On Lorentzian symmetries of quantum information

Quantum Physics [Submitted on 8 Apr 2026] On Lorentzian symmetries of quantum information James Fullwood, Vlatko Vedral, Edgar Guzmán-González A foundational result in relativistic quantum information theory due to Peres, Scudo, and Terno, is that von Neumann entropy is not Lorentz invariant. Motivated by the "It from Qubit" paradigm, here we show that Lorentzian symmetries of quantum information emerge naturally in a pre-spacetime setting, without any reference to external variables such as position or momentum. In particular, we derive the natural action of the restricted Lorentz group \text{SO}^+(1,3) on the internal degrees of freedom of a single qubit from a simple, information-theoretic principle we refer to as preservation of linear entropy. It is then shown that the Lorentz invariance of the linear entropy of a relativistic qubit is a special case of a much more general phenomenon, namely, that any spectral invariant of an operator we term the 'W-matrix' is an \text{SL}(2,\mathbb C)^{\otimes n} invariant scalar. Consequently, the linear n-partite quantum mutual information is shown to be an \text{SL}(2,\mathbb C)^{\otimes n} invariant for all n-qubit states. Finally, we show that the correlation function associated with a pair of qubits in the singlet state yields the Minkowski metric on the space of qubit observables, whose symmetry group is the full Lorentz group \text{SO}(1,3). In accordance with the "It from Qubit" paradigm, our results thus establish the natural emergence of relativistic spacetime structure from intrinsic properties of quantum information. Comments: 6 pages, no figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.07471 [quant-ph]   (or arXiv:2604.07471v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.07471 Focus to learn more Submission history From: Edgar Guzmán González [view email] [v1] Wed, 8 Apr 2026 18:10:27 UTC (14 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)