A research team led by assistant professor Kang Hao Cheong at the Singapore University of Technology and Design (SUTD) has attempted to use concepts from quantum Parrondo’s paradox in pursuit of a working protocol for semiclassical encryption.
The study discovered the chaotic switching for quantum coin Parrondo’s games have similar underlying ideas and working dynamics to encryption. The study titled “Chaotic switching for quantum coin Parrondo's games with application to encryption” was published in the journal Physical Review Research Letter.
Parrondo’s paradox is a phenomenon that leads to a winning outcome from switching between two losing games. The authors introduce the two-sided quantum coin-tossing game that was presented in previous work that random and particular periodic tossing of two quantum coins can turn quantum walkers’ expected position from a losing position into a fair winning position, respectively.
In this game, the quantum walker is given a set of instructions on the method to move based on the results of the quantum coin toss.
After drawing inspiration from the underlying principles of this quantum game, the lead author of the study, Joel Lai from SUTD, detailed, “Suppose I present to you the outcome of the quantum walker at the end of 100 coin tosses, knowing the initial position, can you tell me the sequence of tosses that lead to this outcome?” This task can either be very easy or very difficult.
In the case of random switching, it is almost impossible to determine the sequence of tosses that lead to the end result. However, for periodic tossing, we could get the sequence of tosses rather easily, because a periodic sequence has structure and is deterministic.
Joel Lai, Study Lead Author, Singapore University of Technology and Design
High uncertainty can be experienced in random sequencing. By contrast, periodic sequences are deterministic. This resulted in the option of combining chaotic sequences as a means to perform switching. The researchers found that the use of chaotic switching via a pre-generated chaotic sequence remarkably improved the work.
In the case of an observer who is unaware of parts of the needed information to produce the chaotic sequence, deciphering the sequence of tosses is similar to identifying a random sequence. But for an agent who has data related to ways of generating the chaotic sequence, it is similar to a periodic sequence.
The researchers note that the data on generating the chaotic sequence is analogous to the keys in encryption. By merely knowing the keys and the outcome (i.e. the encrypted message), these results can be inverted to get the original state of the quantum walker (i.e. the original message).
The introduction of chaotic switching, when combined with Parrondo’s paradox, extends the application of Parrondo’s paradox from simply a mathematical tool used in quantum information for classification or identification of the initial state and final outcome to one that has real-world engineering applications
Kang Hao Cheong, Study Senior Author and Assistant Professor, Singapore University of Technology and Design
Lai, J W & Cheong, K H (2021) Chaotic switching for quantum coin Parrondo’s games with application to encryption. Physical Review Research. doi.org/10.1103/PhysRevResearch.3.L022019.