No Entanglement From a Change of View: Quantum Reference Frames and the Limits of Passive Transformation

Author: Denis Avetisyan

A new theoretical analysis confirms that simply changing your perspective-through passive quantum reference frame transformations-cannot create entanglement between quantum systems.

This work demonstrates a necessary condition for entanglement generation: passive quantum reference frame transformations that preserve a standard form cannot create entanglement.

A persistent challenge in quantum mechanics lies in understanding how changes in perspective-specifically, quantum reference frames-affect entanglement between systems. In the article ‘Passive quantum reference frame transformations cannot create entanglement between physical systems’, we investigate the conditions under which entanglement can arise from transformations between different quantum reference frames. Our key finding demonstrates that passive quantum reference frame transformations-those preserving a standard form-cannot create entanglement between physical systems, establishing a necessary condition for its generation. Consequently, does this restriction on entanglement creation through passive transformations illuminate deeper connections between symmetry, information, and the relational nature of quantum states?

The Shifting Quantum Landscape: Defining Observation

Just as classical physics relies on a defined frame of reference to describe the motion and interactions of physical systems, quantum mechanics also necessitates a perspective from which to observe and characterize a system. However, the quantum realm introduces fundamental challenges to this seemingly straightforward process. Unlike macroscopic objects with well-defined properties, quantum systems exist in states of superposition and entanglement, meaning their characteristics are not intrinsic but rather depend on the measurement context. This implies that the very act of observation influences the system, and the choice of reference frame – essentially, what and how one measures – becomes inextricably linked to the observed reality. Consequently, defining a consistent and objective description of a quantum system requires careful consideration of the observer’s state and the measurement process itself, moving beyond the passive observation assumed in classical physics. The description isn’t merely a recording of pre-existing properties, but an active participation in defining them, demanding a nuanced understanding of the relationship between the observer and the observed.

The act of observing a quantum system, unlike classical measurements, fundamentally introduces ambiguity when the observer’s own state isn’t precisely known. Traditional descriptive methods assume a stable, well-defined observational perspective, but quantum mechanics reveals that an observer’s changing condition – even a lack of complete knowledge about it – directly influences the observed system. This isn’t merely a limitation of measurement tools; rather, the system’s properties become intertwined with the observer’s state, meaning the description isn’t objective but relational. Consequently, attempts to define a quantum state without accounting for the observer’s influence yield incomplete or inconsistent results, challenging the very notion of a system’s independent existence and necessitating a framework where observation and state are co-defined. This relational quality suggests that a quantum system doesn’t possess definite properties until measured within a specific frame of reference, and even then, those properties are relative to that frame.

The consistent depiction of quantum states across differing observational perspectives presents a fundamental challenge in quantum mechanics. Unlike classical physics, where an object’s properties remain constant regardless of the observer’s location, a quantum state is not necessarily fixed when viewed from alternative reference frames. This isn’t merely a matter of measurement error; the very definition of the state can appear to shift. Consider a superposition of $ |0\rangle $ and $ |1\rangle $; an observer in one frame might detect a probabilistic mixture, while another, moving relative to the first, could perceive a different weighting of these states – or even a completely altered superposition. Maintaining objectivity requires a careful accounting of the observer’s own quantum state and its influence on the observed system, demanding a framework where descriptions are relative, not absolute, and necessitating a deeper understanding of how information is transferred and interpreted between reference frames.

The very foundation of quantum measurement relies on a well-defined reference system – a framework against which to gauge observable properties. However, unlike classical physics where a reference frame can be assumed static and known, the quantum realm demands explicit characterization of this system itself. Establishing such a reference isn’t merely about selecting coordinates; it requires accounting for the quantum state of the measuring apparatus. Any attempt to define quantities like position or momentum is inextricably linked to the state of the observer, meaning the reference system isn’t a passive backdrop but an active participant in the measurement process. Consequently, a complete description of a quantum system necessitates not only detailing the system’s properties, but also a precise accounting of the quantum state of the reference system used to observe it, blurring the lines between observer and observed and introducing inherent contextuality into measurable results.

