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Queeter Theory: Quantum Underlying Entanglement Event Time Entropy Retention

Jeffrey Alexander Webb

Published Jul 26, 2026• 0 citations
Publisher

Abstract

Description The Quantum Underlying Entanglement Event Time–Entropy Retention model, abbreviated QUEETER, is a speculative framework designed to explore whether the history of a quantum entanglement event can continue to influence a system after that event has already occurred. The model begins with the familiar idea that two or more quantum systems can become entangled. When systems are entangled, their properties are connected through correlations that cannot always be explained by treating each system independently. These correlations can remain observable even when the systems are separated.In ordinary quantum theory, the present condition of a system is described by its quantum state. For realistic systems, this state is often represented by a density matrix, which contains the measurable probabilities, coherences, and correlations available at a given time. QUEETER asks whether this present-state description is always sufficient. Its central proposal is that an entanglement event may leave behind a temporary historical influence. This influence would depend on when the entanglement event occurred and on the amount of entropy produced or encountered after that event. The model calls this continuing influence event retention, or QUEETER retention.Under this proposal, an entanglement event is not treated merely as an instantaneous preparation step. Instead, it is treated as the beginning of a history that may continue to affect later quantum behavior. An entanglement event is any physical interaction that creates or significantly changes entanglement between quantum systems. This event could occur through a controlled quantum gate, the emission of correlated particles, a collision, a shared interaction, or another physical process capable of generating quantum entanglement. QUEETER assigns importance to the time at which this event occurs. That moment becomes the starting point for the event’s retention history. As time passes, the event becomes older. During that period, the system may also interact with its environment, experience thermal noise, undergo measurements, lose energy, or participate in other irreversible processes. QUEETER proposes that both the age of the event and the entropy associated with its later history may influence how much of the event’s original historical effect remains.Time is one of the central elements of the QUEETER model. The model proposes that the influence of an entanglement event gradually weakens as the event becomes older. A recently created entangled system may therefore possess a stronger event-retention effect than a system whose entanglement was created much earlier. This does not simply mean that older systems are expected to have less entanglement. That ordinary effect is already explained by decoherence, noise, and other forms of environmental disturbance.The stronger QUEETER claim is that event age may affect future behavior even when two systems have been adjusted so that their present measurable quantum states are the same. In other words, two systems could appear identical at the beginning of an experiment but evolve differently because one system’s entanglement event happened more recently than the other’s.Entropy is the second major historical element in QUEETER. In this context, entropy represents the irreversible spreading, loss, or inaccessibility of information during the system’s history. A quantum system may accumulate entropy through interactions with a thermal environment, uncontrolled noise, scattering, dissipation, measurement-like processes, or other physical mechanisms that distribute information into surrounding degrees of freedom. QUEETER proposes that greater accumulated entropy exposure reduces event retention. This means that two entangled systems of the same age might still possess different retention values if one experienced a more disruptive or entropy-producing history. The model therefore distinguishes between the system’s present environment and its environmental history. Two systems may currently be held at the same temperature, exposed to the same controls, and placed in the same apparatus while still having experienced different amounts of entropy production in the past. QUEETER suggests that this difference in past entropy exposure may influence later quantum evolution.QUEETER retention is the proposed remaining influence of the original entanglement event. It is not meant to be identical to entanglement itself. A system may still be entangled even after its QUEETER retention has become very small. Similarly, a nonzero retention value would not automatically prove that the system remains strongly entangled. Entanglement refers to a property of the quantum state, while retention refers to the proposed continuing effect of the event history that created or shaped that state. Retention is also not intended to be the same as ordinary coherence. Quantum coherence describes phase relationships that are already visible in the present quantum state. QUEETER retention is meant to carry information about the event’s age and entropy history, even when that information is not directly visible through ordinary measurements of the present reduced state. The model treats retention as an additional descriptive variable. This variable would be strongest near the time of the entanglement event and would gradually fade as time passes and entropy accumulates.Decoherence describes how quantum coherence and entanglement become weakened when a system interacts with its environment. It explains why quantum behavior becomes difficult to observe in large, warm, or uncontrolled systems. QUEETER does not replace decoherence. Instead, it proposes that the rate or pattern of decoherence may temporarily depend on the retained history of the original entanglement event.In the basic protective version of the model, greater retention slightly slows the loss of observable quantum correlations. As retention fades, the system’s behavior gradually returns to the ordinary decoherence rate. This produces the prediction that a recently entangled system may lose correlations differently from an older but otherwise matched system. However, simply observing different decay rates would not be enough to support QUEETER. Ordinary environmental differences can easily produce such an effect. The systems would need to be carefully matched and tested under the same present conditions.Quantum memory refers to a physical system or degree of freedom that stores quantum information. Examples include