Researchers Create Anti-Clockwise Twists in Light Beams, Paving the Way for Quantum Backflow

University of Warsaw physicists achieve a breakthrough in optics, superposing light beams to observe counterintuitive phenomena.

In a groundbreaking study published in the prestigious journal “Optica,” researchers at the University of Warsaw’s Faculty of Physics have successfully superposed two light beams twisted in the clockwise direction, resulting in the creation of anti-clockwise twists in the dark regions of the superposition. This discovery holds significant implications for the study of light-matter interactions and represents a crucial step towards the observation of a peculiar phenomenon known as quantum backflow.

The Nature of Quantum Backflow:

Quantum mechanics introduces a level of complexity when dealing with particles. Unlike classical mechanics, where objects have known positions, quantum particles can exist in multiple positions simultaneously, a state known as superposition. This superposition allows quantum particles to exhibit peculiar behaviors, including the possibility of moving backward or spinning in the opposite direction during certain time periods. This phenomenon, known as backflow, has long fascinated physicists.

Backflow in Classical Optics:

While backflow in quantum systems has not been directly observed, researchers have successfully achieved it in classical optics using beams of light. Theoretical works by Yakir Aharonov, Michael V. Berry, and Sandu Popescu explored the connection between backflow in quantum mechanics and the anomalous behavior of optical waves on a local scale. Optical backflow was first observed by Y. Eliezer et al. through the synthesis of a complex wavefront. Building upon this work, Dr. Anat Daniel et al. from Dr. Radek Lapkiewicz’s group demonstrated this phenomenon in one dimension using the interference of two beams.

The Study: Azimuthal Backflow in Light:

In their latest publication, “Azimuthal backflow in light carrying orbital angular momentum,” the researchers from the University of Warsaw’s Faculty of Physics showcased the backflow effect in two dimensions. By superposing two beams of light twisted in a clockwise direction, they observed counterclockwise twists in the dark regions of the interference pattern. To observe this phenomenon, the researchers utilized a Shack-Hartman wavefront sensor, a system that provides high sensitivity for two-dimensional spatial measurements.

Applications and Implications:

The discovery of backflow in light has significant implications for various fields, including optical trapping, ultra-precise atomic clocks, and the design of super-resolution microscopy techniques. Light beams with azimuthal phase dependence, carrying orbital angular momentum, have already found applications in optical microscopy and optical tweezers, a tool that allows the manipulation of objects at the micro- and nanoscale. This breakthrough paves the way for further exploration of light-matter interactions and the potential development of advanced technologies.

Superoscillations and Playing Beethoven:

The researchers also noted that their demonstration can be interpreted as superoscillations in phase. Superoscillation refers to situations where the local oscillation of a superposition is faster than its fastest Fourier component. This phenomenon was first predicted by Yakir Aharonov and Sandu Popescu in 1990. Professor Michael Berry later illustrated the power of superoscillation by showing that it is theoretically possible to play Beethoven’s Ninth Symphony using only sound waves with frequencies below 1 Hertz. However, the amplitude of waves in the super-oscillatory regions is extremely small, making this application highly impractical.


The University of Warsaw’s Faculty of Physics has achieved a significant milestone in the field of optics with the observation of azimuthal backflow in light. By superposing twisted light beams, the researchers have demonstrated a counterintuitive phenomenon that could revolutionize our understanding of light-matter interactions. This breakthrough opens doors to new applications in optical trapping, atomic clocks, and super-resolution microscopy. Furthermore, the study provides valuable insights into the intriguing connection between backflow in quantum mechanics and superoscillations in waves. As researchers continue to unravel the mysteries of light, the possibilities for technological advancements and scientific discoveries are boundless.

Quantum Computing: Unlocking the Power of the Quantum Frontier

Exploring the Potential and Challenges of Quantum Computing

In the realm of computing, a new frontier is emerging—one that promises to revolutionize the way we solve complex problems. Quantum computing, a field that harnesses the counterintuitive laws of quantum physics, holds the key to unlocking unprecedented computational power. With the ability to solve problems that are beyond the reach of classical computers, quantum computing is poised to transform fields such as cryptography, simulation, and sensing. In this article, we delve into the intricacies of quantum computing, exploring its underlying principles, potential applications, and the challenges that lie ahead.

