Artistic illustration showing the teleportation of two properties
Twice the fun: teleporting two properties of a photon
The values of two inherent properties of one photon – its spin and its orbital angular momentum – have been transferred via quantum teleportation onto another photon for the first time by physicists in China. Previous experiments have managed to teleport a single property, but scaling that up to two properties proved to be a difficult task, which has only now been achieved. The team's work is a crucial step forward in improving our understanding of the fundamentals of quantum mechanics and the result could also play an important role in the development of quantum communications and quantum computers.

Alice and Bob

Quantum teleportation first appeared in the early 1990s after four researchers, including Charles Bennett of IBM in New York, developed a basic quantum teleportation protocol. To successfully teleport a quantum state, you must make a precise initial measurement of a system, transmit the measurement information to a receiving destination and then reconstruct a perfect copy of the original state. The "no-cloning" theorem of quantum mechanics dictates that it is impossible to make a perfect copy of a quantum particle. But researchers found a way around this via teleportation, which allows a flawless copy of a property of a particle to be made. This occurs thanks to what is ultimately a complete transfer (rather than an actual copy) of the property onto another particle such that the first particle loses all of the properties that are teleported.
The protocol has an observer, Alice, send information about an unknown quantum state (or property) to another observer, Bob, via the exchange of classical information. Both Alice and Bob are first given one half of an additional pair of entangled particles that act as the "quantum channel" via which the teleportation will ultimately take place. Alice would then interact the unknown quantum state with her half of the entangled particle, measure the combined quantum state and send the result through a classical channel to Bob. The act of the measurement itself alters the state of Bob's half of the entangled pair and this, combined with the result of Alice's measurement, allows Bob to reconstruct the unknown quantum state. The first experimentation teleportation of the spin (or polarization) of a photon took place in 1997. Since then, the states of atomic spins, coherent light fields, nuclear spins and trapped ions have all been teleported.
But any quantum particle has more than one given state or property – they possess various "degrees of freedom", many of which are related. Even the simple photon has various properties such as frequency, momentum, spin and orbital angular momentum (OAM), which are inherently linked.

More than one

Teleporting more than one state simultaneously is essential to fully describe a quantum particle and achieving this would be a tentative step towards teleporting something larger than a quantum particle, which could be very useful in the exchange of quantum information. Now, Chaoyang Lu and Jian-Wei Pan, along with colleagues at the University of Science and Technology of China in Hefei, have taken the first step in simultaneously teleporting multiple properties of a single photon.
In the experiment, the team teleports the composite quantum states of a single photon encoded in both its spin and OAM. To transfer the two properties requires not only an extra entangled set of particles (the quantum channel), but a "hyper-entangled" set – where the two particles are simultaneously entangled in both their spin and their OAM. The researchers shine a strong ultraviolet pulsed laser on three nonlinear crystals to generate three entangled pairs of photons – one pair is hyper-entangled and is used as the "quantum channel", a second entangled pair is used to carry out an intermediate "non-destructive" measurement, while the third pair is used to prepare the two-property state of a single photon that will eventually be teleported.
Schematic describing the teleportation protocol
Tricky protocol: comparative measurements and teleportation
The image above represents Pan's double-teleportation protocol – A is the single photon whose spin and OAM will eventually be teleported to C (one half of the hyper-entangled quantum channel). This occurs via the other particle in the channel – B. As B and C are hyper-entangled, we know that their spin and OAM are strongly correlated, but we do not actually know what their values are – i.e. whether they are horizontally, vertically or orthogonally polarized. So to actually transfer A's polarization and OAM onto C, the researchers make a "comparative measurements" (referred to as CM-P and CM-OAM in the image) with B. In other words, instead of revealing B's properties, they detect how A's polarization and OAM differ from B. If the difference is zero, we can tell that A and B have the same polarization or OAM, and since B and C are correlated, that C now has the same properties that A had before the comparison measurement.
On the other hand, if the comparative measurement showed that A's polarization as compared with B differed by 90° (i.e. A and B are orthogonally polarized), then we would rotate C's field by 90° with respect to that of A to make a perfect transfer once more. Simply put, making two comparative measurements, followed by a well-defined rotation of the still-unknown polarization or OAM, would allow us to teleport A's properties to C.

