Two statements about lossy compression are often made as analogies rather than proved: that discarding information is “the same as” non-unitary evolution, and that the imaginary parameter of a critical partition function is “the same as” a dissipative flow. We make both precise. First, we show that an optimal lossy code induces a non-unitary evolution of its retained representation: the reduced dynamics is a completely-positive semigroup whose no-jump effective Hamiltonian is non-Hermitian, H_eff = H₀ − iμN̂, where N̂ counts the retained modes and μ is half the information-discard rate; the evolution is unitary if and only if the code is lossless, and the physical requirement that compression discards variance selects the amplitude-damping jump — which yields an imaginary chemical potential −iμN̂ — over dephasing, which would not. Second, we show by Wick rotation that this real-time loss is the imaginary chemical potential of a Euclidean partition function, i.e. a Yang-Lee setup: the discard rate is the Yang-Lee field, and the conserved charge becomes non-analytic at the Yang-Lee edge, driven by the compression loss. We then record an empirical corollary for learned representations: the leading value of the measured correlation exponent is a property of the measurement construction rather than of the data, so the informative quantity is the excess above it. Both results are reached with standard tools, but the identifications they establish — the discard rate of a compressor as an imaginary chemical potential, and as the imaginary field of a Yang-Lee edge — are, to our knowledge, new, and they replace two working analogies with proved statements.
Two statements about lossy compression are often made as analogies rather than proved: that discarding information is “the same as” non-unitary evolution, and that the imaginary parameter of a critical partition function is “the same as” a dissipative flow. We make both precise. First, we show that an optimal lossy code induces a non-unitary evolution of its retained representation: the reduced dynamics is a completely-positive semigroup whose no-jump effective Hamiltonian is non-Hermitian, H_eff = H₀ − iμN̂, where N̂ counts the retained modes and μ is half the information-discard rate; the evolution is unitary if and only if the code is lossless, and the physical requirement that compression discards variance selects the amplitude-damping jump — which yields an imaginary chemical potential −iμN̂ — over dephasing, which would not. Second, we show by Wick rotation that this real-time loss is the imaginary chemical potential of a Euclidean partition function, i.e. a Yang-Lee setup: the discard rate is the Yang-Lee field, and the conserved charge becomes non-analytic at the Yang-Lee edge, driven by the compression loss. We then record an empirical corollary for learned representations: the leading value of the measured correlation exponent is a property of the measurement construction rather than of the data, so the informative quantity is the excess above it. Both results are reached with standard tools, but the identifications they establish — the discard rate of a compressor as an imaginary chemical potential, and as the imaginary field of a Yang-Lee edge — are, to our knowledge, new, and they replace two working analogies with proved statements.
We show that the d+0-dimensional Yang-Lee theory describing classical Ising spins in an imaginary magnetic field can be realized, without post-selection, within a (d−1)+1 open quantum system whose dynamics consist of local unitaries and engineered dissipation. Competition between the coherent unitary and dissipative dynamics drives a transition wherein the time-dependence of a particular class of linear observables changes from damped oscillatory "underdamped" to purely exponential "overdamped" decay. Our construction relies on an extensive number of weak-symmetries of the Lindbladian fixed by the choice of observable but is otherwise exact. Consequently, we show that the dynamics are described by the non-Hermitian generator of the Yang-Lee transfer matrix, leading to an effective Yang-Lee theory defined on the spacetime history of the open system. By locally modifying the dynamics, we directly measure spin correlation functions of the Yang-Lee theory as well as a related "Loschmidt Echo" correlator which we detail. We explicitly show that the required dissipation channels can be obtained through local 2-qubit gates and discuss potential realization on near-term quantum simulator devices. Finally, we generalize our construction to embed arbitrary non-Hermitian Hamiltonians within an open quantum system under Lindbladian time-evolution without post-selection, drawing connections between unconditional open quantum dynamics, exceptional point physics, and non-unitary statistical mechanics.
Lee–Yang theory clearly demonstrates where the phase transition of many-body systems occurs and the asymptotic behavior near the phase transition using the partition function under complex parameters. The complex parameters make the direct investigation of Lee–Yang theory in practical systems challenging. Here we construct a non-Hermitian quantum system that can correspond to the one-dimensional Ising model with imaginary parameters through the equality of partition functions. By adjusting the non-Hermitian parameter, we successfully obtain the partition function under different imaginary magnetic fields and observe the Lee–Yang zeros. We also observe the critical behavior of free energy in vicinity of Lee–Yang zero that is consistent with theoretical prediction. Our work provides a protocol to study Lee–Yang zeros of the one-dimensional Ising model using a single-qubit non-Hermitian system.
