arXiv subjects

Faidon Andreadakis

Publications and source records attributed to Faidon Andreadakis.

10 recordsLinked to original sources

arXiv2025

Mereological Quantum Phase Transitions

We introduce the novel concept of mereological quantum phase transition (m-QPTs). Our framework is based on a variational family of operator algebras defining generalized tensor product structures (g-TPS), a parameter-dependent Hamiltonian, and a quantum scrambling functional. By minimizing the scrambling functional, one selects a g-TPS, enabling a pullback of the natural information-geometric metric on the g-TPS manifold to the parameter space. The singularities of this induced metric -- so-called algebra susceptibility -- in the thermodynamic limit characterize the m-QPTs. We illustrate this framework through analytical examples involving quantum coherence and operator entanglement. Moreover, spin-chains numerical simulations show susceptibility sharp responses at an integrability point and strong growth across disorder-induced localization, suggesting critical reorganizations of emergent subsystem structure aligned with those transitions.

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arXiv2025

An Exact Link between Nonlocal Nonstabilizerness and Operator Entanglement

Nonstabilizerness is a quantum property of states associated with the non-Clifford resources required for their preparation. As a resource, nonstabilizerness complements entanglement, and the interplay between these two concepts has garnered significant attention in recent years. In this work, we establish an exact correspondence between the generation of nonlocal nonstabilizerness and operator entanglement under unitary evolutions. Nonlocal nonstabilizerness refers to nonstabilizerness that cannot be erased via local operations, while operator entanglement generalizes entanglement to operator space, characterizing the complexity of operators across a bipartition. Specifically, we prove that a unitary map generates nonlocal nonstabilizerness if and only if it generates operator entanglement on Pauli strings. Guided by this result, we introduce an average measure of a unitary's Pauli-entangling power, serving as a proxy for nonlocal nonstabilizerness generation. We derive analytical formulas for this measure and examine its properties, including its typical value and upper bounds in terms of the nonstabilizerness properties of the evolution.

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arXiv2024

Tensor Product Structure Geometry under Unitary Channels

In quantum many-body systems, complex dynamics delocalize the physical degrees of freedom. This spreading of information throughout the system has been extensively studied in relation to quantum thermalization, scrambling, and chaos. Locality is typically defined with respect to a tensor product structure (TPS) which identifies the local subsystems of the quantum system. In this paper, we investigate a simple geometric measure of operator spreading by quantifying the distance of the space of local operators from itself evolved under a unitary channel. We show that this TPS distance is related to the scrambling properties of the dynamics between the local subsystems and coincides with the entangling power of the dynamics in the case of a symmetric bipartition. Additionally, we provide sufficient conditions for the maximization of the TPS distance and show that the class of 2-unitaries provides examples of dynamics that achieve this maximal value. For Hamiltonian evolutions at short times, the characteristic timescale of the TPS distance depends on scrambling rates determined by the strength of interactions between the local subsystems. Beyond this short-time regime, the behavior of the TPS distance is explored through numerical simulations of prototypical models exhibiting distinct ergodic properties, ranging from quantum chaos and integrability to Hilbert space fragmentation and localization.

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arXiv2024

A Butterfly Effect in Encoding-Decoding Quantum Circuits

The study of information scrambling has profoundly deepened our understanding of many-body quantum systems. Much recent research has been devote to understanding the interplay between scrambling and decoherence in open systems. Continuing in this vein, we investigate scrambling in a noisy encoding-decoding circuit model. Specifically, we consider an $L$-qubit circuit consisting of a Haar-random unitary, followed by noise acting on a subset of qubits, and then by the inverse unitary. Scrambling is measured using the bipartite algebraic out-of-time-order correlator ($\mathcal{A}$-OTOC), which allows us to track information spread between extensively sized subsystems. We derive an analytic expression for the $\mathcal{A}$-OTOC that depends on system size and noise strength. In the thermodynamic limit, this system displays a \textit{butterfly effect} in which infinitesimal noise induces macroscopic information scrambling. We also perform numerical simulations while relaxing the condition of Haar-randomness, which preliminarily suggest that this effect may manifest in a larger set of circuits.

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arXiv2024

Operator Space Entangling Power of Quantum Dynamics and Local Operator Entanglement Growth in Dual-Unitary Circuits

Operator entanglement is a well-established measure of operator complexity across a system bipartition. In this work, we introduce a measure for the ability of a unitary channel to generate operator entanglement, representing an operator-level generalization of the state-space entangling power. This operator space entangling power is demonstrated to be linked to the scrambling properties of the unitary channel via the recently introduced concept of mutual averaged non-commutativity of quantum operator algebras. An upper bound for the operator space entangling power is identified, corresponding to unitary channels with scrambling properties akin to those of typical unitaries. Additionally, for Hamiltonian dynamics, we find that the short-time growth rate of the operator space entangling power matches the Gaussian scrambling rate of the bipartite out-of-time-order-correlator, establishing a direct link between information scrambling and operator entanglement generation for short time scales. Finally, we examine the average growth of local operator entanglement across a symmetric bipartition of a spin-chain. For dual-unitary circuits, a combination of analytical and numerical investigations demonstrates that the average growth of local operator entanglement exhibits two distinct regimes in relation to the operator space entangling power of the building-block gate.

