Heisenberg's uncertainty principle and recently derived many no-go theorems including the no-cloning theorem and the no-deleting theorem have corroborated the idea that we can never access quantum information without causing disturbance. Here we disprove this presumption by predicting a novel phenomenon, `quantum catalysis of information,' where a system enables an otherwise impossible task by exchanging information through a quantum communication channel. This fact implies that making use of quantum information does not always cause disturbance.
Heisenberg's uncertainty principle and recently derived many no-go theorems including the no-cloning theorem and the no-deleting theorem have corroborated the idea that we can never access quantum information without causing disturbance. Here we disprove this presumption by predicting a novel phenomenon, `quantum catalysis of information,' where a system enables an otherwise impossible task by exchanging information through a quantum communication channel. This fact implies that making use of quantum information does not always cause disturbance.
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.
From the early days of quantum theory, it is felt that the classical ideas about information may need reorientation under a quantum theoretical framework. In quantum theory, where Heisenberg uncertainty principle is the guiding philosophy, a non-commuting observable cannot simultaneously have precisely defined values. In fact, if two observations do not commute, performing a measurement of one observable will necessarily influence the outcome of a subsequent measurement of the other observable. Hence, the act of acquiring information about a physical system inevitably disturbs the state of the system. This is because of the fact that the outcome of a measurement has some random elements due to uncertainty of the initial state of the system. Moreover, acquiring information causes a disturbance, and due to this disturbance the information cannot be copied with perfect fidelity. The information under this framework is termed as quantum information [1].
A branch of quantum information is concerned with transformations that are possible given certain resources: for example, quantum teleportation moves a quantum state from one place to another, aided by entanglement and classical communication. Certain other tasks are provably impossible. But, as surveyed in this review, a surprising fact is that some tasks become possible if another quantum state is present, even if this state is returned untouched at the end of the task. This ``quantum catalysis'' enables a large variety of interesting tasks, with applications ranging from cryptography to thermodynamics.
It is known that the stronger no-cloning theorem and the no-deleting theorem taken together provide the permanence property of quantum information. Also, it is known that the violation of the no-deletion theorem would imply signalling. Here, we show that the violation of the stronger no-cloning theorem could lead to signalling. Furthermore, we prove the stronger no-cloning theorem from the conservation of quantum information. These observations imply that the permanence property of quantum information is connected to the no-signalling and the conservation of quantum information.
Randomness can help one to implement quantum maps that cannot be realized in a deterministic fashion.Recently, it was discovered that explicitly treating a randomness source as a quantum system could double the efficiency as a catalyst for some tasks.In this work, we first show that every quantum channel that can be implemented with a randomness source without leaking information to it must be a catalysis.For that purpose, we prove a new no-go theorem that generalizes the no-hiding theorem, the no-secret theorem that states no quantum information can be shared with other systems as a secret without leaking some information.Second, we show that nondegenerate catalysts should be used classically when no extra dimension is allowed, which leads to the fact that the quantum advantage of a catalytic process strictly comes from the uniformness of the randomness source.Finally, we discuss a method to circumvent the previous result that achieves quantum advantage with nondegenerate catalyst uniformized by employing extra work space.
Abstract: Quantum mechanics, to the broader public, is often introduced through its seemingly paradoxical and counterintuitive principles-most famously the uncertainty principle, the principle of complementarity, and the no-cloning theorem. These ideas have long symbolized the “impossibility features” of the quantum world, setting it apart from the deterministic and predictable framework of classical physics. For decades, such principles fuelled intense debates among both physicists and philosophers, centering on how one should properly interpret the nature of quantum reality. However, as the twentieth century drew to a close, a remarkable shift began to unfold. Rather than treating these peculiar features merely as philosophical curiosities or obstacles to understanding, physicists started exploring whether these very strangenesses of quantum mechanics could be harnessed as resources for practical use. What emerged from this vision was an entirely new scientific discipline-quantum information theory and its technological counterpart, quantum computation. This new field reimagines the counterintuitive traits of quantum systems as powerful tools for accomplishing tasks fundamentally impossible within the classical paradigm. Out of this rethinking arose foundational protocols such as quantum cryptography, offering unprecedented levels of secure communication; quantum dense coding, enabling the transmission of more information using fewer resources; quantum teleportation, allowing the transfer of quantum states across distance without physically moving the particles themselves; and quantum algorithms, capable of solving certain computational problems at speeds unattainable by any classical machine. In this way, what was once regarded primarily as a domain of abstract puzzles and interpretational controversies has transformed into a vibrant, application-oriented science-laying the groundwork for the future of information, computation, and technology itself. Keywords: EPR paradox, Bell’s theorem, Entanglement, Quantum teleportation