We introduce time-dependent variational principles to study the non-unitary dynamics of open quantum many-body systems, including dynamics described by the full Lindblad master equation, the non-Hermitian dynamics corresponding to the no-click limit of the fully post-selected quantum trajectories, and the dynamics described by a hybrid Lindbladian with a control parameter α which interpolates between the full post-selection and averaging over all quantum trajectories. As an application we study the non-unitary dynamics of a lossy or driven-dissipative BCS superconductors, evolving in presence of two-body losses and two-body pumps. We show that the non-Hermitian limit acts as a singular limit of the hybrid dissipative dynamics, leading to a sharp modification of the universal approach to the driven-dissipative steady-states. By considering the dissipative dynamics with pair losses, we show that, as the non-Hermitian limit is approached, the density dynamics sharply evolves from a universal power-law to exponential decay that converges towards a quasi-steady plateau characterized by the freezing of the particle depletion due to pair losses. The reached quasi-stationary density increases as a function of the dissipation rate highlighting the emergence of a non-Hermitian Zeno effect in the lossy dynamics. For the driven-dissipative case, we show that, in the non-Hermitian limit, the system gets trapped into an effective negative temperature state, thus skipping the infinite temperature steady-state reached in the presence of finite contribution of the quantum jumps. We rationalize these findings in terms of the conservation of the length of the pseudospins which, in the non-Hermitian limit, suppresses the effective single-particle losses and pumps acting on the non-condensed particles.
We present the Information Dynamics framework, where quantum mechanics emerges from a more fundamental information field. Two complementary perspectives are offered. First perspective (quantum physics view): The Schrödinger equation is derived as the unitary, dissipation-free limit of a generalized Ginzburg-Landau equation. The information purity pID = ε/(ε+γ) controls the transition between wave-like coherence and particle-like decoherence. Second perspective (information superconductor view): In the limit pID → 1, the information field behaves as an information superconductor — a dissipation-free flow of information, analogous to electrical superconductivity. The Schrödinger equation becomes the “London equation” of this information superfluid. The information purity pID = ε/(ε+γ) is the KPI. It measures the coherence of the information flow — the fraction of the information field that remains in a pure, superconducting state. It does not correspond to any conserved quantity in physics. Instead, it is an information‑theoretic score: high pID means clean, wave‑like, nonlocal behavior; low pID means noisy, particle‑like, classical behavior. We invert two landmark 2025 experiments: the MIT wave-particle duality test and the BESIII Bell test. Using pID as a pre-defined parameter (not a post-hoc fit), we obtain pID = 0.875 ± 0.012 from the MIT visibility intercept, and pID = 0.966 ± 0.004 from the BESIII S parameter. These results show that wave-particle duality and quantum nonlocality are two facets of the same information-theoretic principle. The Value of Information Dynamics: A New Perspective, Not Just New Predictions Information Dynamics is not intended to replace or overturn the current physical laws. Its role is analogous to that of a high‑level programming language—the binary code compiled from a high‑level language may be functionally identical to hand‑written assembly, yet the value of the high‑level language lies in simpler abstractions, greater unifying power, and the ability to solve complex problems. Similarly, starting solely from binary code, there are several ways to prove the existence of a high‑level programming language (e.g., bootstrapping, cross‑platform consistency, solving problems impractical in binary, information compression, extensibility, etc.). However, each of these approaches requires substantial time and broad collaboration. This paper serves only as the beginning of such an ambitious endeavor, presenting the core ideas and initial constructions. This paper takes only the first step—demonstrating the basic syntax and core ideas of Information Dynamics as a “high‑level language.” We sincerely invite colleagues in the academic community to collaborate and together complete this grand bootstrapping project. Upload note: This is the preprint version updated on April 4, 2026. All figures, data, and code are included in the GitHub repository: https://github.com/hkaiopen/InformationDynamics_Quantum/