atomic ensembles, trapped particles, optical systems, or environmental modes that preserve information about earlier interactions. QUEETER retention is intended to be conceptually different. It is not initially described as a separate physical storage device or memory qubit. It is described as a property associated with the entanglement event and its history. This distinction is difficult to maintain scientifically. If the proposed retention effect can be explained by an unnoticed environmental memory, then QUEETER would not require a new physical theory. It would instead represent a different way of describing an already known memory process. For QUEETER to become genuinely distinct, it would need to predict something that cannot be reproduced by including the relevant environment and memory degrees of freedom in an ordinary quantum model.Non-Markovian quantum dynamics describes situations in which the future behavior of a system depends on its earlier interactions. In a simple memoryless process, the future depends only on the present state. In a non-Markovian process, information can flow between the system and the environment, allowing earlier events to influence later behavior. This area of physics is closely related to the idea behind QUEETER.For that reason, QUEETER cannot claim originality merely because it introduces history-dependent quantum behavior. That general idea is already well established. The proposed distinction is more specific. QUEETER suggests that the time and entropy history of a particular entanglement event may act as an additional effective state variable, even when the ordinary present quantum state and the relevant present environment have been matched. This is a much stronger claim because it suggests that the conventional description may be incomplete unless the event-retention history is included.The basic test of QUEETER uses two groups of entangled quantum systems. The first group has a recent entanglement-event history. The second group has an older entanglement-event history or has experienced more entropy-producing interactions. At first, the groups would naturally have different present states because the older or more disturbed group may have suffered more decoherence. To make the experiment meaningful, researchers would need to match the present quantum states of the two groups. This could involve carefully controlled noise, filtering, state preparation, or other procedures that bring both groups to nearly the same measured density matrix. The experimenters would then place both groups in the same test environment. They would expose the systems to the same controls, the same temperature, the same noise conditions, the same measurement schedule, and the same observation period.The later quantum correlations of the two groups would then be measured. Under the conventional null hypothesis, systems with the same complete relevant state and the same dynamics should produce the same future measurement statistics. Under QUEETER, the systems may evolve differently because their event-retention values are different.The primary QUEETER prediction is that two systems with nearly identical present quantum states may display different future correlation-decay behavior if their entanglement-event histories differ. In the protective version of the model, the system with the more recent and lower-entropy history retains its correlations for slightly longer.

DOI
10.5281/zenodo.21613246

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Description The Quantum Underlying Entanglement Event Time–Entropy Retention model, abbreviated QUEETER, is a speculative framework designed to explore whether the history of a quantum entanglement event can continue to influence a system after that event has already occurred. The model begins with the familiar idea that two or more quantum systems can become entangled. When systems are entangled, their properties are connected through correlations that cannot always be explained by treating each system independently. These correlations can remain observable even when the systems are separated.In ordinary quantum theory, the present condition of a system is described by its quantum state. For realistic systems, this state is often represented by a density matrix, which contains the measurable probabilities, coherences, and correlations available at a given time. QUEETER asks whether this present-state description is always sufficient. Its central proposal is that an entanglement event may leave behind a temporary historical influence. This influence would depend on when the entanglement event occurred and on the amount of entropy produced or encountered after that event. The model calls this continuing influence event retention, or QUEETER retention.Under this proposal, an entanglement event is not treated merely as an instantaneous preparation step. Instead, it is treated as the beginning of a history that may continue to affect later quantum behavior. An entanglement event is any physical interaction that creates or significantly changes entanglement between quantum systems. This event could occur through a controlled quantum gate, the emission of correlated particles, a collision, a shared interaction, or another physical process capable of generating quantum entanglement. QUEETER assigns importance to the time at which this event occurs. That moment becomes the starting point for the event’s retention history. As time passes, the event becomes older. During that period, the system may also interact with its environment, experience thermal noise, undergo measurements, lose energy, or participate in other irreversible processes. QUEETER proposes that both the age of the event and the entropy associated with its later history may influence how much of the event’s original historical effect remains.Time is one of the central elements of the QUEETER model. The model proposes that the influence of an entanglement event gradually weakens as the event becomes older. A recently created entangled system may therefore possess a stronger event-retention effect than a system whose entanglement was created much earlier. This does not simply mean that older systems are expected to have less entanglement. That ordinary effect is already explained by decoherence, noise, and other forms of environmental disturbance.The stronger QUEETER claim is that event age may affect future behavior even when two systems have been adjusted so that their present measurable quantum states are the same. In other words, two systems could appear identical at the beginning of an experiment but evolve differently because one system’s entanglement event happened more recently than the other’s.Entropy is the