Physicists reveal universal speed limit on quantum information scrambling

Theoretical physicists in the US have discovered a "speed limit" on the time taken for quantum information to spread through larger systems. Publishing their results in Physical Review Letters, Amit Vikram and colleagues at the University of Maryland have proved for the first time that this minimum time is closely linked with a system's entropy and temperature, perhaps paving the way for a deeper understanding of quantum information across a wide range of physical settings.

Sharing information

In 1974, Stephen Hawking proposed for the first time that black holes aren't entirely black. As well as emitting thermal radiation (now known as "Hawking radiation"), they also exhibit thermodynamic properties including temperature and an entropy proportional to their surface area.

Since entropy is a measure of the information carried by a system, this means a black hole's surface effectively stores a finite number of "qubits": the quantum equivalent of classical bits, each capable of storing quantum information as a superposition of two states simultaneously. In this way, the black hole's temperature as described by Hawking governs how these qubits interact and evolve over time.

In 2008, theoretical physicists Yasuhiro Sekino and Leonard Susskind took this idea a step beyond the abstract black hole picture. In the duo's conjecture, "systems of qubits at a certain temperature may take a minimum amount of time to share information with each other, which depends on the number of qubits and the temperature," Vikram explains. "This sharing of information is called 'scrambling,' and it effectively 'spreads' the information in each particle across the full system."

Searching for a speed limit

In the years since Sekino and Susskind's conjecture, theorists have studied the scrambling of quantum information in extensive detail. But one aspect of the concept that eluded mathematically exact predictions was the idea of a temperature-dependent "speed limit" on the scrambling process itself.

In 2024, Vikram and Victor Galitski at the University of Maryland revisited the idea through the lens of the energy-time uncertainty principle: a cornerstone of quantum theory which posits the more that is known about the energy of a quantum system, the less is known about the minimum time needed for it to change into a distinguishably different state, and vice versa. As a result, there is a minimum time needed for quantum systems to change, imposed by their well-defined energy levels.

"We developed our version to provide a speed limit on the scrambling process," Vikram continues. "But our previous version could not be applied directly here, and we had to find a way to introduce a temperature dependence, and use certain rigorous mathematical bounds to translate that into a speed limit."

Linking with temperature and entropy

In their latest study, Vikram and Galitski expanded their theory further with insights from mathematician Laura Shou. Through their analysis, the trio concluded a clear relationship between the final entropy, the initial temperature, and the time taken to scramble a given number of units of quantum information.

"We show that this kind of exact entropy- and temperature-dependent speed limit exists in every quantum system, where the previous expectation was that such speed limits only exist for systems in which each interaction only involves a few particles talking to each other," Vikram explains.

With a deeper understanding of this speed limit, theorists could be far better placed to understand the emergence of thermal behavior in large-scale quantum systems, including emerging architectures for quantum computing and information processing. Even further, the result could be used to explore concepts from the origins of some forms of chaos, to the possibility of practical technologies for quantum teleportation, alongside more concrete theories of black hole radiation.

"Our result implies that whichever quantum system one considers, all these processes related to scrambling can fundamentally settle in only after a certain minimum time, which we show how to rigorously calculate in general," says Vikram.