approaches.

quant-ph↗