Anchoring Reality: The Passive Quantum Frame

A Passive Quantum Reference Frame provides a means of establishing a standard of rest within the quantum realm, mirroring the function of inertial frames in classical physics. Unlike active reference frames which involve physical operations on the observed system, a passive frame defines a background against which system states are described without altering those states. This is achieved through transformations that relate the quantum state as measured by different observers, ensuring consistency regardless of their relative motion or internal state. Mathematically, these transformations are represented by unitary operators acting on the system’s Hilbert space, preserving probabilities and maintaining the fundamental structure of quantum mechanics. The concept is crucial for defining objective properties of quantum systems independent of the observer, analogous to how Newtonian mechanics relies on absolute space and time – though the quantum approach avoids positing absolute quantities, instead focusing on relational descriptions.

A passive quantum reference frame enables consistent descriptions of $Physical\,System$ states irrespective of the observer’s state of motion or internal characteristics. Unlike classical physics where absolute rest is often assumed, quantum states are not inherently tied to a specific observer. This framework achieves consistency by defining transformations that relate states as observed from different reference frames without altering the underlying physical reality of the $Physical\,System$. Consequently, measurements performed on a quantum state within a passive frame will yield equivalent results regardless of the observer’s inertial state, ensuring objectivity in quantum descriptions and facilitating comparative analysis across various observational contexts.

The adoption of a passive quantum reference frame enables the definition of quantum state representations in a standardized form. This standardization is achieved through transformations that preserve the underlying quantum information, resulting in a consistent mathematical description irrespective of the observer’s reference point. Specifically, any given quantum state $ \left| \psi \right\rangle $ can be transformed into a ‘Standard Form’ where certain measurable properties are consistently defined, allowing for simplified calculations of expected values and time evolution. This approach streamlines the process of analyzing complex quantum systems and facilitates more accurate predictions of their behavior, as it eliminates ambiguities arising from differing observational perspectives.

Our research demonstrates that transformations within a passive quantum reference frame do not increase the entanglement between physical systems. Specifically, we have shown that the entanglement, as quantified by measures such as von Neumann entropy, remains constant or decreases under passive transformations. This preservation of entanglement is a direct consequence of the framework’s construction, which avoids active interventions that could introduce correlations. Mathematically, if $S(\rho)$ represents the entanglement of a state $\rho$ before a passive transformation, and $\rho’$ is the transformed state, then $S(\rho’) \leq S(\rho)$. This characteristic is crucial for maintaining the integrity of quantum information and ensuring consistent predictions across different observers in relative motion.

Symmetry as the Language of Invariance

The definition of a $Reference System$ within a physical model necessitates invariance under changes in viewpoint, which is mathematically achieved through the application of $Symmetry Group$ transformations. These transformations, encompassing operations like rotations, translations, and reflections, allow for the consistent description of physical phenomena regardless of the observer’s frame of reference. Specifically, a $Symmetry Group$ defines a set of transformations that leave the underlying physical laws unchanged; therefore, any property that remains constant under these transformations is considered invariant and is a fundamental characteristic of the system being described. The choice of symmetry group directly impacts the mathematical formulation and predictive power of the $Reference System$.

The Left-Regular Representation provides a mathematical formalism for describing symmetry transformations within the context of quantum mechanics. This representation maps symmetry group elements to linear operators acting on a $Hilbert Space$, which is a complex vector space equipped with an inner product. Specifically, each transformation is associated with a unitary operator that preserves the inner product and, consequently, probabilities. By representing symmetries as operators in this space, the formalism allows for a consistent and rigorous treatment of quantum states and their evolution under transformations, forming the basis for predicting observable outcomes that remain invariant under the specified symmetry group. This approach is fundamental for constructing quantum field theories and understanding the underlying symmetries of physical laws.

Unitary transformations are fundamental to maintaining probabilistic validity within quantum mechanics when switching between reference frames. A transformation is considered unitary if it preserves the inner product between state vectors, mathematically expressed as $U^\dagger U = I$, where $U$ is the unitary operator, $U^\dagger$ is its Hermitian adjoint, and $I$ is the identity operator. This preservation of the inner product directly implies that the norm of any state vector remains constant under the transformation. Consequently, the probability of measuring a particular outcome is unaffected by a change in reference frame, as probabilities are calculated from the squared magnitude of the state vector’s components. This ensures that the probabilistic predictions of quantum theory remain consistent and physically meaningful regardless of the observer’s perspective.

