Common origin of no-cloning and no-deleting principles - Conservation of information

Deletion of imperfect cloned copies

In this work, we design a deleting machine and shown that for some given condition on machine parameters, it gives slightly better result than P-B deleting machine [5,6]. Also it is shown that for some particular values of the machine parameters it acts like Pati-Braunstein deleting machine. We also study the combined effect of cloning and deleting machine, where at first the cloning is done by some standard cloning machines such as Wootters-Zurek [1] and Buzek-Hillery [2] cloning machine and then the copy mode is deleted by Pati-Braunstein deleting machine or our prescribed deleting machine. …

No-deleting and no-cloning principles as consequences of conservation of quantum information

We show that the no-deleting and no-cloning principles are implications of information conservation principle. This is unlike in classical physics, where cloning and deleting are possible, independently of information conservation. Connections with the second law of thermodynamics are also discusssed.

Stronger no-cloning, no-signalling and conservation of quantum information

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.

Impossibility of deleting an unknown quantum state

A photon in an arbitrary polarization state cannot be cloned perfectly. But suppose that at our disposal we have several copies of an unknown photon. Is it possible to delete the information content of one or more of these photons by a physical process? Specifically, if two photons are in the same initial polarization state is there a mechanism that produces one photon in the same initial state and the other in some standard polarization state. If this can be done, then one would create a standard blank state onto which one could copy an unknown state approximately, by deterministic cloning or…

Relations between cloning and the universal NOT from conservation laws

We discuss certain relations between cloning and the NOT operation that can be derived from conservation laws alone. Those relations link the limitations on cloning and the NOT operation possibly imposed by {\em other} laws of Nature. Our result is quite general and holds both in classical and quantum-mechanical worlds, for both optimal and suboptimal operations, and for bosons as well as fermions.

Unified quantum no-go theorems and transforming of quantum states in a restricted set

The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. It remains an open problem of finding general forbidden principles to unify these results. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed state in Hilbert space of finite dimension. Two general forms include the no-clon…

Quantum catalysis of information

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.

不可能通过幺正演化共轭一个未知量子态

Impossible to conjugate an unknown quantum state via a unitary evolution

本文提出不可共轭定理，证明无法通过通用物理设备或线性/幺正操作共轭未知任意量子态，补充了量子信息领域的基本限制定理。

Algorithmic No-Cloning Theorem

We introduce the notions of algorithmic mutual information and rarity of quantum states. These definitions enjoy conservation inequalities over unitary transformations and partial traces. We show that a large majority of pure states have minute self algorithmic information. We provide an algorithmic variant to the no-cloning theorem, by showing that only a small minority of quantum pure states can clone a non negligible amount of algorithmic information. We also provide a chain rule inequality for quantum algorithmic entropy. We show that rarity does not increase under POVM measurements.