A new way to think about quantum machines
Henry Yuen, a professor at Columbia University, is rewriting the rules of computing. He is building a new theory to understand problems where both the inputs and outputs are quantum, revealing surprising connections between cryptography, black holes, and the limits of classical and quantum machines, Qazinform News Agency correspondent reports, citing Quantum Magazine.
At its core, computer science is about turning inputs into outputs. You enter two numbers into a calculator and get their product. Some tasks, like breaking a large number into prime factors, are much harder, but the basic idea is the same: transform information into an answer.
For decades, researchers in computational complexity theory have studied why some problems are harder than others. They found that certain tasks that challenge ordinary computers can be much easier for quantum machines, which use the strange rules of quantum physics.
But according to Yuen, this traditional approach leaves out a bigger question.
In standard theory, problems always begin and end with ordinary data, strings of 0s and 1s. What happens in between can involve quantum methods, but the inputs and outputs stay classical.
Yuen is leading an effort to build a new “fully quantum” theory where both the inputs and outputs are quantum. Traditional theory, he argues, is largely silent on such problems. It may not be enough to understand this new class of tasks.
Quantum envelopes
In classical cryptography, a method called bit commitment works like placing a message in a sealed envelope. It keeps the message secret and prevents changes until it is opened. These systems rely on the idea that certain math problems are too hard to solve.
But if the “envelope” itself is quantum, the rules change. Even unlimited classical computing power might not be enough to break it. The challenge becomes less about math and more about physics.
This raises a major open question: Are classical and fully quantum problems deeply connected, or are they fundamentally different?
Black holes and entangled particles
Yuen and his collaborators have begun mapping this new territory. In a recent paper, they showed that several very different-looking quantum problems are actually equal in difficulty.
At the heart of this discovery is a key idea from quantum information theory known as Uhlmann’s theorem. It deals with entangled particles, which share a linked state. The theorem describes how closely one quantum state can be transformed into another when only limited actions are allowed.
Yuen’s team reframed this as a quantum-to-quantum problem: How hard is it to make that transformation? What tools are required?
Surprisingly, they found that many problems connect back to this same core challenge. One example is decoding Hawking radiation from a black hole. What seems like a problem from space physics turns out to be closely tied to the same transformation question.
Bit commitment, black hole decoding, and compressing quantum information all appear to revolve around the same central task.
For over 30 years, researchers have explored where quantum computers outperform classical ones. Yuen’s goal is broader: to understand whether quantum problems with quantum inputs and outputs form a world of their own.
If they do, complexity theory may need to expand in ways researchers are only beginning to imagine.
Earlier, Qazinform News Agency reported that UAE will build its first space-to-ground quantum communication network.