The Power of Quantum Computing: Superposition, Interference, and Entanglement

At the heart of quantum computing lies the quantum bit, or qubit. Unlike classical bits, which can only exist in states of 0 or 1, a qubit can exist in a state that is a combination of both. This property, known as superposition, allows quantum computers to perform calculations in parallel, exponentially increasing their computational power with each additional qubit. However, the true power of quantum computing comes from the interplay of superposition, interference, and entanglement. Interference allows qubits to combine constructively or destructively, amplifying correct solutions and suppressing wrong answers. Entanglement, on the other hand, establishes a unique correlation between qubits, enabling computational speed-ups that surpass classical computers.

Applications of Quantum Computing: Cryptography, Simulation, and Sensing

Quantum computing has the potential to revolutionize fields such as cryptography, simulation, and sensing. In the realm of cryptography, quantum computers pose both an opportunity and a challenge. They have the potential to crack current encryption algorithms, necessitating the development of post-quantum cryptography. The National Institute of Standards and Technology has already selected quantum-resistant algorithms to prepare for the future. Quantum Helical Piers simulation, envisioned by physicist Richard Feynman, offers the ability to predict outcomes in the quantum realm, advancing fields such as chemistry and materials science. Quantum sensing, with its enhanced sensitivity and precision, has applications in environmental monitoring, medical imaging, and more.

Bridging the Quantum and Classical Worlds: Quantum Internet and Cryptography

Initiatives such as the development of a quantum internet aim to bridge the gap between quantum and classical computing. A quantum internet would enable the interconnection of quantum computers and could be secured using quantum cryptographic protocols like quantum key distribution. These protocols provide ultra-secure communication channels that are resistant to computational attacks, including those using quantum computers. While the field of quantum computing continues to evolve, the development of new algorithms, particularly in machine learning, remains a critical area of research.

Overcoming Challenges: Decoherence and Error Correction

Despite the promising potential of quantum computing, there are significant challenges to overcome. Quantum computers are highly sensitive to their environments, leading to decoherence, where qubits rapidly lose their quantum states. Building large-scale quantum computing systems requires effective methods of suppressing and correcting quantum errors. Research in hardware and software development, led by startups and industry giants like Google and IBM, aims to overcome these challenges and deliver on the promise of quantum speed-ups.


Quantum computing represents a new frontier in scientific and technological innovation. With its ability to solve problems beyond the reach of classical computers, quantum computing holds the potential to revolutionize fields such as cryptography, simulation, and sensing. While practical applications are still emerging, the field is at a crucial juncture, with early signs of quantum advantage being demonstrated. Ongoing research, collaboration between academia and industry, and the enthusiasm of the next generation of scientists ensure that the field of quantum computing will continue to progress. As we navigate the challenges ahead, quantum computing may soon become as disruptive as the arrival of generative AI, ushering in a new era of computational power.

Exploring the Intricacies of Quantum Mechanics: Unveiling the Secrets of the Microscopic World

Understanding the Wave-Particle Duality and Quanta

Quantum mechanics, the branch of physics that unravels the mysteries of the microscopic world, has revolutionized our understanding of atomic and subatomic particles. By introducing concepts like wave-particle duality and quantization, this theory has challenged traditional notions of how particles behave. In this article, we will delve into the fundamental principles of quantum mechanics, exploring its implications and the impact it has had on scientific progress and technological advancements.

Wave-Particle Duality and Quanta

At the heart of quantum mechanics lies the concept of wave-particle duality, which suggests that objects at the quantum level can exhibit both particle-like and wave-like properties. This duality is particularly evident in the behavior of quanta, the smallest discrete units of natural phenomena in a bound state. For instance, photons, the quanta of electromagnetic radiation, can exhibit both particle and wave characteristics.

Quantization in Quantum Mechanics

Quantization, a key principle in quantum mechanics, refers to the restriction of certain properties, such as energy and momentum, to discrete values for particles in a bound state. Unlike macroscopic objects, whose properties can vary continuously, particles at the quantum level can only possess specific energy levels. This phenomenon explains the discrete energy levels of electrons in an atom, laying the foundation for understanding atomic structure.

