双旋量、振子代数和量子比特：相对论量子信息的显协变方法
Two-spinors, oscillator algebras, and qubits: Aspects of manifestly covariant approach to relativistic quantum information
摘要：
本文的第一部分回顾了2-旋量方法在相对论量子比特中的应用（Minkowski空间中的四元组和2-qubit状态之间的类比，通过零方向定义的qubit和它们对于消除Peres-Scudo-Terno现象的作用，由Pauli-Lubanski矢量定义的相对论极化算子的优点和缺点，对非均匀SL（2，（C））。第二部分涉及通过谐振子李代数（不一定采取不可约表示）量子化的电磁场。与非相对论性单线态相反，人们必须区分最大对称态和EPR态。这种区别是EPR关联的“奇怪”相对论性质的来源之一。作为一个例子，EPR平均显式计算的线性极化状态，反对称的螺旋度和动量。结果采取熟悉的形式$\pm p\cos 2(α-β)$独立的谐振子代数的表示的选择。参数$p$由探测器的光谱特性和EPR态的选择决定，但与探测器效率无关。简要分析了真空纠缠和真空对贝尔不等式的破坏。这些效应与真空态的不等价概念有关。技术附录讨论了我在场量化中使用的表示的详细信息。特别地，M形δ序列用于定义在零处正则的狄拉克δ。
英文摘要：
The first part of the paper reviews applications of 2-spinor methods to relativistic qubits (analogies between tetrads in Minkowski space and 2-qubit states, qubits defined by means of null directions and their role for elimination of the Peres-Scudo-Terno phenomenon, advantages and disadvantages of relativistic polarization operators defined by the Pauli-Lubanski vector, manifestly covariant approach to unitary representations of inhomogeneous SL(2,C)). The second part deals with electromagnetic fields quantized by means of harmonic oscillator Lie algebras (not necessarily taken in irreducible representations). As opposed to non-relativistic singlets one has to distinguish between maximally symmetric and EPR states. The distinction is one of the sources of `strange' relativistic properties of EPR correlations. As an example, EPR averages are explicitly computed for linear polarizations in states that are antisymmetric in both helicities and momenta. The result takes the familiar form $\pm p\cos 2(α-β)$ independently of the choice of representation of harmonic oscillator algebra. Parameter $p$ is determined by spectral properties of detectors and the choice of EPR state, but is unrelated to detector efficiencies. Brief analysis of entanglement with vacuum and vacuum violation of Bell's inequality is given. The effects are related to inequivalent notions of vacuum states. Technical appendices discuss details of the representation I employ in field quantization. In particular, M-shaped delta-sequences are used to define Dirac deltas regular at zero.
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。
