Bosonic Quantum Conditional Mutual Information and Bose-Einstein Condensation

Anupam Ghosh

Home/Archive/arXiv

arXiv · 2610.16626

Bosonic Quantum Conditional Mutual Information and Bose-Einstein Condensation

Anupam Ghosh

View original source ↗Read source document ↗Export metadata ↓

Abstract

This article aims to introduce the bosonic asymmetric quantum conditional mutual information (QCMI), $I_{B}(A; B|C)$, as a rigorously defined information-theoretic quantity for continuous-variable (bosonic) systems. After defining $I_{B}(A; B|C)$ through quantum instruments on infinite-dimensional Fock spaces, we prove that Bose-Einstein condensation (BEC) induces a logarithmic divergence $ I_{B}(A; B|C) \geq α\log_2 (N_{0}^C+1)$, which further establishes $I_{B}(A; B|C)$ as a quantum-information order parameter for BEC with power-law scaling near the critical point. We provide the complete five-step proof of this result, connecting measurement back-action, off-diagonal long-range order, and Jensen's inequality. In the condensed phase, the effective causal propagation velocity is set by the Bogoliubov sound speed $c_s$ in the long-wavelength limit, and vanishes continuously at the superfluid--Mott-insulator transition. Applications to composite bosons, the BEC--BCS crossover, and a quantum-gas-microscope measurement protocol are presented. Finally, we demonstrate how the reduced bosonic QCMI serves as a finite-size scaling probe analogous to the Binder cumulant.

Explore related subjects

quant-ph nlin.SI

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Anupam Ghosh. 2026-10-12. Bosonic Quantum Conditional Mutual Information and Bose-Einstein Condensation. https://arxiv.org/abs/2610.16626

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

KEEP EXPLORING

Related papers

arXiv2026

All you need is Trotter

The work here enables a cost scaling of $\tilde{O}\left( \frac{T ^{1+o(1)}\,{\rm log}^2 (1/ε)}{\varepsilon}\right)$ and maximum depth $\tilde{O}\left( \frac{T^{1+o(1)}\,{\rm log} (1/ε)}{\varepsilon}\right)$ for estimating observables after some Hamiltonian evolution $e^{i H T}$ using no extra block-encoding qubits, where $ε$ is the algorithmic error of the target Hamiltonian evolution and $\varepsilon$ is the statistical error from the observable estimation. Throughout, $\tilde{O}$ suppresses factors that are doubly logarithmic in $1/ε$ (i.e. ${\rm polyloglog}(1/ε)$), which are subdominant to the displayed ${\rm polylog}(1/ε)$ factors. This is achieved through product formulas, stable interpolation (Chebyshev), and to calculate the needed fractional queries, cardinal sine interpolation is used. This is an improvement over similar work using interpolation methods which have a superlinear scaling of the form $5^p T^{1+1/p}$, where $p$ is the order of the product formula used and an improvement on required qubits over Quantum Signal Processing methods while maintaining scaling with ${\rm polylog}{1/ε}$. This is accomplished through an optimized and variable (with $T$) order $p$. The slightly better $\log^2(1/ε)$ compared to $\log^3(1/ε)$ comes from the use of cardinal sine interpolation compared to other methods using Chebyshev interpolation and product formulas. The work presented here also provides an alternative to Quantum Signal Processing techniques to calculate observables or amplitudes after a fractional query evolution with a cost $O(T\log{1/ε})$ through this cardinal sine interpolation.

quant-ph↗

arXiv2026

Noncontextuality inequalities for prepare-transform-measure scenarios

We provide the first systematic technique for deriving witnesses of contextuality in prepare-transform-measure scenarios. More specifically, we show how linear quantifier elimination can be used to compute a polytope of correlations consistent with generalized noncontextuality in such scenarios. This polytope is specified as a set of noncontextuality inequalities that are necessary and sufficient conditions for observed data in the scenario to admit of a classical explanation relative to any linear operational identities, if one ignores some constraints from diagram preservation. While including these latter constraints generally leads to tighter inequalities, it seems that nonlinear quantifier elimination would be required to systematically include them. We also provide a linear program which can certify the nonclassicality of a set of numerical data arising in a prepare-transform-measure experiment. We apply our results to get a robust noncontextuality inequality for transformations that can be violated within the stabilizer subtheory. Finally, we give a simple algorithm for computing all the linear operational identities holding among a given set of states, of transformations, or of measurements.

quant-ph↗

arXiv2026

A General Framework for Gradient-Based Optimization of Superconducting Quantum Circuits using Qubit Discovery as a Case Study

Engineering the Hamiltonian of a quantum system is fundamental to the design of quantum systems. Automating Hamiltonian design through gradient-based optimization can dramatically accelerate this process. However, computing the gradients of eigenvalues and eigenvectors of a Hamiltonian--a large, sparse matrix--relative to system properties poses a significant challenge, especially for arbitrary systems. Superconducting quantum circuits offer substantial flexibility in Hamiltonian design, making them an ideal platform for this task. In this work, we present a comprehensive framework for the gradient-based optimization of superconducting quantum circuits, leveraging the SQcircuit software package. By addressing the challenge of calculating the gradient of the eigensystem for large, sparse Hamiltonians and integrating automatic differentiation within SQcircuit, our framework enables efficient and precise computation of gradients for various circuit properties or custom-defined metrics, streamlining the optimization process. We apply this framework to the qubit discovery problem, demonstrating its effectiveness in identifying qubit designs with superior performance metrics. The optimized circuits show improvements in a heuristic measure of gate count, upper bounds on gate speed, decoherence time, and resilience to noise and fabrication errors compared to existing qubits. While this methodology is showcased through qubit optimization and discovery, it is versatile and can be extended to tackle other optimization challenges in superconducting quantum hardware design.

quant-ph↗