Wave Functions and the Quantum World

In quantum mechanics, particles can also be described as waves through the use of wave functions. These mathematical representations define the probability distribution of a particle’s position, momentum, and other properties. Just as waves in the macroscopic world constantly shift and change, so do the wave functions of quantum particles, reflecting their inherent uncertainty.

Quantum vs. Classical Mechanics

Quantum mechanics stands in stark contrast to classical mechanics, which governs the behavior of macroscopic objects. While classical mechanics describes the world we perceive with our senses, quantum mechanics unveils the peculiar behavior of particles at the microscopic level. The development of quantum mechanics was driven by the need to reconcile the discrepancies between classical physics and experimental observations.

Quantum Mechanics and Scientific Progress

The emergence of quantum mechanics in the early 20th century revolutionized our understanding of the physical world. It provided explanations for phenomena that classical physics couldn’t account for, such as blackbody radiation and the photoelectric effect. Quantum mechanics offered a comprehensive framework that reconciled the wave-particle duality and paved the way for further scientific exploration.

Impact on Science and Technology

The impact of quantum mechanics extends far beyond theoretical physics. It has led to groundbreaking technological advancements, including the development of lasers, transistors, and medical imaging devices. Modern devices like smartphones rely on the wave nature of electrons, a concept understood through quantum mechanics. Furthermore, the emerging fields of quantum computing and quantum networks harness the quantized nature of particles to store and transfer information.


Quantum mechanics has unraveled the enigmatic behavior of particles at the atomic and subatomic level, challenging our preconceived notions of the physical world. Through the concepts of wave-particle duality and quantization, this theory has not only deepened our understanding of nature but also paved the way for numerous scientific and technological breakthroughs. As we continue to explore the intricacies of quantum mechanics, new possibilities and applications are bound to emerge, reshaping our future in ways we have yet to imagine.

Uncertainty beyond the Uncertainty Principle

Extending the Wigner-Araki-Yanase Theorem to Continuous and Unbounded Observables

In the world of quantum mechanics, Heisenberg’s uncertainty principle has long been a fundamental concept, dictating that the precision with which two observables can be measured simultaneously is limited. However, a new extension to an old theory, known as the Wigner-Araki-Yanase (WAY) theorem, challenges this notion even further. According to this theorem, if two observables do not commute and one of them is conserved, the other cannot be measured with arbitrary precision, even if the conserved observable is not measured at all.

For decades, the WAY theorem has been applied to observables with discrete and bounded values, such as spin. However, Yui Kuramochi of Kyushu University and Hiroyasu Tajima of the University of Electro-Communications have recently proven that the WAY theorem also encompasses observables that are continuous and unbounded, such as position. This breakthrough not only resolves a long-standing problem in quantum mechanics but also holds promise for practical applications in quantum optics.

The Challenge of Extending the WAY Theorem

The challenge in extending the WAY theorem to continuous and unbounded observables lies in how to represent an unbounded observable mathematically. Kuramochi and Tajima tackled this problem by avoiding direct consideration of the unbounded observable, instead focusing on an exponential function derived from it. This exponential function forms a one-parameter unitary group, with its spectrum of eigenvalues contained within the complex plane’s unit circle. By leveraging this boundedness, the researchers were able to apply existing quantum information techniques to complete their proof.

Implications for Position and Momentum Measurements

One of the significant implications of the extended WAY theorem is that it imposes limits on the precision with which a particle’s position can be measured, even if its momentum is not measured simultaneously. This finding challenges the conventional understanding derived from Heisenberg’s uncertainty principle, which suggests that the precision of one observable can be improved by not measuring the other. The extended WAY theorem highlights the intrinsic limitations of measuring certain observables, even in the absence of simultaneous measurements.

Applications in Quantum Optics

Beyond its theoretical implications, the extended WAY theorem holds practical value in the field of quantum optics. Quantum versions of transmission protocols often involve pairs of observables, similar to position and momentum, that do not commute. Kuramochi and Tajima’s theorem could provide a framework for setting limits on the performance of quantum transmission protocols compared to classical ones. By understanding the fundamental limitations imposed by the extended WAY theorem, researchers can better design and optimize quantum communication systems.

