发布时间 : 星期四 文章量子力学中的Jaynes-Cummings模型态演化分析(胡丽红)更新完毕开始阅读
华东交通大学毕业设计（论文）
附录
Teleporting an Unknown Quantum State via Dual Classical and
Einstein-Podolsky-Rosen Channels
An unknown quantum state
? can be disassembled into, then later
reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations. To do so the sender, “Alice” and the receiver, “Bob” must prearrange the sharing of an EPR-correlated pairs of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum system, and sends Bob the classical result of this measurement. Knowing this, Bob can convert the state of his EPR particle into an exact replica of the unknown state
? which Alice destroyed.
The existence of long range correlations between Einstein-Podolsky-Rosen (EPR) pairs of particles raises the question of their use for information transfer. Einstein himself used the word “telepathically” in this context. It is known that instantaneous information transfer is definitely impossible. Here we show that EPR correlations can nevertheless assist in the “teleportation” of an intact quantum state from one place to another, by a sender who knows neither the state to be teleported nor the location of the intended receiver.
Suppose one observer, whom we shall call “Alice”, has been given a quantum
1system such as a photon or spin? particle, prepared in a state ? unknown to
2her, and she wishes to communicate to another observer, “Bob”, sufficient information about the quantum system for him to make an accurate copy of it. Knowing the state vector ? itself would be sufficient information, but in general there is no way to learn it. Only if Alice knows before-hand that ? belongs to a given orthonormal set can she make a measurement whose result will allow her to make an accurate copy of ?. Conversely, if the possibilities for ? include two or more nonorthogonal states, then no measurement will yield sufficient information
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胡丽红 量子力学中的Jaynes-Cummings模型态演化分析
to prepare a perfectly accurate copy.
A trivial way for Alice to provide Bob with all the information in ? would be to send the particle itself. If she wants to avoid transferring the original particle, she can make it interact unitarily with another system, or “ancilla”, initially in a known state a0, in such a way that after the interaction the original particle is left in a standard state ?0 and the ancilla is in an unknown state a containing complete information about ?. If Alice now sends Bob the ancilla (perhaps technically easier than sending the original particle), Bob can reverse her actions to prepare a replica of her original state?. This “spin-exchange measurement” illustrates an essential feature of quantum information: it can be swapped from one system to another, but it cannot be duplicated or “cloned”. In this regard it is quite unlike classical information, which can be duplicated at will. The most tangible manifestation of the nonclassicality of quantum information is the violation of Bell’s inequalities observed in experiments on EPR states. Other manifestations include the possibility of quantum cryptography, quantum parallel computation, and the superiority of interactive measurements for extracting information from a pair of identically prepared particles.
The spin-exchange method of sending full information to Bob still lumps classical and nonclassical information together in a single transmission. Below, we show how Alice can divide the full information encoded in ? into two parts, one purely classical and the other purely nonclassical, and send them to Bob through two different channels. Having received these two transmissions, Bob can construct an accurate replica of ?. Of course Alice’s original ? is destroyed in the process, as it must be to obey the no-cloning theorem. We call the process we are about to describe teleportation, a term from science fiction meaning to make a person or object disappear while an exact replica appears somewhere else. It must be emphasized that our teleportation, unlike some science fiction version, defies no
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华东交通大学毕业设计（论文）
physical laws. In particular, it cannot take place instantaneously or over a spacelike interval, because it requires, among other things, sending a classical message from Alice to Bob. The net result of teleportation is completely prosaic: the removal of
? from Alice’s hands and its appearance in Bob’s hands a suitable time later. The
only remarkable feature is that, in the interim, the information in ? has been cleanly separated into classical and nonclassical parts. First we shall show how to teleport the quantum state ? of a spin?teleportation of more complicated states.
1 particle. Later we discuss 239
胡丽红 量子力学中的Jaynes-Cummings模型态演化分析
通过经典和爱因斯坦-波多尔斯基-罗斯（EPR）双重通道来传送
一个未知的量子态
一个未知的量子态?可以被分解成纯经典信息和纯非经典的爱因斯坦-波多尔斯基-罗斯（EPR）相互关系，也可以由这两者重建。所以发送器“爱丽丝”和接收器“鲍勃”必须预先安排一个共享的与EPR相关联的对颗粒。爱丽丝对她的EPR粒子和那个未知的量子系统做了一个联合测量，并且把这个测量的经典结果发送给了鲍勃。知道了这个，鲍勃就可以把他的EPR粒子转换为被爱丽丝毁灭的未知态?的一个原滋原味的复制品。
EPR对粒子之间的长期相关性增加了把他们运用于信息传送的问题。爱因斯坦自己在这篇文章中用到了“心灵感应地”这个词。众所周知，瞬间的信息传递肯定是不可能的。在此我们将说明EPR相关联然而还是可以通过一个既不知道被心灵运输的态又不知道预期中接收者的地点的发送者，帮助一个完整的量子态从一个到另外一个地方的“心灵传送”。
假设一个观测者，我们称之为“爱丽丝”，已经被给定了一个量子系统，比如说一个光子或者一个旋转?1的粒子，这个给定的量子系统处于一个对爱丽2丝来说是未知的态中。她想把有关于这个量子系统的充分的信息传输给另外一个观测者“鲍勃”以便可以让他做出一个这个系统的精确的复制品。容易知道状态适量?本身就是一个充分的信息源，但是总而言之我们还是无法具体得知。如果爱丽丝事先知道?属于一个给定的正交系统，那么她就可以做测量，得到的结果会可以使她做出一个?的精确复制品。相反，如果?可能包含两个或者更多的非正交的态，那么将没有任何一种测量会提供充分的信息来完美的精确复制这个态。
一个让爱丽丝提供?态里所有的信息的繁琐的方法就是发送这个粒子本身。如果她想避免传递原始的粒子，她可以使之与另外一个已知初始态处于a0的系统，或者称作“助手系统”。通过这种方法，在经过相互作用后，原始的粒子就处于一个标准态?0，而助手系统处于一个包含了有关于态?的完整信息
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