The notion of time in quantum mechanics remains an intricate and multifaceted concept, frequently juxtaposed against the backdrop of thermodynamic evolution and information propagation. This paper introduces the framework of Many-Body Quantum Age Synchronization (MQAS), proposing a novel paradigm wherein the temporal progression of a quantum system is intrinsically tied to its internal structural properties rather than merely tracking external classical clocks. We define the effective quantum age, denoted as tau_Q, as a functional mapping f(S, C, I), where S represents quantum entropy, C quantifies quantum coherence, and I captures the information complexity of the system. Extending this definition to many-body configurations, we investigate whether interacting quantum subsystems can spontaneously exhibit temporal alignment, such that tau_Q^(1) = tau_Q^(2) = ... = tau_Q^(K), a phenomenon we term quantum age synchronization. By analyzing both closed unitary dynamics and open quantum system dissipation, we derive the master equations governing the evolution of the quantum age and establish the conditions under which synchronization emerges. Furthermore, we explore the potential implications of MQAS for establishing novel quantum metrological protocols, redefining time measurement at microscopic scales, and understanding the thermodynamic cost of temporal coordination in quantum networks.
The notion of time in quantum mechanics remains an intricate and multifaceted concept, frequently juxtaposed against the backdrop of thermodynamic evolution and information propagation. This paper introduces the framework of Many-Body Quantum Age Synchronization (MQAS), proposing a novel paradigm wherein the temporal progression of a quantum system is intrinsically tied to its internal structural properties rather than merely tracking external classical clocks. We define the effective quantum age, denoted as tau_Q, as a functional mapping f(S, C, I), where S represents quantum entropy, C quantifies quantum coherence, and I captures the information complexity of the system. Extending this definition to many-body configurations, we investigate whether interacting quantum subsystems can spontaneously exhibit temporal alignment, such that tau_Q^(1) = tau_Q^(2) = ... = tau_Q^(K), a phenomenon we term quantum age synchronization. By analyzing both closed unitary dynamics and open quantum system dissipation, we derive the master equations governing the evolution of the quantum age and establish the conditions under which synchronization emerges. Furthermore, we explore the potential implications of MQAS for establishing novel quantum metrological protocols, redefining time measurement at microscopic scales, and understanding the thermodynamic cost of temporal coordination in quantum networks.
Can synchronization -- the widespread spontaneous emergence of coordinated dynamics in classical nonlinear systems -- also occur in the quantum regime? This question has recently sparked intense research into collective behavior and temporal self-organization in quantum systems. Typical quantum features such as the linearity of time evolution and the presence of quantum noise seem to hinder the appearance of synchrony at the microscopic level. At the same time, quantum coherence and quantum correlations may provide novel mechanisms for enhancing synchronization beyond its classical counterpart. We here survey recent theoretical and experimental advances in quantum synchronization, ranging from the characterization of synchronous oscillations and genuinely nonclassical forms of synchrony to many-body synchronization on quantum networks.
Open quantum many-body systems are an important setting that allows us to study the interplay between dissipation and interactions, contributing to a more accurate description of real-life phenomena and experiments, and providing new features to be exploited both on theoretical and technological grounds. This thesis deals with the study of such systems across a wide range of settings. Beyond providing the theoretical tools to analyze and understand this framework, the thesis also addresses some important and modern concepts. A key goal is to show how dissipation enables the realization of new phases of matter, such as quantum synchronization and time-crystal phases. To achieve this, various theoretical tools will be employed, ranging from path integral formalism to a Lindblad master equation approach. These same tools will also allow us to pursue another important goal: studying the dynamics of many-body systems subject to continuous measurements. This will lead to observing the emergence of a recently discovered phenomenon, known as measurement-induced phase transitions, and will provide a natural framework for addressing the complexity arising from the stochastic nature of quantum measurements. This thesis constitutes a modern and comprehensive view of the field of open quantum many-body systems, with a special focus on novel phases of matter emerging from interactions with an external environment or with a measuring device.
We present a relational framework in which temporal structure is not fundamental but emerges from correlations within a globally stationary quantum state. Each subsystem includes an internal clock, and conditional states evolve effectively with respect to these internal readings. The construction naturally extends to relativistic motion, gravitational redshift, and cosmological expansion, leading to a unified emergent-time functional valid across diverse physical regimes. The theory reproduces classical time dilation, predicts correlation-dependent deviations from standard evolution, and suggests that non-interacting or massless particles exhibit negligible internal time. These consequences open directions for conceptual and experimental investigations in the foundations of temporal physics, from multi-clock quantum systems to precision metrology and cosmological settings. In particular, the framework suggests measurable deviation from standard quantum evolution for highly entangled systems and predicts negligible internal time for massless particles.
A key conceptual achievement of special relativity was the abandonment of absolute time and the introduction of an operational definition of simultaneity through clock synchronization. Building on Einstein’s operational treatment of simultaneity, we extend the logic of clock synchronization to the quantum domain. Within the Overtime interpretation, quantum systems evolve in an internal time τ that becomes related to the observer’s time t only through synchronization. Measurement is thus understood as a temporal embedding rather than a physical collapse. Crucially, this resolution requires no new ontological entities—no additional state vectors, hidden variables, collapse mechanisms, or cosmological boundary conditions. The parameter τ is simply the standard ordering parameter of the Schrödinger equation, reinterpreted as system-intrinsic. This approach preserves all standard quantum predictions, maintains relativistic causality, and offers a unified conceptual framework for superposition, entanglement, delayed-choice phenomena, and the apparent discontinuity of measurement. The interpretation naturally aligns with the operational logic of special relativity and clarifies the role of entropy and the arrow of time in distinguishing macroscopic and microscopic systems.
Natural and engineered classical systems are replete with examples of synchronization, understood as the adjustment of rhythms of physical systems. Such synchronization is at the heart of the stability of several classical technologies, such as mechanical bridges and electrical networks. Given the advent of quantum simulation and computation technologies, it is natural to study a quantum analogue of synchronization and explore novel applications. This review surveys synchronization in few and many-body quantum systems, measures that quantify them, and their applications to quantum technologies.
Quantum clock synchronization (QCS) aims to establish a shared temporal reference between distant nodes by exploiting uniquely quantum phenomena such as entanglement, single-photon interference, and quantum correlations. In contrast to classical synchronization and time-transfer techniques, which are limited by signal propagation delays, atmospheric disturbances, and oscillator drift, QCS protocols offer the potential to surpass classical precision bounds and enhance resilience against adversarial manipulations. As precise and secure time synchronization underpins distributed quantum networks, navigation systems, and emerging quantum Internet infrastructures, understanding QCS principles, capabilities, and implementation challenges has become increasingly important. This survey provides a unified and critical overview of the rapidly growing QCS research landscape, highlighting fundamentals, protocol types, enabling resources, performance constraints, security considerations, and practical implementations of QCS. We first introduce the theoretical underpinnings of QCS, including entanglement-assisted time transfer, Hong-Ou-Mandel interference-based synchronization, and quantum slow-clock transport. We then categorize the main QCS protocols, ranging from ticking-qubit and entanglement-based schemes to time-of-arrival correlation methods, conveyor-belt synchronization, and quantum-enhanced two-way time transfer. This organization clarifies the relationships between protocol families and their achievable precision advantages over classical methods. Key quantum resources such as spontaneous parametric down-conversion-based entangled photon pairs, Greenberger-Horne-Zeilinger and W multipartite states, squeezed and frequency-entangled light, quantum frequency combs, and quantum memories are reviewed in the context of scalability and robustness.