second major historical element in QUEETER. In this context, entropy represents the irreversible spreading, loss, or inaccessibility of information during the system’s history. A quantum system may accumulate entropy through interactions with a thermal environment, uncontrolled noise, scattering, dissipation, measurement-like processes, or other physical mechanisms that distribute information into surrounding degrees of freedom. QUEETER proposes that greater accumulated entropy exposure reduces event retention. This means that two entangled systems of the same age might still possess different retention values if one experienced a more disruptive or entropy-producing history. The model therefore distinguishes between the system’s present environment and its environmental history. Two systems may currently be held at the same temperature, exposed to the same controls, and placed in the same apparatus while still having experienced different amounts of entropy production in the past. QUEETER suggests that this difference in past entropy exposure may influence later quantum evolution.QUEETER retention is the proposed remaining influence of the original entanglement event. It is not meant to be identical to entanglement itself. A system may still be entangled even after its QUEETER retention has become very small. Similarly, a nonzero retention value would not automatically prove that the system remains strongly entangled. Entanglement refers to a property of the quantum state, while retention refers to the proposed continuing effect of the event history that created or shaped that state. Retention is also not intended to be the same as ordinary coherence. Quantum coherence describes phase relationships that are already visible in the present quantum state. QUEETER retention is meant to carry information about the event’s age and entropy history, even when that information is not directly visible through ordinary measurements of the present reduced state. The model treats retention as an additional descriptive variable. This variable would be strongest near the time of the entanglement event and would gradually fade as time passes and entropy accumulates.Decoherence describes how quantum coherence and entanglement become weakened when a system interacts with its environment. It explains why quantum behavior becomes difficult to observe in large, warm, or uncontrolled systems. QUEETER does not replace decoherence. Instead, it proposes that the rate or pattern of decoherence may temporarily depend on the retained history of the original entanglement event.In the basic protective version of the model, greater retention slightly slows the loss of observable quantum correlations. As retention fades, the system’s behavior gradually returns to the ordinary decoherence rate. This produces the prediction that a recently entangled system may lose correlations differently from an older but otherwise matched system. However, simply observing different decay rates would not be enough to support QUEETER. Ordinary environmental differences can easily produce such an effect. The systems would need to be carefully matched and tested under the same present conditions.Quantum memory refers to a physical system or degree of freedom that stores quantum information. Examples include atomic ensembles, trapped particles, optical systems, or environmental modes that preserve information about earlier interactions. QUEETER retention is intended to be conceptually different. It is not initially described as a separate physical storage device or memory qubit. It is described as a property associated with the entanglement event and its history. This distinction is difficult to maintain scientifically. If the proposed retention effect can be explained by an unnoticed environmental memory, then QUEETER would not require a new physical theory. It would instead represent a different way of describing an already known memory process. For QUEETER to become genuinely distinct, it would need to predict something that cannot be reproduced by including the relevant environment and memory degrees of freedom in an ordinary quantum model.Non-Markovian quantum dynamics describes situations in which the future behavior of a system depends on its earlier interactions. In a simple memoryless process, the future depends only on the present state. In a non-Markovian process, information can flow between the system and the environment, allowing earlier events to influence later behavior. This area of physics is closely related to the idea behind QUEETER.For that reason, QUEETER cannot claim originality merely because it introduces history-dependent quantum behavior. That general idea is already well established. The proposed distinction is more specific. QUEETER suggests that the time and entropy history of a particular entanglement event may act as an additional effective state variable, even when the ordinary present quantum state and the relevant present environment have been matched. This is a much stronger claim because it suggests that the conventional description may be incomplete unless the event-retention history is included.The basic test of QUEETER uses two groups of entangled quantum systems. The first group has a recent entanglement-event history. The second group has an older entanglement-event history or has experienced more entropy-producing interactions. At first, the groups would naturally have different present states because the older or more disturbed group may have suffered more decoherence. To make the experiment meaningful, researchers would need to match the present quantum states of the two groups. This could involve carefully controlled noise, filtering, state preparation, or other procedures that bring both groups to nearly the same measured density matrix. The experimenters would then place both groups in the same test environment. They would expose the systems to the same controls, the same temperature, the same noise conditions, the same measurement schedule, and the same observation period.The later quantum correlations of the two groups would then be measured. Under the conventional null hypothesis, systems with the same complete relevant state and the same dynamics should produce the same future measurement statistics. Under QUEETER, the systems may evolve differently because their event-retention values are different.The primary QUEETER prediction is that two systems with nearly identical present quantum states may display different future correlation-decay behavior if their entanglement-event histories differ. In the protective version of the model, the system with the more recent and lower-entropy history retains its correlations for slightly longer.