Non-unitary dynamics in quantum mechanics arise in open quantum systems, where the interaction between the system and its environment is not negligible. One way this coupling can be realised is through measurement, where the backaction from the measurement apparatus induces non-unitary dynamics in the system. An effective non-Hermitian description arises within the no-jump approximation of a measured system, in which the time-evolved states are explicitly normalised at all times. Non-Hermiticity in quantum Hamiltonians gives rise to non-unitary time evolution and possibly complex energy eigenvalues, which can lead to a rich phenomenology with no Hermitian counterpart. In this thesis, we explore these two interconnected concepts related to non-unitary dynamics: non-Hermiticity and measurements. However, instead of effective non-Hermiticity, we consider the cases where non-Hermiticity is realised exactly. This setup necessitates a treatment under the self-consistent frameworks of non-Hermitian quantum mechanics in order to restore its probabilistic interpretation. Concretely, the self-consistent metric formalism restores unitarity of the evolution through a modified Hilbert space endowed with a dynamical metric. Through comparative studies using exactly solvable models, we find that the physics of the two approaches of non-Hermitian quantum mechanics is fundamentally different. This has a profound physical impact in terms of defect production in quenches across an exceptional point (EP). We demonstrate this through a non-Hermitian system hosting both PT-symmetric and PT-broken modes subject to a linear quench. Our results highlight the role played by the EP and the spontaneous breaking of the PT-symmetry in contributing to a non-zero defect density, even in the limit of an infinitely slow drive. Further, we uncover generalised transformations underpinning the results, which are incorporated in the dynamical metric. Going beyond purely theoretical considerations, we implement two novel dilation schemes to emulate the metric dynamics in a digital quantum simulator. Our protocols enable controlled access to all PT-symmetry regimes and to a direct tomography of the dynamical metric, opening the possibility of studying a new kind of non-Hermitian physics in engineered matter. To explore the second theme of the thesis, we investigate the dynamics of entanglement entropy in the continuously monitored Bose-Hubbard model. Our numerical data reveals a counterintuitive enhancement of superfluid correlations in a parameter regime, in which the entanglement entropy increases with the onsite repulsion strength in the presence of measurement. This phenomenon arising from the interplay between hopping, interaction, and measurement, is also present in the effective central charge extracted from a fit of the logarithmic scaling form of the entropy. In summary, this thesis reveals the richness of non-unitary quantum dynamics. Through an in-depth study of the different aspects of non-Hermitian systems, we illustrate the non-trivial physics uncovered only with the consideration of the dynamical metric. By bridging theoretical insights and physical realisation through novel dilation protocols realisable in engineered matter, our work lays the groundwork for further exploration of dynamical aspects in non-Hermitian and monitored quantum systems.
In a compression-based account of charge, five distinct objects share the single name “charge”: a global conserved charge , an einselected reduced record , a -odd Yang–Lee ordering operator , a decaying Gaussian occupation , and a trajectory charge-transfer count . We separate them inside an instrumented, charge-conserving open quantum process and ask which relations are invariants of the full process and which are only diagnostics of a monitoring scheme or of the no-jump conditional slice. In minimal completely-positive models we establish: (i) [THM] if every jump commutes with and , charge-diagonal monitoring makes the reduced record an exact fixed point, and [CALC] its survivor -algebra is the two-dimensional diagonal (charge-sector) algebra; a charge-violating perturbation makes it a finite-lifetime metastable record whose lifetime rises with the monitoring rate in the strong-monitoring (Zeno) branch. (ii) [THM] -covariance does not imply charge conservation — amplitude damping is covariant yet lowers the occupation. (iii) [CALC] the asymptotic () stationary fixed-point -algebra obeys a three-way classification: for a bare record; with unchanged charge centre when a non-abelian seed survives (intra-sector protected structure); and a refined centre when a second abelian label survives. Charge labels all asymptotic survivors iff the stationary and there are no nonzero-frequency peripheral modes; the weaker excludes neither intra-sector survivors nor rotating (nonzero-frequency) peripheral modes, which are counted separately from . (iv) [CALC] a genuine finite-time trajectory Lee–Yang zero of a two-site transport counting statistics exists (complex Newton root, residual , winding number one); we do not call it an edge. The two strongest results are negative: [NEG] the no-jump effective Hamiltonian is not a representation invariant of the physical generator — at an exceptional point the eigenvalue splitting opens from to under a redundant Lindblad representation that leaves fixed to , so the exceptional point itself is not a process invariant; and [NEG] in the stated model, at a no-jump exceptional point no non-analyticity of the physical scaled cumulant generating function is detected in the scanned range. One minimal model simultaneously instantiates three charge objects () and two derived dynamical objects (); and remain comparison entries supplied by other minimal models / companions. In that model the conserved record and the zero-generating transferred charge are different objects: the ledger and language are unified, but a direct, representation-invariant bridge from the record to the dynamical Lee–Yang zeros is not established. We do not derive , a dynamic exponent , or any universality class.