Researchers from the Centre for Quantum Technologies and Department of Physics at the National University of Singapore have been studying quantum correlations, a consequence of Bell’s theorem, to understand their power in contrast to Local Hidden Variables (LHV). They have found it challenging to find simple examples of quantum correlations that require more than one bit of communication to simulate. The researchers have also explored what could and could not be simulated with just a single bit of classical communication. Their findings could potentially lead to advancements in quantum technologies and communication systems.
What is the Significance of Quantum Correlations in Communication?
Quantum correlations, a consequence of Bell’s theorem, have been a topic of interest in the field of quantum technologies. These correlations, which cannot be simulated with Local Hidden Variables (LHV) alone, have been studied to understand their power in contrast to LHV and compared to one another. One way to understand this is by determining how much additional resources are needed to supplement LHV in order to simulate these quantum correlations.
The research conducted by Peter Sidajaya and Valerio Scarani from the Centre for Quantum Technologies and Department of Physics at the National University of Singapore, focuses on the amount of communication needed to simulate these quantum correlations. They have found that it has been surprisingly difficult to find simple examples of quantum correlations whose simulation requires more than one bit of communication.
How Does Classical Communication Compare to Quantum Correlations?
The researchers have investigated the average amount of communication needed to simulate the entanglement of a system of a generic dimension. They have also explored what could and could not be simulated with just a single bit of classical communication. For two qubits, 1-bit is provably enough to simulate all the statistics of the maximally entangled state and of a whole range of weakly-entangled states.
However, some researchers have tried to search for a correlation that could not be simulated by 1-bit. These correlations can be sought for in Bell scenarios with mAB inputs and oAB outputs for Alice and Bob. The set of 1-bit correlations forms a polytope akin to the local polytope but includes signalling behaviours and is thus embedded in the full probability space.
What is the Smallest Example of Quantum Correlation?
In their paper, Sidajaya and Scarani report the simplest example to date, which lives in the (5, 2, 5, 5) Bell scenario. The previously known smallest case was living in the (7, 3, 16, 16) scenario. The proof is built on the observation that the maximisation of the 1-bit score is equivalent to finding the best partition in which the sum of the local scores in the two subgames is maximal.
How Can Quantum Correlations be Simulated?
The researchers present a method to find the 1-bit bound that is faster than a brute force approach. They also present their Bell inequality and the corresponding correlation that lies outside the 1-bit polytope. The statistics of interest can be generated by suitable measurements on the maximally entangled state of two five-dimensional systems. This comes within the range of challenging but feasible experimental demonstrations.
What is the Future of Quantum Correlations in Communication?
The research provides a deeper understanding of quantum correlations and their role in communication. Their findings could potentially lead to advancements in quantum technologies and communication systems. However, more research is needed to further explore and understand the complexities of quantum correlations.
A new article titled “Beating one bit of Communication with Quantum Correlations in Smaller Dimension” was published on February 4, 2024. The authors of this study are Peter Sidajaya and Valerio Scarani. The article was published on arXiv, a repository of electronic preprints approved for publication after moderation, hosted by Cornell University. The study can be accessed through the DOI: https://doi.org/10.48550/arxiv.2402.02723.