Quantum systems are rarely isolated from their surroundings. These hidden environments can retain information and return it later, producing correlated errors in quantum computers and complicating the interpretation of experiments. On a quantum processor, for example, one job can therefore leave an environmental trace that affects the next, even after the qubits themselves have been reset. Learning how this hidden influence persists and affects later behavior is therefore important, but the environment is often impossible to measure directly, and fully reconstructing its effects through tomography rapidly becomes impractical. Here, we introduce a response matrix that uses controlled interventions and observations of the system alone to reveal the temporal structure of environmental memory. The matrix records how future observations change across different controlled histories. Its spectrum characterizes how memory is structured and how it persists under specified system resets, while suitable linear combinations of its entries can rule out specified classical models of that memory. Because its history-future queries can be evaluated independently, numerical response matrices can be assembled in parallel. We establish the framework theoretically, characterize response spectra in an interacting spin process, and certify quantum memory in a two-qubit benchmark. This approach turns system observations into a probe of inaccessible environments and could support the diagnosis of correlated noise, tests of open system models, and memory-aware control design.
Quantum entanglement, a bizarre phenomenon where two or more particles become linked in such a way that they share the same fate, remains one of the most intriguing and debated aspects of quantum mechanics. This research investigates a novel theoretical framework designed to quantitatively analyze the time scale of entanglement propagation, ultimately providing insights into the fundamental nature of this phenomenon and its potential applications across diverse fields. We propose a 'Quantum Entanglement Time Scale' (QET) concept, predicated on the observation of entanglement's propagation as a measurable phenomenon, allowing for precise predictions regarding its temporal evolution. The core mechanism involves a dynamic model integrating quantum measurement and entanglement dynamics, aiming to quantify the rate at which entangled particles can diverge. This work explores the implications of this model for understanding and potentially controlling entanglement, pushing beyond current theoretical limitations and offering a path toward more predictable quantum interactions.
The act of measurement on a quantum state is supposed to "dephase" (dephasing refers to the phenomenon that the states lose phase coherence; then the phases get randomized in interaction with a bath of other oscillators, which is referred to as "decoherence"), then "decohere" and "collapse" (or more precisely "register" and "reduce") the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside standard quantum-mechanical evolution and not calculable from Schrödinger's equation. Progress has, however, been made in studying this problem with two main calculation tools-one uses a time-independent Hamiltonian, while a rather more general approach proving that decoherence occurs under some generic conditions. The two general approaches to the study of wave-function collapse are as follows. The first approach, called the "consistent" or "decoherent"' histories approach, studies microscopic histories that diverge probabilistically and explains collapse as an event in our particular history. The other, referred to as the "environmental decoherence" approach studies the effect of the environment upon the quantum system, to explain wave-function decoherence which is produced by irreversible effects of various sorts. However, as we know, wave-function collapse is not related to thermal connection with the environment, rather, it is inherent to how measurements are performed by macroscopic apparata. In the "environmental decoherence" approach, one studies decoherence using a Markovian-approximated Master equation to study the time-evolution of the reduced density matrix (post dephasing) and obtains the long-time dependence of the off-diagonal elements of this matrix. The calculation in this paper studies the evolution of a quantum system starting with "dephasing" followed by the effects of the environment with some differences from prior analyses. We start from the Schrödinger equation for the state of the system, with a time-dependent Hamiltonian that reflects the actual microscopic interactions that are occurring. Then we systematically solve (exactly) for the time-evolved state, without invoking a Markovian approximation when writing out the effective time-evolution equation, i.e., keeping the evolution unitary until the end. This approach is useful, and it shows that the system wave-function will explicitly "un-collapse" if the measurement apparatus is sufficiently small. However, in the limit of a macroscopic system, this "dephasing" quickly leads to "decoherence"-collapse is a temporary state that will simply take extremely long (of the order of multiple universe lifetimes) to reverse. This has been attempted previously and our calculation is particularly simple and calculable. We make some connections to the work by Linden et al. while