Probabilistic exact deletion and probabilistic no-signalling

对‘选择公理与无信号原理’的评论

Comment on 'The axiom of choice and the no-signalling principle'

本文反驳了arXiv:2206.08467中关于确定性无信号资源强于概率性资源的主张，指出确定性资源本质上是概率性资源，并提出可测量性假设以完善论证。

Simulating all non-signalling correlations via classical or quantum theory with negative probabilities

Many-party correlations between measurement outcomes in general probabilistic theories are given by conditional probability distributions obeying the non-signalling condition. We show that any such distribution can be obtained from classical or quantum theory, by relaxing positivity constraints on either the mixed state shared by the parties, or the local functions which generate measurement outcomes. Our results apply to generic non-signalling correlations, but in particular they yield two distinct quasi-classical models for quantum correlations.

基于无信号原理的量子克隆基本极限

Fundamental limits on quantum cloning from the no-signalling principle

本文基于无信号原理和远程态制备，在统一框架中重新推导了概率性与确定性量子克隆机最大保真度的上界，并将其应用于量子密码学中若干重要状态子集。

Can error in quantum deletion machines be beneficial for deletion?

In this paper, a generalized input state dependent deletion machine called probabilistic quantum deletion machine is proposed. Considering the Pati-Braunstein deletion machine as a benchmark, the machine is characterized by its deletion probability and the probability of error in deletion. It is observed that there are parameters for which increase in error in deletion can increase the fidelity of deletion. It is also shown that the Pati-Braunstein deletion machine is easily derivable for a certain value of deletion probability. Further the deletion machine can offer better fidelity of deletio…

Causal influence in operational probabilistic theories

We study the relation of causal influence between input systems of a reversible evolution and its output systems, in the context of operational probabilistic theories. We analyse two different definitions that are borrowed from the literature on quantum theory -- where they are equivalent. One is the notion based on signalling, and the other one is the notion used to define the neighbourhood of a cell in a quantum cellular automaton. The latter definition, that we adopt in the general scenario, turns out to be strictly weaker than the former: it is possible for a system to have causal influenc…

Quantum no-deleting principle and some of its implications

Unmeasureability of a quantum state has important consequences in practical implementation of quantum computers. Like copying, deleting of an unknown state from among several copies is prohibited. This is called no-deletion prinicple. Here, we present a no deleting principle for qudits. We obtain a bound on $N$-to-$M$ deleting and show that the quality of deletion drops exponentially with the number of copies to be deleted. In addition, we investigate conditional, state-dependent and approximate quantum deleting of unknown states. We prove that unitarity does not allow us to delete copies from…

Quantum probabilistic encryption scheme based on conjugate coding

We present a quantum probabilistic encryption algorithm for a private-key encryption scheme based on conjugate coding of the qubit string. A probabilistic encryption algorithm is generally adopted in public-key encryption protocols. Here we consider the way it increases the unicity distance of both classical and quantum private-key encryption schemes. The security of quantum probabilistic private-key encryption schemes against two kinds of attacks is analyzed. By using the no-signalling postulate, we show that the scheme can resist attack to the key. The scheme's security against plaintext att…

非线性量子动力学中的超光速信号传递与混沌

Superluminal signalling and chaos in nonlinear quantum dynamics

本文重新审视Gisin关于非线性量子动力学导致超光速信号传递的不可行定理，研究张量积希尔伯特空间上具有混沌特征的全局非线性动力学，并证明即使放宽无限制假设，三类通信协议一般仍可实现超光速信息传递，同时给出一个例外实例。

On the Probabilistic Compatibility of Special Relativity and Quantum Mechanics

In this paper we introduce the three main notions of probability used by physicists and discuss how these are to be used when invoking spacelike separated observers in a relativistic format. We discuss a standard EPRB experiment and concentrate upon problems of the interpretation of probabilities. We promote a particularly conservative interpretation of this experiment (which need not invoke an objective notion of collapse) where probabilities are, tentatively, passively Lorentz invariant. We also argue that the Heisenberg picture is preferable in relativistic situations due to a conflict betw…

Information processing in generalized probabilistic theories

I introduce a framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others. From two simple assumptions, a tensor product rule for combining separate systems can be derived. Certain features, usually thought of as specifically quantum, turn out to be generic in this framework, meaning that they are present in all except classical theories. These include the non-unique decomposition of a mixed state into pure states, a theorem involving disturbance of a system on measurement (suggesting that the possibility of secure key distri…

Multipartite Composition of Contextuality Scenarios

Contextuality is a particular quantum phenomenon that has no analogue in classical probability theory. Given two independent systems, a natural question is how to represent such a situation as a single test space. In other words, how separate contextuality scenarios combine into a joint scenario. Under the premise that the the allowed probabilistic models satisfy the No Signalling principle, Foulis and Randall defined the unique possible way to compose two contextuality scenarios. When composing strictly-more than two test spaces, however, a variety of possible composition methods have been co…

Causality and local determinism versus quantum nonlocality

The entanglement and the violation of Bell and CHSH inequalities in spin polarization correlation experiments (SPCE) is considered to be one of the biggest mysteries of Nature and is called quantum nonlocality. In this paper we show once again that this conclusion is based on imprecise terminology and on the lack of understanding of probabilistic models used in various proofs of Bell and CHSH theorems. These models are inconsistent with experimental protocols used in SPCE. This is the only reason why Bell and CHSH inequalities are violated. A probabilistic non-signalling description of SPCE, c…

因果结构的范畴语义

A categorical semantics for causal structure

本文提出一种范畴框架，用于在包括经典与量子理论在内的过程理论中建模细粒度因果结构，统一描述半因果、非信号及量子梳等过程，并支持局部固定但全局不确定的因果排序。

经典、量子与一般概率态判别轮廓

Classical, quantum, and general probabilistic state-discrimination profiles

本文刻画了经典、量子与一般概率理论中态判别轮廓的可行区域，建立了层级关系，并给出了三态情形下的精确边界与量子界猜想。