Perfect protocol

One of the most challenging steps for the researchers was to link together the two comparative measurements. Referring to the "joint measurements" box in the image above, we begin with the comparative measurement of A and B's polarization (CM-P). From here, either one of three scenarios can take place – one photon travels along path 1 to the middle box (labelled "non-destructive photon-number measurement"); no photons enter the middle box along path 1; or two single photons enter the middle box along path 1.
The middle box itself contains the second set of entangled photons mentioned previously (not shown in figure) and one of these two entangled photons is jointly measured with the incoming photons from path 1. But the researcher's condition is that if either no photons or two photons enter the middle box via path 1, then the measurement would fail. Indeed, what the middle box ultimately shows is that exactly one photon existed in path 1, and so exactly one photon existed in path 2, given that two photons (A and B) entered CM-P. To show that indeed one photon existed in path two required the third and final set of entangled photons in the CP-OAM box (not shown), where the OAM's of A and B undergo a comparative measurement.
The measurements ultimately result in the transfer or teleportation of A's properties onto C – although it may require rotating C's (as yet unknown) polarization and OAM depending on the outcomes of the comparative measurements, but the researchers did not actually implement the rotations in their current experiment. The team's work has been published in the journal Nature this week. Pan tells physicsworld.com that the team verified that "the teleportation works for both spin-orbit product state and hybrid entangled state, achieving an overall fidelity that well exceeds the classical limit". He says that these "methods can, in principle, be generalized to more [properties], for instance, involving the photon's momentum, time and frequency".

Verification verdicts

Physicist Wolfgang Tittel from the University of Calgary, who was not involved in the current work (but wrote an accompanying "News and Views" article in Nature) explains that the team verified that the teleportation had indeed occurred by measuring the properties of C after the teleportation. "Of course, the no-cloning theorem does not allow them to do this perfectly. But it is possible to repeat the teleportation of the properties of photon A, prepared every time in the same way, many times. Making measurements on photon C (one per repetition) allows reconstructing its properties." He points out that although the rotations were not ultimately implemented by the researchers, they found that "the properties of C differed from those of A almost exactly by the amount predicted by the outcomes of the comparative measurements. They repeated this large number of measurements for different preparations of A, always finding the properties of C close to those expected. This suffices to claim quantum teleportation".
While it is technically possible to extend Pan's method to teleport more than two properties simultaneously, this is increasingly difficult because the probability of a successful comparative measurement decreases with each added property. "I think with the scheme demonstrated by [the researchers], the limit is three properties. But this does not mean that other approaches, either other schemes based on photons, or approaches using other particles (e.g. trapped ions), can't do better," says Tittel.
Pan says that to teleport three properties, their scheme "needs the experimental ability to control 10 photons. So far, our record is eight photon entanglement. We are currently working on two parallel lines to get more photon entanglement." Indeed, he says that the team's next goal is to experimentally create "the largest hyper-entangled state so far: a six-photon 18-qubit Schrödinger cat state, entangled in three degrees-of-freedom, polarization, orbital angular momentum, and spatial mode. To do this would provide us with an advanced platform for quantum communication and computation protocols".
The work is published in Nature.


听Andon Zeilinger教授介绍量子隔空传输技术（下）
断章师爷

接着A.Zeilinger教授比较详细地介绍了量子隔空传输技术的概念以及这门处于探索阶段的崭新领域的发展历史、现实状况和未来走向。

假设未来世界的A城有一个小女孩Alice，她打算玩一个游戏用隔空传输的方式把信息送给B城的小男孩Bob。a和b是一对处于量子纠缠状态的粒子，前者为Alice所有，后者则在Bob手中。此外Alice还有另一颗粒子x，处于未知的量子状态。Alice对她拥有的粒子a和x进行了一次贝尔状态的测量，又用通常的经典方法(例如打个电话或投张明信片)把测量结果告诉Bob。Bob发现他手头的那颗粒子b也复制上了x粒子的量子状态。这就表明借助于一对处于量子纠缠状态的粒子a和b，在A城的Alice获得的信息(x粒子的量子状态)顷刻之间就被隔空传输作用送到了在B城的Bob手头的那颗粒子b上了。

