Virtual broadcast maps can have a significant impact on quantum information processing. Photo by Fractal Hassan/Unsplash
In a new study, scientists have proposed the concept of "virtual quantum broadcasting", which provides a workaround to the long-standing cloning-free theorem, thus opening up new possibilities for the transmission of quantum information.
The study, published in Physical Review Letters, outlines a virtual broadcast map that can be "virtually" created for relevant copies. Through a series of four theorems, the researchers established the feasibility of a graph that could create correlated copies of quantum states over time.
In addition, the researchers demonstrated the robustness of the specification framework, demonstrated its physical approximation to a generic cloner, and detailed how to implement the profile.
Virtual quantum broadcasting is expected to avoid the limitations imposed by the unclonability theorem by leveraging time-based correlations to influence many areas of quantum information processing.
Why can't we copy and paste?
Although quantum mechanics is very powerful, it is built to prevent information from being copied or duplicated. The quantum state encapsulates all the relevant information in the system and collapses or changes into one of the possible outcomes of the measurement when measured or observed.
This means that we can't replicate the state because it needs to be measured to do that. This principle is known as the unclonability theorem. In short, you can't copy and paste quantum information like you would with classical data.
This limitation poses a significant obstacle to quantum communication systems that rely on the efficient transmission and reproduction of quantum information.
The research team, consisting of Professor Arthur Parzygnat of the Massachusetts Institute of Technology, Professor James Fullwood of Hainan University, Professor Francesco Buscemi of Nagoya University, and Professor Giulio Chiribella of the University of Hong Kong, explained their motivations to Phys.org.
They were inspired by this question posed by the unclonability theorem. Their goal is to study the evolution of quantum states over time and understand what "correlation does not mean causation" means for pure quantum states.
Virtual Quantum Broadcasting
"Our solution to this problem is to introduce virtual quantum broadcasting channels, which, while not really a physical process, have many important applications in quantum information processing," explains Professor Parzygnat.
Unlike traditional methods of reproduction, which are prohibited by the unclonability theorem, these virtual broadcast channels or maps operate virtually, meaning they do not involve direct physical copying.
Instead, the diagram establishes correlations between different instances of quantum states, effectively allowing information to be transmitted without violating the fundamental principles of quantum mechanics.
The virtual broadcast map is unique and satisfies the three simple axioms listed by the researchers in Theorem 1. The axioms governing virtual broadcast maps ensure consistency under the following variations:
- Frame of reference.
- Symmetry between the receiving ends.
- The ability to replicate classical information that is not affected by decoherence.
These are the basic requirements for virtual broadcast maps.
The researchers further demonstrated (in Theorem 2) that a physical approximation of this mapping can be created using a universal cloner, a device that can make the most faithful copies of arbitrary quantum states possible.
Next, the researchers showed how to achieve a broadcast graph by decomposition (Theorem 3). It determines that the mapping can be broken down into two operations:
- The measurement and preparation protocol involves performing virtual measurements on a quantum system to create a virtual measurement of a quantum system.
- Next, two copies of the virtual quantum states are generated based on the results of the virtual measurements performed in the previous step.
Finally, they establish (in theorem 4) the equivalence between the action of the temporal evolution function and the action of the virtual broadcast map in an arbitrary state. This means that the virtual broadcast graph behaves like a time operation, allowing the creation of relevant virtual copies of quantum states over time.
"The most intriguing feature of this work is that the diagram has a unique feature of a simple set of natural requirements. That's why we call it canonical. This, in turn, seems to point to an entirely new part of quantum theory, that is, its temporal-like structure remains largely unexplored," explains Professor Buscemi.
Impact on quantum applications
By establishing the virtual quantum broadcast theorem, researchers have brought many new possibilities to quantum computing, quantum information, and quantum cryptography.
"One direction that I find particularly interesting, and which is currently working with Professor Parzygnat, is how a virtual broadcast state might encode measurement statistics for two classes of spatiotemporal separation measurements in a given lab," Professor Fullwood said.
This phenomenon shows that, as mentioned above, the virtual broadcast state captures not only the expected value, but also the probability of the joint measurement result.
This supports the interpretation of virtual broadcasting as a spatiotemporal process that reflects the flow of quantum information over time, "similar to how space-time encapsulates the evolution of space over time," Professor Fallwood added.
The researchers also noted that virtual broadcasting reveals the hidden structures behind many quantum information technologies. Professor Chiribella explains this with an example in the context of quantum communication, "A natural way for eavesdroppers to exploit quantum communication channels is by trying to replicate quantum states. ”
"It turns out that the best approximation to replicate quantum states is to implement a physical approximation of virtual broadcasting. ”
This understanding can enhance security measures in quantum communications by providing insights into potential eavesdropping techniques and their countermeasures.
The researchers point out that we have entered a new field of quantum theory that was previously considered unorthodox or off-limits, such as the direct measurement of the precision of quantum devices allowed by virtual broadcast maps.
"Perhaps the answers to many of the fundamental questions can be found here," Professor Buscemi concluded.
More information: Arthur J. Parzygnat et al., Virtual Quantum Broadcasting, Physical Review Letters (2024). DOI：10.1103/PhysRevLett.132.110203。 On arXiv: DOI:10.48550/arxiv.2310.13049
Journal Information: Physical Review Letters arXiv