arXiv subjects

Peyman Azodi

Publications and source records attributed to Peyman Azodi.

10 recordsLinked to original sources

arXiv2024

Measuring Entanglement by Exploiting its Anti-symmetric Nature

Despite significant progress in experimental quantum sciences, measuring entanglement entropy remains challenging. Through a geometric perspective, we reveal the intrinsic anti-symmetric nature of entanglement. We prove that most entanglement measures, such as von Neumann and Renyi entropies, can be expressed in terms of exterior products, which are fundamentally anti-symmetric. Leveraging this, we propose utilizing the anti-symmetric nature of fermions to measure entanglement entropy efficiently, offering a resource-efficient approach to probing bipartite entanglement.

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arXiv2024

Emergence of Light Cones in Long-range Interacting Spin Chains Is Due to Destructive Interference

Despite extensive research on long-range interacting quantum systems, the physical mechanism responsible for the emergence of light cones remains unidentified. This work presents a novel perspective on the origins of locality and emergent light cones in quantum systems with long-range interactions. We identify a mechanism in such spin chains where effective entanglement light cones emerge due to destructive interference among quantum effects that entangle spins. Although long-range entangling effects reach beyond the identified light cone, due to destructive interference, entanglement remains exponentially suppressed in that region, ultimately leading to the formation of the light cone. We demonstrate that this interference not only drives but is also necessary for the emergence of light cones. Furthermore, our analysis reveals that reducing the interaction range weakens this interference, surprisingly increasing the speed of entanglement transport, an effect that opens new experimental opportunities for investigation.

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arXiv2023

Entanglement Propagation in Integrable Heisenberg Chains from a New Lens

The exact single-magnon entanglement evolution in Heisenberg chains is obtained using the Quantum Correlation Transfer Function (QCTF) formulation. A dual, i.e., frequency and time-domain, analysis shows that the transient dynamics of individual spins' entanglement is described via a Bessel function of the first kind. Through QCTF, we bypass the evaluation of the full system's state for the purpose of obtaining entanglement. Although it is known that the observable entanglement edge is formed by the arrival of a stream of quasi-particles that travel with the maximum group velocity, we show how the early quasi-particles travel faster than the maximum group velocity of the chain and contribute to entanglement production. Our results can be extended to the multi-magnon regime, therefore opening up the means to better interpret equilibration dynamics and thermodynamics in Heisenberg chains.

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arXiv2023

Dynamics and Geometry of Entanglement in Many-Body Quantum Systems

A new framework is formulated to study entanglement dynamics in many-body quantum systems along with an associated geometric description. In this formulation, called the Quantum Correlation Transfer Function (QCTF), the system's wave function or density matrix is transformed into a new space of complex functions with isolated singularities. Accordingly, entanglement dynamics is encoded in specific residues of the QCTF, and importantly, the explicit evaluation of the system's time dependence is avoided. Notably, the QCTF formulation allows for various algebraic simplifications and approximations to address the normally encountered complications due to the exponential growth of the many-body Hilbert space with the number of bodies. These simplifications are facilitated through considering the \textit{patterns}, in lieu of the elements, lying within the system's state. Consequently, a main finding of this paper is the exterior (Grassmannian) algebraic expression of many-body entanglement as the collective areas of regions in the Hilbert space spanned by pairs of projections of the wave function onto an arbitrary basis. This latter geometric measure is shown to be equivalent to the second-order R\'enyi entropy. Additionally, the geometric description of the QCTF shows that characterizing features of the reduced density matrix can be related to experimentally observable quantities. The QCTF-based geometric description offers the prospect of theoretically revealing aspects of many-body entanglement, by drawing on the vast scope of methods from geometry.

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arXiv2022

Stability and quasi-Periodicity of Many-Body Localized Dynamics

The connection between entanglement dynamics and non-equilibrium statistics in isolated many-body quantum systems has been established both theoretically and experimentally. Many-Body Localization (MBL), a phenomenon where interacting particles in disordered (i.e., random) chains fail to thermalize, exemplifies this connection. However, the systematic proof of critical phenomena such as MBL remains challenging due to the lack of robust methods for analyzing many-body entanglement dynamics. In this paper, we identify MBL through quasi-periodic dynamics in the entanglement evolution of subsystems in a disordered Heisenberg chain. This new form of characterizing MBL, through stable quasi-periodic dynamics of entanglement -- where stable means they persist in the thermodynamic limit -- concretely distinguishes between two competing scenarios: fully localized behavior of subsystems or slowly, exponentially slow in disorder, thermalizing subsystems -- a heated controversy in the literature. Utilizing perturbation theory, we derive the entanglement dynamics of single spins through an infinite perturbative series, while also modeling rare Griffiths regions (locally thermal inclusions). Our results prove that in regimes of sufficiently strong disorder, the entanglement evolution of individual subsystems remains quasi-periodic in the thermodynamic limit, thereby providing concrete evidence for the stability of MBL dynamics in disordered Heisenberg chains. This behavior contrasts with the widely reported logarithmic growth of subsystem entanglement in the MBL phase. We show that the logarithmic growth observed in prior studies arises from statistical ensemble averaging, which is prohibited due to the intrinsic non-ergodic dynamics characteristic of MBL systems, rooted in their quasi-periodic features.