1997年由A.Zeilinger教授领导的奥地利因斯布鲁克大学(Universität Innsbruck)的工作小组用实验手段具体实施了上述科学童话中Alice和Bob玩的游戏。他们的实验装置展示在一张示意图上，主要由光子源、(量子)纠缠产生器、光路系统和检测系统等部分组成。

示意图的左方是作为光子源的一个短脉冲紫外激光管S。中间是一个称为自发参量下转换器SPDC(spontaneous parametric down-conversion的缩写)的装置，用来产生纠缠态的光子对，主要是一块晶体和一些附加的光学元件。左上方是传送信息的A(Alice)，右下方是接收信息的B(Bob)，左下方是辅助的确认装置C(Confirmation)。A由两个单光子检测器和一个光线分束器(beam splitter)组成；B也由两个单光子检测器和一个验偏振的光分束器组成；C仅有一个单光子检测器。SPDC的前方(右面)设置了两条光路：一条L1向上通往A；另一条L2向下通往B。SPDC的后方(左面)也设置了两条光路：一条L3向上通往A，其中联有一个起偏振（极化）器P；另一条L4向下通往C。A、B和C之间没有任何相互作用，也没有动力学上任何其它方式的耦合。

S发出的紫外脉冲自左向右射入SPDC，打在晶体上，发生的散射作用使得单个紫外光子会以一定的概率转换成为两个能量较低的（譬如红外）光子。由于晶体的光学特性，使得这对新产生的光子a和b处于彼此纠缠的量子状态。光子a和b穿过晶体分别经过光路L1和L2抵达A和B。当然，晶体形成的纠缠光子对也有被反射回去的，例如光子对c和d。当光子d经过光路L3时，由于起偏振器P的作用使得它形成了特殊的极化状态x。当C的检测器测得光子c时，表明呈x态的光子d也经过L3抵达了A。光子a和d分在A处的光分束器汇合，再被两个单光子检测器分别测得。A将检测的结果用通常的方法告知B，后者通过该处的验偏振光线分束器发现光子b也呈x态的极化。这就证明了x态通过隔空传输的方式从A处的a光子传送到了与之纠缠的B处的b光子。

A.Zeilinger教授示出了一些有关的实物照片和测量的实验结果。该文入选英国《自然》杂志特刊物理学百年经典之作，被称为有里程碑意义的成就。接着他又简略地报导了这以后的十来年中该领域的发展和目前达到的水准。2004年他和维也纳大学的同事在多瑙河畔将量子隔空传输的距离提高到600米。2007年他们又在非洲西北海岸的加那利群岛（Canary islands）相距144公里的两处观察到了量子纠缠的信息。世界各国的科学家相继制备了三光子、四光子、五光子、六光子纠缠态，并成功地实施了它们的隔空传输。近年的文章甚至报导已经制备了十个量子比特的纠缠态。A.Zeilinger教授屡屡提及一位姓Pan的中国学者。

演讲持续了大约三刻钟，在听众的掌声中结束。接着是听众向A.Zeilinger教授提问，大都是些好奇的科普层面的问题。对于这些问题，A.Zeilinger教授做了个统一的回答。他认为，测量一个光子的极化这样一个作用，立即迫使纠缠的第二个光子采纳了一个与之互补的值。即使两个纠缠的光子处于不同的星系，这种变化也能在瞬间发生。科学家们已经进入了将量子纠缠作为处理信息的途径。所谓量子隔空传输指的是相隔两处的纠缠光子没有任何时间上的延误，可以进行性质的传送。这种隔空传输递送的并不是具体的物质而只是光子的属性。然而，这种量子属性的传递又与简单的“拷贝”作用不同，传送的那个光子可以把它的全部属性都传送到第二个光子，但是它本身却没有失去任何自己的属性。这种现象只是存在于量子世界，因此称之为量子隔空传输。当然，这两个光子并没有发生任何运动，它们仍然“留守”在各自的原地。然而迄今为止，科学家们只能将对象局限于光子范围（偶尔也有原子），对于尺度较大的物体，却一无所知。因为，即使能从理论上论证其可行性存在的话，具体实施的困难也是超乎意料的艰巨。例如象科幻片中展示的那样，转眼之间将人从一个星球迁送到另一个星球的事，有很多难以逾越的鸿沟。首先，基于物理原因，被迁送者必须与执行迁送任务的环境完全隔离，必须是整个的真空。这对于被遣送者的健康绝对是有影响的。其次，这实际上是将某个人的全部属性转移到另一个人身上。这就意味着，重新制造了一个人，他（或者她）不再具有任何他（或者她）自己原来的属性，譬如头发、眼睛和皮肤的色泽，四肢、骨骼的尺寸，内脏器官的健康程度，……甚至头脑的容量和思维能力等等。这是违反伦理和道德的，当然这也是疯狂到不能想象的。