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arXiv2023

Long-time Quantum Scrambling and Generalized Tensor Product Structures

Much recent work has been devoted to the study of information scrambling in quantum systems. In this paper, we study the long-time properties of the algebraic out-of-time-order-correlator ("$\mathcal{A}$-OTOC") and derive an analytical expression for its long-time average under the non-resonance condition. The $\mathcal{A}$-OTOC quantifies quantum scrambling with respect to degrees of freedom described by an operator subalgebra $\mathcal{A}$, which is associated with a partitioning of the corresponding system into a generalized tensor product structure. Recently, the short-time growth of the $\mathcal{A}$-OTOC was proposed as a criterion to determine which partition arises naturally from the system's unitary dynamics. In this paper, we extend this program to the long-time regime where the long-time average of the $\mathcal{A}$-OTOC serves as the metric of subsystem emergence. Under this framework, natural system partitions are characterized by the tendency to minimally scramble information over long time scales. We consider several physical examples, ranging from quantum many-body systems and stabilizer codes to quantum reference frames, and perform the minimization of the $\mathcal{A}$-OTOC long-time average both analytically and numerically over relevant families of algebras. For simple cases subject to the non-resonant condition, minimal $\mathcal{A}$-OTOC long-time average is shown to be related to minimal entanglement of the Hamiltonian eigenstates across the emergent system partition. Finally, we conjecture and provide evidence for a general structure of the algebra that minimizes the average for non-resonant Hamiltonians.

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arXiv2022

Coherence generation, symmetry algebras and Hilbert space fragmentation

Hilbert space fragmentation is a novel type of ergodicity breaking in closed quantum systems. Recently, an algebraic approach was utilized to provide a definition of Hilbert space fragmentation characterizing \emph{families} of Hamiltonian systems based on their (generalized) symmetries. In this paper, we reveal a simple connection between the aforementioned classification of physical systems and their coherence generation properties, quantified by the coherence generating power (CGP). The maximum CGP (in the basis associated to the algebra of each family of Hamiltonians) is exactly related to the number of independent Krylov subspaces $K$, which is precisely the characteristic used in the classification of the system. In order to gain further insight, we numerically simulate paradigmatic models with both ordinary symmetries and Hilbert space fragmentation, comparing the behavior of the CGP in each case with the system dimension. More generally, allowing the time evolution to be any unitary channel in a specified algebra, we show analytically that the scaling of the Haar averaged value of the CGP depends only on $K$. These results illustrate the intuitive relationship between coherence generation and symmetry algebras.

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arXiv2022

Operational Quantum Mereology and Minimal Scrambling

In this paper we will attempt to answer the following question: what are the natural quantum subsystems which emerge out of a system's dynamical laws? To answer this question we first define generalized tensor product structures (gTPS) in terms of observables, as dual pairs of an operator subalgebra $\cal A$ and its commutant. Second, we propose an operational criterion of minimal information scrambling at short time scales to dynamically select gTPS. In this way the emergent subsystems are those which maintain the longest informational identity. This strategy is made quantitative by defining a Gaussian scrambling rate in terms of the short-time expansion of an algebraic version of the Out of Time Order Correlation (OTOC) function i.e., the $\cal A$-OTOC. The Gaussian scrambling rate is computed analytically for physically important cases of general division into subsystems, and is shown to have an intuitive and compelling physical interpretation in terms of minimizing the interaction strength between subsystems.

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arXiv2022

No ((n, k, d < 127)) code can violate the quantum Hamming bound

It is well-known that pure quantum error correcting codes (QECCs) are constrained by a quantum version of the Hamming bound. Whether impure codes also obey such a bound, however, remains a long-standing question with practical implications for the efficacy of QECCs. We employ a combination of previously derived bounds on QECCs to demonstrate that a subset of all codes must obey the quantum Hamming bound. Specifically, we combine an analytical bound due to Rains with a numerical bound due to Li and Xing to show that no ((n,k,d < 127)) code can violate the quantum Hamming bound.

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arXiv2022

Scrambling of Algebras in Open Quantum Systems

Many quantitative approaches to the dynamical scrambling of information in quantum systems involve the study of out-of-time-ordered correlators (OTOCs). In this paper, we introduce an algebraic OTOC ($\mathcal{A}$-OTOC) that allows us to study information scrambling of generalized quantum subsystems under quantum channels. For closed quantum systems, this algebraic framework was recently employed to unify quantum information-theoretic notions of operator entanglement, coherence-generating power, and Loschmidt echo. The main focus of this work is to provide a natural generalization of these techniques to open quantum systems. We first show that, for unitary dynamics, the $\mathcal{A}$-OTOC quantifies a generalized notion of information scrambling, namely between a subalgebra of observables and its commutant. For open quantum systems, on the other hand, we find a competition between the global environmental decoherence and the local scrambling of information. We illustrate this interplay by analytically studying various illustrative examples of algebras and quantum channels. To complement our analytical results, we perform numerical simulations of two paradigmatic systems: the PXP model and the Heisenberg XXX model, under dephasing. Our numerical results reveal connections with many-body scars and the stability of decoherence-free subspaces.

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