Some Results in Quantum Information Theory

Omar Fawzi

Shai Machnes

Developing intuition about quantum information theory problems is difficult, as is verifying or ruling-out of hypothesis. We present a Matlab package intended to provide the QIT community with a new and powerful tool-set for quantum information theory calculations. The package covers most of the "QI textbook" and includes novel parametrization of quantum objects and a robust optimization mechanism. New ways of re-examining well-known results is demonstrated. QLib is designed to be further developed and enhanced by the community and is available for download at www.qlib.info

Nicolas C. Menicucci

Giacomo Mauro D’Ariano, Giulio Chiribella, Paolo Perinotti

Quantum information theory is a wide area of investigation, which includes two main subjects: quantum computation and quantum communication. The success of quantum computation theory is due to a positive result: Shor's algorithm. The algorithm provides factorization of integers in a much more efficient way with respect to what is achieved not only by present-day computers, but even by the most powerful conceivable computers based on classical physics. On the other hand, the success of quantum communication is due to the intrinsic security of ideal quantum cryptographic protocols, and thus relies on a negative result, that is the impossibility of reading quantum information without scrambling it in an unrecoverable way. The no information without disturbance property spawns other no-go theorems, which represent some of the most famous and classic results in quantum information theory. Among these results one can certainly list the no-cloning theorem, stating the impossibility of copying quantum information. This impossibility is clearly a consequence of the impossibility of extracting information without disturbing it. Indeed, if we could copy exactly the state of a system, reproducing it on another system of the same type, then we would also be able to iterate this process, and produce as many copies as we want. We could then extract all the information we are interested in from the copies, keeping the original intact. This argument is so simple, but hides a very deep point about quantum information, and more generally about any type of information that can be purified. Suppose indeed that there exists a measurement allowing us to determine the state of a system, with absolute precision. We could then use such a measurement on the system, and once we know its exact state, we can in principle re-prepare the same state as many times as we want. If copying the state is forbidden within a theory, we must then conclude that, in that theory, measuring the state is forbidden, too! This is exactly the case in theories with purification, and in particular in quantum theory. In quantum theory, determining the state of a system is impossible. We can only have some information about what state our system is prepared in. The information may be accurate, but it will never be certain. This could be practically the case in classical theory, too.

Guillaume Aubrun, Stanisław Szarek

Fatemeh Moradi Kalarde, Xiangling Xu, Marc-Olivier Renou

The manuscript [arXiv:2603.19208] proposes a physically motivated postulate to select the appropriate formulation of quantum theory over real Hilbert spaces, ruling out the theory considered in [Nature 600, 625-629 (2021)] in favour of an alternative theory which reproduces the predictions of standard complex quantum information theory. Here, we argue that, to qualify as a general physical principle, this postulate should also hold in fermionic quantum information theory, the standard framework describing information encoded in the presence or absence of identical fermions. We show, however, that it fails in this framework. More broadly, our result highlights the importance of confronting proposed foundational principles with fermionic quantum information theory, a point that also deserves further examination in recent related works such as [arXiv:2503.17307] and [arXiv:2504.02808].