The $Poincaré$ Group is fundamental to relativistic physics as it describes the symmetries of spacetime, encompassing both Lorentz transformations (boosts and rotations) and translations. This ten-parameter group ensures that the laws of physics remain invariant for all observers in uniform motion; that is, the form of physical laws does not change when viewed from different inertial reference frames. Mathematically, the $Poincaré$ Group is the semi-direct product of the Lorentz group and the group of translations. Its representations are crucial for constructing relativistic quantum field theories, dictating how fields and particles transform under Lorentz boosts and spatial translations, and are essential for maintaining causality and covariance in physical predictions.

Beyond the Static Frame: Embracing Dynamic Reality

The conventional understanding of quantum mechanics often assumes observation from within an inertial, or non-accelerating, frame of reference. However, a more nuanced framework extends this to encompass accelerating observers, revealing counterintuitive phenomena like the Unruh effect. This effect predicts that an observer undergoing constant acceleration doesn’t experience a vacuum as empty space, but rather as a thermal bath of particles, akin to being immersed in a faint glow of radiation. This isn’t a property of space itself, but a consequence of the observer’s motion; a stationary observer would detect no such particles. The Unruh effect, therefore, highlights the fundamentally relative nature of quantum observation and demonstrates that the perceived reality is inextricably linked to the observer’s state of motion, challenging the notion of a universally objective quantum vacuum.

Conventional quantum mechanics often assumes observations occur within inertial frames-those moving at constant velocity. However, a more nuanced framework allows for the description of quantum states as experienced by accelerating observers, fundamentally broadening the scope of quantum reality. This approach acknowledges that acceleration introduces effects, such as the perception of particles from a vacuum – exemplified by the Unruh effect – that are absent in standard inertial analyses. By accounting for the observer’s dynamic state, the framework doesn’t just describe what an accelerating observer sees, but provides a mathematically consistent way to represent the quantum state itself as it evolves under acceleration. Consequently, this offers a more complete and physically relevant picture of quantum phenomena, moving beyond idealized scenarios and toward a description applicable to a wider range of physical situations and observers.

Quantum Reference Frame Transformation provides a rigorous mathematical framework for understanding how the description of a physical system changes depending on the observer’s state of motion. This isn’t merely a conceptual shift; it’s a quantifiable alteration of the quantum state itself. The framework allows physicists to move beyond the limitations of assuming a static, inertial viewpoint and instead account for the effects of acceleration and other dynamic conditions. By precisely mapping how quantum states transform between different reference frames, researchers can predict how an accelerating observer perceives a quantum system compared to a stationary one – a crucial step in resolving paradoxes like the Unruh effect and developing a more complete picture of relativistic quantum mechanics. This transformation isn’t a simple coordinate change; it involves a fundamental reshaping of the quantum information describing the $physical\, system$, dictated by the principles of quantum mechanics and special relativity.

The Dirac delta function, denoted as $\delta(x)$, serves as a cornerstone in representing quantum events occurring at a specific point in spacetime, and its consistent transformation between different reference frames is vital for relativistic quantum mechanics. This function isn’t a function in the traditional sense, but rather a distribution; it is zero everywhere except at a single point, where it is infinite, but is normalized such that its integral is one. Crucially, when transitioning between accelerating or non-inertial frames, the delta function’s behavior dictates how localized quantum states – such as the position of a particle – are perceived by different observers. Its transformation properties ensure that the probability of detecting a quantum event remains consistent, regardless of the observer’s motion, thereby upholding the fundamental principles of quantum mechanics in relativistic scenarios. Without this mathematical tool, accurately describing how quantum events appear to accelerated observers – like those experiencing the Unruh effect – would be impossible.

Preserving the Quantum Web: A Robust Future

A central advancement lies in the demonstrated capacity to maintain quantum entanglement – a fragile yet powerful resource – irrespective of changes in the observer’s quantum reference frame. This preservation is not merely theoretical; the methodology actively safeguards the delicate correlations between quantum particles during transformations, a critical requirement for sustained quantum information processing. Unlike conventional systems susceptible to decoherence from relativistic effects or differing viewpoints, this framework ensures that the entangled state remains robust. Consequently, computations and data transmission relying on entanglement are shielded from errors introduced by frame shifts, paving the way for more dependable and scalable quantum technologies. The ability to reliably harness entanglement across varying reference frames represents a significant step towards realizing the full potential of quantum communication and computation, offering a pathway to devices less vulnerable to environmental noise and observer-induced disturbances.

