Bartosz Regula from the RIKEN Center for Quantum Computing and Ludovico Lami from the University of Amsterdam have shown, through probabilistic calculations, that there may be indeed, as had been hypothesized, a rule of “entropy” for the phenomenon of quantum entanglement. This finding could help drive a greater understanding of quantum entanglement, which is a key resource that underlies much of the facility of future quantum computers. Little is currently understood concerning the optimal ways to make an efficient use of it, despite it being the main target of research in quantum information science for a long time.
The second law of thermodynamics, which says that a system can never move to a state with lower “entropy,” or order, is one of the crucial fundamental laws of nature, and lies on the very heart of physics. It’s what creates the “arrow of time,” and tells us the remarkable proven fact that the dynamics of general physical systems, even extremely complex ones equivalent to gases or black holes, are encapsulated by a single function, its “entropy.”
There may be a complication, nonetheless. The principle of entropy is understood to use to all classical systems, but today we’re increasingly exploring the quantum world. We at the moment are going through a quantum revolution, and it becomes crucially essential to know how we will extract and transform the expensive and fragile quantum resources. Particularly, quantum entanglement, which allows for significant benefits in communication, computation, and cryptography, is crucial, but because of its extremely complex structure, efficiently manipulating it and even understanding its basic properties is usually far more difficult than within the case of thermodynamics.
The issue lies within the proven fact that such a “second law” for quantum entanglement would require us to indicate that entanglement transformations will be made reversible, identical to work and warmth will be interconverted in thermodynamics. It is understood that reversibility of entanglement is far more difficult to make sure than the reversibility of thermodynamic transformations, and all previous attempts at establishing any type of a reversible theory of entanglement have failed. It was even suspected that entanglement might actually be irreversible, making the hunt an unimaginable one.
Of their latest work, published in Nature Communications, the authors solve this long-standing conjecture by utilizing “probabilistic” entanglement transformations, that are only guaranteed to achieve success among the time, but which, in return, provide an increased power in converting quantum systems. Under such processes, the authors show that it’s indeed possible to determine a reversible framework for entanglement manipulation, thus identifying a setting by which a novel “entropy of entanglement” emerges and all entanglement transformations are governed by a single quantity. The methods they used may very well be applied more broadly, showing similar reversibility properties also for more general quantum resources.
In response to Regula, “Our findings mark significant progress in understanding the essential properties of entanglement, revealing fundamental connections between entanglement and thermodynamics, and crucially, providing a significant simplification within the understanding of entanglement conversion processes. This not only has immediate and direct applications within the foundations of quantum theory, but it would also help with understanding the final word limitations on our ability to efficiently manipulate entanglement in practice.”
Looking toward the longer term, he continues, “Our work serves because the very first evidence that reversibility is an achievable phenomenon in entanglement theory. Nevertheless, even stronger types of reversibility have been conjectured, and there may be hope that entanglement will be made reversible even under weaker assumptions than we’ve got made in our work — notably, without having to depend on probabilistic transformations. The problem is that answering these questions appears significantly tougher, requiring the answer of mathematical and information-theoretic problems which have evaded all attempts at solving them so far. Understanding the precise requirements for reversibility to carry thus stays a captivating open problem.”