Future Directions and Impact

The extension of the WAY theorem to continuous and unbounded observables opens up new avenues for research in quantum mechanics. This breakthrough not only expands our understanding of the fundamental principles governing quantum systems but also paves the way for practical applications in various fields, including quantum optics and quantum information processing. The implications of the extended WAY theorem may lead to the development of more robust quantum technologies and a deeper understanding of the fundamental nature of the quantum world.


The extension of the Wigner-Araki-Yanase theorem to continuous and unbounded observables represents a significant advancement in quantum mechanics. The work of Kuramochi and Tajima not only resolves a long-standing problem but also offers practical applications in quantum optics. By demonstrating the limitations of measuring certain observables, even in the absence of simultaneous measurements, this theorem challenges the conventional understanding derived from Heisenberg’s uncertainty principle. As researchers continue to explore the implications of the extended WAY theorem, we can expect further advancements in quantum technologies and a deeper understanding of the intricacies of the quantum world.

Certified Entangled: Physicists Develop a Method to Recover Quantum Entanglement

Researchers refine entanglement certification strategies to recover initial entanglement, challenging the need for complete trust in quantum state sources.

Quantum entanglement, a phenomenon that has perplexed scientists for decades, plays a crucial role in various fields, from quantum communication to quantum computation. However, certifying entanglement in a quantum system has always posed a challenge, as traditional testing methods destroy the entanglement in the process. But now, physicists from the Korea Advanced Institute of Science and Technology (KAIST) have developed a groundbreaking technique that allows for the recovery of entanglement after certification, eliminating the need for complete trust in quantum state sources.

A Mysterious State with a Precise Definition:

Entanglement, a concept within quantum mechanics, refers to the inseparable connection between two or more quantum systems. In an entangled system, the subsystems cannot be seen as independent entities, leading to the famous adage that “the whole is greater than its parts.” Certifying entanglement is crucial for researchers working in the field, as it provides a way to verify the existence of this mysterious state.

Refining Entanglement Certification Strategies:

The KAIST team, led by physicist Hyeon-Jin Kim, focused on refining conventional entanglement certification (EC) strategies to recover entanglement post-certification. Conventionally, there are three EC strategies: witnessing, steering, and Bell nonlocality. Each strategy involves deriving inequalities that, if violated, certify the presence of entanglement. However, these strategies typically result in the complete destruction of the initial entanglement.

The Key to Recovery: Weak Measurement:

To overcome the challenge of recovering entanglement, the researchers introduced weak measurement into the certification process. Weak measurement is a process that probes a quantum system without sharply disturbing its subsystems, allowing them to remain entangled. In contrast, projective measurements, commonly used in conventional EC strategies, completely destroy entanglement.

The KAIST team incorporated a control parameter for the strength of measurement on each subsystem and re-derived the certifying inequality to include these parameters. By iteratively preparing the qubit system in the state to be certified and performing weak measurements, they collected statistics to check for the violation of the certification inequality. Once a violation occurred, indicating the presence of entanglement, they further implemented suitable weak measurements to recover the initial entangled state with some probability.

Lifting the Trust Assumption:

The researchers demonstrated their theoretical proposal using a photonic setup called a Sagnac interferometer. They found that as the measurement strength increased, the reversibility of entanglement decreased, but the certification level remained high. This suggests the existence of a measurement strength “sweet spot” where entanglement could be certified without significant loss and subsequently recovered.

In real-world experiments, trusting the entanglement source to consistently produce the same state becomes challenging. The KAIST team tackled this issue by applying their method to a noisy source that produced a mixture of an entangled and a separable state over time. By employing weak measurements at different time steps, they successfully certified and recovered entanglement from the mixture, eliminating the need for complete trust in the source.


The breakthrough by the KAIST physicists in developing a method to recover entanglement after certification represents a significant advancement in the field of quantum entanglement. By incorporating weak measurements and refining certification strategies, they have challenged the traditional notion that entanglement must be destroyed to be certified. This research opens up new possibilities for harnessing entanglement in practical applications, paving the way for more secure quantum communication and enhanced quantum computing capabilities.