也有些业内人士提了些比较深入的专门问题，我不太听得懂。比如这样的实验对于量子理论的非局域性和隐变数有何意义？A.Zeilinger教授认为他们得到的结果证实了量子理论的非局域性，但是还未能肯定或者否定隐变数的存在，也就是未能肯定量子理论的描述是否完备。不过，他又嘟哝了一句，只有在确切地说明隐变数的物理起因和可观测性时，这种隐变数理论才有意义。对于听众询问的量子隔空传输实验中涉及到的具体技术细节问题，他都不厌其烦地逐一作了解答。此外，有一位听众对三个以上的光子能否形成真正的量子纠缠状态持怀疑态度，他质疑这种“纠缠”仅仅只是形式上符合纠缠的定义而已。对此，A.Zeilinger教授表示很难解释，因为彼此的理念上存在着分歧，他建议对方可以去参看一篇刊载在美国《科学》杂志上的专论，对类似的问题作过详细的解释。A.Zeilinger教授很快地从电脑中查得该文发表的年、月、卷和页数，在告知对方的同时又再次声明，如果认同该文的观点，也就不难理解他的实验结果，否则所有的解释都是徒然的。

我对该领域一无所知，所以只有洗耳恭听的份。我仅仅是从材料学科的角度好奇地问了一声使得光子产生纠缠的晶体是何种材料？A.Zeilinger教授回答是β相硼酸钡(beta barium borate)。回家后，我查阅了一下。得知这种硼酸钡是性能良好的非线性光学材料，可透过的波段范围和实现相位匹配的波段范围较宽，损伤阀值较高，光学匀称性较好，二阶非线性光学系数较高。正是β相硼酸钡的这种非线性光学性能，才使得入射的紫外光子通过散射形成一对彼此纠缠的红外光子。如前所述，当一束紫外激光射向一块非线性晶体时，射出的激光会转换成为两束频率较低的红外光。如果其中某一束的极化方向是水平的话，那么另一束则是竖直的。可以通过调节入射角，使得这两束从晶体出射的红外光的圆锥面发生重叠。在与这两个圆锥面相隔一定距离处作一个截面，该截面与两个圆锥面的交线是两个相交的圆，圆上两个对称的交点上的红外光子，彼此处于纠缠状态。然而，我猜测对于三个以上光子的纠缠，可能须选择另外的材料，因为β相硼酸钡的三阶非线性光学系数比二阶非线性光学系数要低一个数量级左右。

有一个女学生问他：“A.Zeilinger教授，您做出了如此震惊世界的工作，是否考虑过摘取诺贝尔物理学奖？” A.Zeilinger教授不露声色地说了一句：“诺贝尔评奖委员会考虑的是做出严肃的决定；我考虑的是做自己喜欢的事情。”众人报以热烈的掌声，他礼貌地鞠躬致意。