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arXiv2021

Lyapunov-Based Stabilization and Control of Closed Quantum Systems

A Lyapunov-based method is presented for stabilizing and controlling of closed quantum systems. The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite operator in the Lyapunov function provides additional degrees of freedom for the designer. The stabilization process is analyzed regarding two distinct cases for this operator in terms of its vanishing or non-vanishing commutation with the Hamiltonian operator of the undriven quantum system. To cope with the global phase invariance of quantum states as a result of the quantum projective measurement postulate, equivalence classes of quantum states are defined and used in the proposed Lyapunov-based analysis and design. Results show significant improvement in both the set of stabilizable quantum systems and their invariant sets of state trajectories generated by designed control signals. The proposed method can potentially be applied for high-fidelity quantum control purposes in quantum computing frameworks.

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arXiv2017

Lyapunov-Based Stabilization and Control of the Stochastic Schrodinger Equation

This paper presents a detailed Lyapunov-based theory to control and stabilize continuously-measured quantum systems, which are driven by Stochastic Schrodinger Equation (SSE). Initially, equivalent classes of states of a quantum system are defined and their properties are presented. With the help of equivalence classes of states, we are able to consider global phase invariance of quantum states in our mathematical analysis. As the second mathematical modelling tool, the conventional Ito formula is further extended to non-differentiable complex functions. Based on this extended Ito formula, a detailed stochastic stability theory is developed to stabilize the SSE. Main results of this proposed theory are sufficient conditions for stochastic stability and asymptotic stochastic stability of the SSE. Based on the main results, a solid mathematical framework is provided for controlling and analyzing quantum system under continuous measurement, which is the first step towards implementing weak continuous feedback control for quantum computing purposes.

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arXiv2017

Stochastic Boundedness of State Trajectories of Stable LTI Systems in the Presence of Nonvanishing Stochastic Perturbation

This paper studies stochastic boundedness of trajectories of a nonvanishing stochastically perturbed stable LTI system. First, two definitions on stochastic boundedness of stochastic processes are presented, then the boundedness is analyzed via Lyapunov theory. In this proposed theorem, it is shown that under a condition on the Lipchitz constant of the perturbation kernel, the trajectories remain stochastically bounded in the sense of the proposed definitions and the bounds are calculated. Also, the limiting behavior of the trajectories have been studied. At the end an illustrative example is presented, which shows the effectiveness of the proposed theory.

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arXiv2016

Uncertainty decomposition of quantum networks in SLH framework

This paper presents a systematic method to decompose uncertain linear quantum input-output networks into uncertain and nominal subnetworks, when uncertainties are defined in SLH representation. To this aim, two decomposition theorems are stated, which show how an uncertain quantum network can be decomposed into nominal and uncertain subnetworks in cascaded connection and how uncertainties can be translated from SLH parameters into state-space parameters. As a potential application of the proposed decomposition scheme, robust stability analysis of uncertain quantum networks is briefly introduced. The proposed uncertainty decomposition theorems take account of uncertainties in all three parameters of a quantum network and bridge the gap between SLH modeling and state-space robust analysis theory for linear quantum networks.

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arXiv2016

Robust Stability of Uncertain Quantum Input-Output Networks

This paper presents a systematic method to analyze stability and robustness of uncertain Quantum Input-Output Networks (QIONs). A general form of uncertainty is introduced into quantum networks in the SLH formalism. Results of this paper are built up on the notion of uncertainty decomposition wherein the quantum network is decomposed into nominal (certain) and uncertain sub-networks in cascade connection. Sufficient conditions for robust stability are derived using two different methods. In the first approach, a generalized small-gain theorem is presented and in the second approach, robust stability is analyzed within the framework of Lyapunov theory. In the second method, the robust stability problem is reformulated as feasibility of a Linear Matrix Inequality (LMI), which can be examined using the well-established systematic methods in the literature.

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