A groundbreaking achievement has emerged from the collaborative efforts of researchers at the University of Ottawa, together with Danilo Zia and Fabio Sciarrino from Sapienza University of Rome. Their groundbreaking work introduces an inventive technique that permits the real-time visualization of the wave function of entangled photons. These elementary particles, which constitute the core of light, have been visualized using a unique analogy involving a common object – shoes. Within the realm of quantum mechanics, the concept of entanglement is likened to the act of selecting a shoe at random. The intriguing facet of entanglement draws parallels with identifying one shoe, which in turn instantaneously unveils information about its corresponding pair. What's remarkable is that this holds true regardless of the physical distance that separates them. However, a certain level of uncertainty shrouds this identification process until the precise moment of observation occurs.

At the heart of quantum mechanics lies the concept of the wave function. This concept provides a comprehensive understanding of a particle's quantum state. In the context of the shoe analogy, this “wave function” would encapsulate attributes like left or right orientation, size, color, and other relevant characteristics. The wave function empowers quantum scientists with the ability to predict the probable outcomes of a variety of measurements performed on a quantum entity. These measurements encompass factors such as position, velocity, and more.

This predictive capability holds immense significance, particularly within the swiftly advancing realm of quantum technology. In this context, having an understanding of a quantum state, whether it is generated or input into a quantum computer, facilitates the process of testing the computer itself. Furthermore, the quantum states utilized in quantum computing are notably intricate, often involving numerous entities that exhibit strong non-local correlations—referred to as entanglement.

The task of knowing the wave function of a quantum system of this nature is a formidable one. This is where the concept of quantum state tomography, or quantum tomography for short, comes into play. Conventional approaches, built on projective operations, require an extensive number of measurements. As the complexity of the quantum system increases, so does the number of measurements required, leading to a rapid escalation in complexity.

Previous experiments employing these techniques demonstrated that characterizing or measuring the high-dimensional quantum state of two entangled photons could demand a significant amount of time, potentially stretching to hours or even days. Moreover, the quality of the results obtained is highly susceptible to noise and is contingent on the intricacy of the experimental setup.

The projective measurement approach to quantum tomography can be conceptualized as the process of examining the shadows of a high-dimensional object, projected onto various surfaces from independent perspectives. Researchers can only perceive these shadows, which then allow them to deduce the shape, or state, of the complete object. To draw a parallel, consider the realm of computed tomography (CT) scans, where a three-dimensional object's information is reconstructed using a series of two-dimensional images.

However, in the domain of classical optics, another method exists for reconstructing a three-dimensional object. This technique is known as digital holography, and it revolves around capturing a single image, referred to as an interferogram. This image is obtained by interfering the light scattered by the object with a reference light.

The team, under the leadership of Ebrahim Karimi, who holds the position of Canada Research Chair in Structured Quantum Waves and serves as the co-director of the uOttawa Nexus for Quantum Technologies (NexQT) research institute, expanded upon this concept in the context of pairs of photons.

The process of reconstructing a biphoton state entails overlaying it with a presumably well-known quantum state. Subsequently, the spatial distribution of positions where two photons simultaneously arrive is analyzed. This simultaneous arrival of photons is often referred to as a coincidence image. The photons in question can originate from either the reference source or the unknown source. Quantum mechanics dictates that it's impossible to identify the source of the photons.

This phenomenon results in an interference pattern that holds the key to reconstructing the unknown wave function. Crucially, the success of this experiment was made possible by employing an advanced camera that possesses the capability to record events with nanosecond precision on each individual pixel.

Dr. Alessio D'Errico, a postdoctoral fellow at the University of Ottawa and one of the co-authors of the study, emphasized the immense advantages that this innovative approach offers. Notably, this method stands as an exponential improvement over previous techniques, as it demands only minutes or seconds rather than the protracted timeline of days. Additionally, the detection time remains unaffected by the complexity of the quantum system, effectively resolving the long-standing challenge of scalability associated with projective tomography.

The implications of this research stretch far beyond the boundaries of academia. The potential ramifications encompass the acceleration of quantum technology advancements, including enhanced quantum state characterization, improvements in quantum communication, and the development of novel quantum imaging methodologies.

The results of this pioneering study, titled “Interferometric imaging of amplitude and phase of spatial biphoton states,” have been published in the esteemed journal Nature Photonics.

Source: University of Ottawa