Quantum States Encode Information With Real Numbers, Complex Numbers Not Required

Researchers from the German Aerospace Center (DLR) and Heinrich Heine University Düsseldorf (HHU) have challenged a long-held assumption in quantum mechanics, demonstrating the theory doesn’t necessarily require the use of complex numbers. Publishing their findings in Physical Review Letters, the team revealed quantum states, traditionally described with both real and imaginary components, can be encoded using only real numbers. This alternative formulation maintains experimental consistency with standard quantum mechanics, suggesting imaginary numbers may be a practical calculation tool rather than a fundamental necessity. “This means that both frameworks yield identical predictions for any conceivable experiment,” explains Professor Dr. Dagmar Bruß, indicating that within this framework, imaginary numbers can be replaced with real number formulations; the American Physical Society has recognized the significance of this work with a “Highlight” feature in Physics Magazine.

Real Number Formulation Challenges Standard Quantum Postulates

This alternative formulation doesn’t discard established quantum predictions, but rather re-examines the underlying postulates upon which the theory is built, specifically addressing limitations within a 2023 study by Renou et al. published in Nature 600, 625. The team, led by Professor Dr. Dagmar Bruß and doctoral researcher Pedro Barrios Hita, identified a more flexible approach to formalizing how quantum systems combine, opening the door to a real-number-based quantum framework. Traditionally, quantum states are defined by both a real component representing amplitude and an imaginary component representing phase; this construct has been considered essential for describing processes like quantum entanglement and coherence, crucial for emerging technologies such as quantum computers and secure communication. Their findings, published in Physical Review Letters, detail a physically motivated alternative to the previously restrictive postulates, allowing for a consistent description of quantum mechanics using only real numbers.

The significance of this research has been recognized by the American Physical Society, which featured the work as a “Highlight” in its Physics Magazine, signaling its importance to the broader physics community. It offers a different, potentially more intuitive, way to understand the quantum world, suggesting imaginary numbers are not fundamentally required and can, in principle, be replaced by alternative formulations utilizing only real numbers.

Entanglement and Coherence in Microscopic Quantum Phenomena

The exploration of microscopic quantum phenomena centers on refining our understanding of entanglement and coherence, properties vital for emerging technologies like quantum computing and secure communication. Researchers are increasingly focused on the mathematical frameworks used to describe these effects, questioning long-held assumptions about the necessity of complex numbers in quantum mechanics. Traditionally, quantum states rely on both real and imaginary numbers, with the imaginary component representing the crucial “phase” of a quantum particle, but recent work challenges this reliance, suggesting alternative formulations are possible. This investigation stemmed from a prior study published in Nature which concluded complex numbers were essential under standard postulates (Renou et al., Nature 600, 625 (2023)); however, Professor Dr. Bruß and her team identified a more flexible approach. The implications extend beyond purely theoretical considerations; a formulation based on real numbers could simplify certain quantum calculations and potentially unlock new avenues for manipulating quantum states.

While the practical impact remains to be seen, this work signifies a shift in perspective, suggesting that the mathematical tools we use to describe the quantum world may not be as fixed as previously believed, and that alternative, equally accurate descriptions are within reach. The team’s findings offer a new lens through which to examine the foundations of quantum mechanics and its applications.