在提问过程中发生了一段意外的插曲。有一位气宇轩昂的中年同胞，站起来兴奋地说道：“A.Zeilinger教授，您报告中提到的那位潘教授和我就在同一所大学工作。潘教授在国内的研究得到我们国家和大学领导的全力支持。对于您在量子隔空传输领域中取得的成就，我向您表示热烈的祝贺！对于您无私地培养中国留学生的崇高精神，我向您致以由衷的敬意！” A.Zeilinger教授客气地表示了谢意，并夸奖这些年来Pan做出的工作很了不起，深得国际同行的推许。接下去这位同胞的口气一转说道：“但是，A.Zeilinger教授，我曾经看到过一段您与达赖喇嘛的视频对话，觉得实在难以理解。您一个国际著名的物理学家竟然会赞同达赖喇嘛这样一个宗教骗子对于原子的观点。这个达赖喇嘛不学无术，他所谓的原子观点完全是疯狂的。（该同胞口中说的是“crazy”，后经坐在他边上一位年轻中国学生的低声提示，才改为“absurd”）。我实在不明白，您为何要赞同他的胡说八道。何况，达赖喇嘛还是一个分裂主义者，他是我们中国的敌人!”说完，他颇为自得地坐了下去。A.Zeilinger教授听完他的话后，笑眯眯地解释道：“达赖喇嘛关于原子的叙述是否如阁下所说的胡说八道，我相信各人有各人的看法。至于达赖喇嘛作为一个宗教领袖，请容许我对他在国际政治空间的定位和所发挥的作用，保留自己的判断。今天我是作为一个物理学家在这儿介绍自己的工作，无意与阁下就上述这些问题展开讨论，好吗。谢谢！”中年同胞顿时面露悻悻的神色，想再次立起身来，终被旁边的青年学生劝阻而未果。不知该中年同胞究系何方神圣？

听了近一个小时的报告，这些天来又翻阅了些有关的书籍，对于量子纠缠和量子隔空传输算是有了一些扫盲式的肤浅了解。因此拉拉扯扯地写出了上面的文字。下面再续上几句不经之谈。

（1）关于A.爱因斯坦在与以N.波尔为首的哥本哈根学派的那场关于量子力学理论的世纪论争中成了输家的结论，我（个人）认为是一家之言。尽管A.爱因斯坦在1930年的布鲁塞尔会议上不得不承认哥本哈根学派的解释是没有矛盾的，但是他坚持量子力学的统计描述并不是完整的“图像”。他说：“量子力学理论是不完备的，波函数并不能精确描写单个系统的状态.它所涉及的是许多系统，只是一个‘系综’”。而且A.爱因斯坦始终坚持“我不能真正地相信（量子理论），因为它不能调解物理学应该表示时间和空间中的实在以及摆脱鬼魅的超距作用的观念。”[1]加州大学伯克利分校的Henry Stapp认为“贝尔定理是科学史上最深奥的发现。”康奈尔大学的N.D.Mermin则认为“EPR的发表正是‘科学史上最深奥的发现’的基础。”据说1962年N.波尔去世后，人们在他办公室的黑板上看到还画着A.爱因斯坦在第6届索尔维（Solvay）会议上提出的那个带有一个可以用快门来启闭的小孔的光箱草图。显然N.波尔至死还在思索他那位伟大对手深邃而高远的思想和无人企及的灵感。

（2）虽然在微观物理中，量子力学的计算结果能对实验结果提供准确的预言，但是必须承认量子力学的物理基础还是不够完备的，尚有待改进。例如那个被誉为“科学史上最深奥的发现”的贝尔不等式的推导中都或多或少地引入一些辅助性的假设，这些假设难以用实验直接验证。所有至今完成的贝尔定理的实验验证，没有一个实验能够完全满足贝尔定理所有内涵的要求[2]。

(3)1965年的物理学诺奖获得者，被誉为上世纪“最聪明的美国物理学家”费曼教授( Richard Feynman 19181-988)说过：“我认为我可以肯定地说，现在没有人理解量子力学。”。现代宇宙论的数学结构理论创立者罗杰.彭罗斯爵士(Sir Roger Penrose 1931-)则认为“尽管量子理论非常精确，令人难以置信的精确，且具有难以置信的数学上的美，但也是荒谬之极。”

（全文完）

注释
[1]参见The Born Einstein Letters, with comments by M.Born,Walker,New York(1971).(e.g., in March 1948).
[2] 参见Article on Bell's Theorem by Abner Shimony in the Stanford Encyclopedia of Philosophy (2004).

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