Tutorial Notes on One-Party and Two-Party Gaussian States

No-signalling-based version of Zurek's derivation of quantum probabilities: A note on "Environment-assisted invariance, entanglement, and probabilities in quantum physics"

Zurek has derived the quantum probabilities for Schmidt basis states of bipartite quantum systems in pure joint states, from the assumption that they should be not be affected by one party's action if the action can be undone by the other party (``envariance of probability'') and an auxiliary assumption. We argue that a natural generalization of the auxiliary assumption is actually strong enough to yield the Born rule itself, but that Zurek's argument and protocol can be adapted to do without this assumption, at the cost of using envariance of probability in both directions. We consider altern…

Quantum Finance: a tutorial on quantum computing applied to the financial market

Previously only considered a frontier area of Physics, nowadays quantum computing is one of the fastest growing research field, precisely because of its technological applications in optimization problems, machine learning, information security and simulations. The goal of this article is to introduce the fundamentals of quantum computing, focusing on a promising quantum algorithm and its application to a financial market problem. More specifically, we discuss the portfolio optimization problem using the \textit{Quantum Approximate Optimization Algorithm} (QAOA). We not only describe the main …

Essentially All Gaussian Two-Party Quantum States are a priori Nonclassical but Classically Correlated

Duan, Giedke, Cirac and Zoller (quant-ph/9908056) and, independently, Simon (quant-ph/9909044) have recently found necessary and sufficient conditions for the separability (classical correlation) of the Gaussian two-party (continuous variable) states. Duan et al remark that their criterion is based on a "much stronger bound" on the total variance of a pair of Einstein-Podolsky-Rosen-type operators than is required simply by the uncertainty relation. Here, we seek to formalize and test this particular assertion in both classical and quantum-theoretic frameworks. We first attach to these states …

The GHZ state in secret sharing and entanglement simulation

In this note, we study some properties of the GHZ state. First, we present a quantum secret sharing scheme in which the participants require only classical channels in order to reconstruct the secret; our protocol is significantly more efficient than the trivial usage of teleportation. Second, we show that the classical simulation of an n-party GHZ state requires at least n log n - 2n bits of communication. Finally, we present a problem simpler than the complete simulation of the multi-party GHZ state, that could lead to a no-go theorem for GHZ state simulation.

Parts of Quantum States

It is shown that generic N-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the information in almost all N-party pure states is in the set of reduced states of just over half the parties. For N even, the reduced states in fewer than N/2 parties are shown to be an insufficient description of almost all states (similar results hold when N is odd). It is noted that Real Algebraic Geometry is a natural framework for any analysis of parts of quantum states: two simple polynomials, a quadra…

五个入门问题：在量子计算机上求解二次无约束二元优化模型

Five Starter Problems: Solving Quadratic Unconstrained Binary Optimization Models on Quantum Computers

本教程面向学生与行业从业者，介绍在IBM门电路架构与D-Wave量子退火机两类现有量子设备及模拟器上求解QUBO模型的方法，含实例、算法基础与实现指南，是量子求解复杂QUBO的入门资源。

关于随机量子电路的复制张量网络讲座笔记

Lecture Notes on Replica Tensor Networks for Random Quantum Circuits

本文介绍了利用复制张量网络技术分析随机量子电路的方法，通过张量收缩计算平均可观测量，并展示了其在清洁和噪声电路中的应用，还介绍了相关工具库。

讲义：使用MCTDH-X研究多体量子动力学

Lecture Notes: many-body quantum dynamics with MCTDH-X

本讲义基于2023年海德堡MCTDH暑期学校，系统介绍多组态含时Hartree方法及MCTDH-X软件，涵盖理论、工作流程、基准测试与高级功能，为研究多体量子动力学提供全面指导。

Quantum Entanglement and Communication Complexity

We consider a variation of the multi-party communication complexity scenario where the parties are supplied with an extra resource: particles in an entangled quantum state. We show that, although a prior quantum entanglement cannot be used to simulate a communication channel, it can reduce the communication complexity of functions in some cases. Specifically, we show that, for a particular function among three parties (each of which possesses part of the function's input), a prior quantum entanglement enables them to learn the value of the function with only three bits of communication occurri…

Information Causality is a Special Point in the Dual of the Gray-Wyner Region

Information Causality contributes to the program of deriving fundamentals of quantum theory from information theoretic principles. It puts restrictions on the amount of information learned by a party (Bob) from the other party (Alice) in a one-way communication scenario: Bob receives an index b, and after a one-way communication from Alice, tries to recover the b-th bit of Alice's input. In this manuscript we note that Information Causality is indeed a point in the dual of the Gray-Wyner region in the case where Alice's input bits are chosen independently at random. The main motivation of this…

Quantum Steering

Quantum correlations between two parties are essential for the argument of Einstein, Podolsky, and Rosen in favour of the incompleteness of quantum mechanics. Schrödinger noted that an essential point is the fact that one party can influence the wave function of the other party by performing suitable measurements. He called this phenomenon quantum steering and studied its properties, but only in the last years this kind of quantum correlation attracted significant interest in quantum information theory. In this paper the theory of quantum steering is reviewed. First, the basic concepts of stee…