doing so. The calculation in this paper has interesting implications for the interpretation of the Wigner's friend experiment, as well as the Mott experiment, which is explored in "Connection to some general theoretical results" and "Recurrence times" (especially the enumerated points in "Recurrence times"). The upshot is that as long as Wigner's friend is macroscopically large (or uses a macroscopically large measuring instrument), no one needs to worry that Wigner would see something different from his friend. Indeed, Wigner's friend does not even need to be conscious during the measurement that she conducts. It also allows one to reasonably interpret some of the more recent thought experiments proposed. In particular, as a result of the mathematical analysis, the short-time behavior of a collapsing system, at least the one considered in this paper, is not exponential. Instead, it is the usual Fermi-golden rule result. The long-term behavior is, of course, still exponential. This is a second novel feature of the paper-we connect the short-term Fermi-golden rule (quadratic-in-time behavior) transition probability to the exponential long-time behavior of a collapsing wave-function in one continuous mathematical formulation.
Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics. Recently, the study of quantum quenches revealed that these concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure state maintains the system at zero entropy, local properties at long times are captured by a statistical ensemble with nonzero thermodynamic entropy, which is the entanglement accumulated during the dynamics. Therefore, understanding the entanglement evolution unveils how thermodynamics emerges in isolated systems. Alas, an exact computation of the entanglement dynamics was available so far only for noninteracting systems, whereas it was deemed unfeasible for interacting ones. Here, we show that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the steady state and its excitations, leads to a complete understanding of the entanglement dynamics in the space-time scaling limit. We thoroughly check our result for the paradigmatic Heisenberg chain.
Quantum entanglement, a fundamental property of quantum mechanics, presents a unique challenge to traditional entropy calculations. This paper explores the development of a novel entropy calculation model based on quantum entanglement, aiming to improve the precision of measuring and predicting the evolution of entangled states. The core mechanism leverages the non-linear properties of entangled states to enable a more profound statistical analysis of quantum system evolution. The proposed model offers a significant advancement in quantifying the entanglement entropy, which has implications for quantum information security and quantum computation. This work addresses limitations of existing approaches by focusing on a fundamentally new framework for analyzing entanglement dynamics. The key contribution is the creation of an entanglement entropy measure that transcends classical approximations, offering a more accurate and robust representation of entanglement's statistical properties.
Quantum density matrices provide a complete operational description of measurement outcomes at a given time, yet it is well known that identical reduced states can arise from inequivalent interaction histories. In non-Markovian settings, these hidden histories can influence future dynamics under re-interaction, leading to divergent evolution despite identical instantaneous observables. This work addresses the structural gap between measurement completeness and evolutionary predictability in standard quantum state descriptions. We formalize this gap by introducing a minimal extension of the quantum state that preserves all standard measurement statistics while explicitly tracking interaction memory. The construction is defined through an extended state space equipped with a canonical marginal map onto the usual density-matrix formalism, ensuring full compatibility with the Born rule, complete positivity, and no-signaling. Within this framework, quantum states are shown to be operationally equivalent for measurement yet generically non-equivalent for future evolution. A concrete two-qubit model is presented to illustrate the core mechanism. Two preparation histories yield identical reduced density matrices—one storing coherence in system-environment correlations and the other dissipating it through decoherence. Under a subsequent memory-coupling interaction, these states evolve differently, demonstrating that reduced quantum states are insufficient to determine future dynamics in the presence of interaction memory. This example mirrors experimentally accessible echo and recoherence protocols and can be simulated exactly using standard quantum tools. The results clarify that no modification of quantum mechanics is required: the observed divergence arises from untracked correlations rather than hidden variables or observer-dependent effects. By separating measurement completeness from evolutionary completeness, this work provides a precise language for non-Markovian dynamics, coherence recovery, and history-dependent qubit behavior. The framework offers a structured basis for analyzing decoherence, error mitigation, and memory effects in realistic quantum systems without altering the predictions of standard quantum theory.