Michal Horodecki, Ryszard Horodecki, Aditi Sen De, Ujjwal Sen
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Impossibility of cloning and deleting of unknown states are important restrictions on processing of information in the quantum world. On the other hand, a known quantum state can always be cloned or deleted. However if we restrict the class of allowed operations, there will arise restrictions on the ability of cloning and deleting machines. We have shown that cloning and deleting of known states is in general not possible by local operations. This impossibility hints at quantum correlation in the state. We propose dual measures of quantum correlation based on the dual restrictions of no local …
No-Cloning and No-Deleting theorems are verified with the constraint on local state transformations via the existence of incomparable states. Assuming the existence of exact cloning or deleting operation defined on a minimum number of two arbitrary states, an incomparable pair of states of the joint system between two parties can be made to compare under deterministic LOCC. We have restricted our proof with the assumption that the machine states of the cloning or deleting operations do not keep any information about the input states. We use the same setting to establish the no-cloning and no-d…
Cloning, deleting, and hiding in modal quantum theory
本研究针对基于有限域的模态量子理论（MQT）玩具模型，分析了克隆、删除和隐藏相关的不可行结果，发现克隆与删除在MQT中仍被禁止，但模态量子比特信息可完全隐藏于两个纠缠模态量子比特的关联中。
Coherence, being at the heart of interference phenomena, is found to be an useful resource in quantum information theory. Here we want to understand quantum coherence under the combination of two fundamentally dual processes, viz., cloning and deleting. We found the role of quantum cloning and deletion machines with the consumption and generation of quantum coherence. We establish cloning as a cohering process and deletion as a decohering process. Fidelity of the process will be shown to have connection with coherence generation and consumption of the processes.
We quantify the amount of correlation generated between two different output modes in the process of im- perfect cloning and deletion processes. We use three different measures of correlations and study their role in determining the fidelity of the cloning and deletion. We obtain a bound on the total correlation generated in the successive process of cloning and deleting operations. This displays a new kind of complementary relationship between the quantum correlation required in generating a copy of a quantum state and the amount of correlation required in bringing it back to the original sta…
In conventional quantum mechanics, quantum no-deleting and no-cloning theorems indicate that two different and nonorthogonal states cannot be perfectly and deterministically deleted and cloned, respectively. Here, we investigate the quantum deleting and cloning in a pseudo-unitary system. We first present a pseudo-Hermitian Hamiltonian with real eigenvalues in a two-qubit system. By using the pseudo-unitary operators generated from this pseudo-Hermitian Hamiltonian, we show that it is possible to delete and clone a class of two different and nonorthogonal states, and it can be generalized to a…
We discuss the role of the notion of information in the description of physical reality. We consider theories for which dynamics is linear with respect to stochastic mixing. We point out that the no-cloning and no-deleting principles emerge in any such theory, if law of conservation of information is valid, and two copies contain more information than one copy. We then describe the quantum case from this point of view.
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. …
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.
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…
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.
A simple and unifying method to show the perfect error-correcting condition is provided based on the quantum mutual information. The one-to-one parameterization of quantum operations and the properties of the quantum relative entropy are used effectively in this paper, where the equivalence between the subspace transmission and the entanglement transmission is clearly presented. We also revisit a variant of the no-cloning and no-deleting theorem based on an information-theoretical tradeoff between two parties for the reversibility of quantum operations, and demonstrate that the no-cloning and …
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…
An alternative kind of deleting/erasing operation is introduced which differs from the commonly used {\it controlled-not} (C-not) conditional logical operation $-$to flip to a standard, `zero' value the (classical or quantum) state of the last copy in a chain, in a deletion process. It is completely reversible, in the classical case, possessing a most natural cloning operation counterpart. We call this deleting procedure R-deletion since, in a way, it can be viewed as a `randomization' of the standard C-not operator. It has the remarkable property of by-passing in a simple manner the `impossib…
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.
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.
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。
Imperative Quantum Programming with Ownership and Borrowing in Guppy
本文提出一种结合线性类型与指令式语义的量子类型系统，并在 Guppy 语言中实现，以在指令式量子编程中保持安全保证。
Recently, Kavan Modi \emph{et al.} found that masking quantum information is impossible in bipartite scenario in [Phys. Rev. Lett. \textbf{120}, 230501 (2018)]. This adds another item of the no-go theorems. In this paper, we present some new schemes different from error correction codes, which show that quantum states can be masked when more participants are allowed in the masking process. Moreover, using a pair of mutually orthogonal Latin squares of dimension $d$, we show that all the $d$ level quantum states can be masked into tripartite quantum systems whose local dimensions are $d$ or $d+…
Recently, apparent nonphysical implications of non-Hermitian quantum mechanics (NHQM) have been discussed in the literature. In particular, the apparent violation of the no-signaling theorem, discrimination of nonorthogonal states, and the increase of quantum entanglement by local operations were reported, and therefore NHQM was not considered as a fundamental theory. Here we show that these and other no-go principles (including the no-cloning and no-deleting theorems) of conventional quantum mechanics still hold in finite-dimensional non-Hermitian quantum systems, including parity-time symmet…
We consider causality respecting (CR) quantum systems interacting with closed timelike curves (CTCs), within the Deutsch model. We introduce the concepts of popping up and elimination of quantum information and use them to show that no-cloning and no-deleting, which are true in CR quantum systems, are no more valid in the same that are interacting with CTCs. We also find limits on the possibility of creation of entanglement between a CR system and a CTC, and the same between two CR systems in the presence of a CTC. We prove that teleportation of quantum information, even in its approximate ver…
Linearity and unitarity are two fundamental tenets of quantum theory. Any consequence that follows from these must be respected in the quantum world. The no-cloning theorem and the no-deleting theorem are the consequences of the linearity and the unitarity. Together with the stronger no-cloning theorem they provide permanence to quantum information, thus, suggesting that in the quantum world information can neither be created nor be destroyed. In this sense quantum information is robust, but at the same time it is also fragile because any interaction with the environment may lead to loss of in…
Inspired by classical ("actual") Quantum Theory over $\mathbb{C}$ and Modal Quantum Theory (MQT), which is a model of Quantum Theory over certain finite fields, we introduce General Quantum Theory as a Quantum Theory -- in the København interpretation -- over general division rings with involution, in which the inner product "is" a $(σ,1)$-Hermitian form $φ$. This unites all known such approaches in one and the same theory, and we show that many of the known results such as no-cloning, no-deleting, quantum teleportation and super-dense quantum coding, which are known in classical Quantum Theor…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。