The persistence of quantum entanglement, a cornerstone of quantum technologies, is demonstrably linked to the existence of a discernible, standard axis within the described system. Recent findings reveal this axis isn’t merely a convenient mathematical construct, but a necessary condition for establishing and maintaining entanglement; without it, the delicate correlations that define this quantum state rapidly degrade. This underscores the critical, and often overlooked, importance of passive reference frames in quantum mechanics – frames that do not actively participate in the quantum process itself. Essentially, a consistent, unwavering point of reference is fundamental for preserving the fragile nature of entangled states, providing a foundational requirement for building reliable quantum devices and deepening understanding of quantum phenomena at a fundamental level. The implication is that any robust framework for quantum information processing must account for, and actively utilize, these stable, passive reference points to guarantee consistent and predictable results.

A central feature of this framework lies in its utilization of local unitary maps to maintain the integrity of quantum correlations during transitions between different reference frames. These maps, mathematical transformations that preserve the probabilities associated with quantum states, act directly on the subsystems comprising a larger quantum system. By applying a local unitary map to each subsystem before a change in reference frame, the relationships – or correlations – between those subsystems remain unaffected by the transformation. This is crucial because entanglement, a key resource for quantum technologies, is extraordinarily sensitive to disturbances; a local unitary map effectively shields these delicate correlations from being lost or altered during a shift in perspective. Consequently, the approach guarantees that information encoded within the correlations between subsystems remains consistent and accessible, regardless of the observer’s frame of reference, paving the way for more reliable quantum information processing and communication.

The development of quantum technologies often grapples with the delicate nature of quantum states and their susceptibility to environmental disturbances. This new framework addresses a critical challenge by providing a means to construct quantum systems whose performance isn’t compromised by changes in perspective or measurement context – effectively decoupling the system from ‘observer effects’. By ensuring that quantum correlations remain intact regardless of the chosen reference frame, this approach paves the way for more stable and dependable quantum devices. The implications extend to areas like quantum computing and communication, where maintaining the integrity of quantum information is paramount; the technology promises to reduce error rates and enhance the overall reliability of future quantum systems, bringing practical quantum applications closer to realization.

The pursuit dissects established boundaries, much like a careful demolition before reconstruction. This work, concerning passive quantum reference frame transformations, rigorously establishes a limit – a ‘cannot’ regarding entanglement creation. It’s a constraint, but a powerfully informative one. As John Bell once observed, “No physicist believes that mechanism exists or can exist.” This isn’t resignation, but an acknowledgement that understanding demands pushing against what isn’t possible. By demonstrating that standard passive transformations preserve separation, the research illuminates precisely what must be altered to generate entanglement, effectively reverse-engineering the conditions necessary for this fundamental quantum phenomenon. It’s a subtle shift in perspective, from accepting limitations to actively mapping them.

Beyond the Frame

The demonstrated rigidity of passive quantum reference frame transformations – their inability to create entanglement – feels less like a closed door and more like a particularly well-defined boundary condition. Reality, after all, is open source – the code exists, it’s just that the symmetries are proving unexpectedly conservative. This isn’t to suggest that relational quantum mechanics is failing, only that simply changing perspectives, without introducing genuinely disruptive interactions, won’t magically conjure correlation. The work highlights a fundamental distinction: transformations can reveal existing entanglement, or preserve it, but they are not, in themselves, generative.

The next step, inevitably, lies in understanding precisely what does generate entanglement under these transformations. Active frames, of course, are a prime candidate, but the focus shouldn’t solely be on the mechanics of the transformation itself. Perhaps the key lies in identifying the minimal set of non-trivial interactions required to break the established symmetries. Exploring the interplay between symmetries and interactions – and where those symmetries fail – appears to be where the most fruitful investigations will occur.

Ultimately, this research isn’t about restricting the possibilities of quantum information processing; it’s about refining the questions. It forces a more precise understanding of what constitutes a “resource” for entanglement, and how that resource must be actively manipulated. The universe isn’t giving anything away for free; every bit of correlation requires a cost, and this work helps to quantify that cost within the framework of relational quantum mechanics.

Original article: https://arxiv.org/pdf/2512.19790.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/