量子密码学三巨头现场问答

2018 年 12 月 26 日 科学出版社

2018年9月1日，量子密码学奠基人Artur Ekert、Charles Bennett、Gilles Brassard 做客墨子沙龙。在他们关于量子科学的科普报告之后，三位科学家就现场观众提出的各个方面的问题进行了回答。在他们的回答中，不仅让人感受到科学家渊博的知识、睿智的思维，更让人直接感受到他们对每个问题的尊重，以及他们自身对事物有不同看法时展现出的真性情。

Artur Ekert 英国牛津大学数学研究所量子物理学教授、新加坡国立大学量子技术中心主任

Charles Bennett IBM研发中心物理学家、信息理论家、现代量子信息理论创始人之一

Gilles Brassard 蒙特利尔大学教授、加拿大研究学会主席

视频

中文

提问1：为什么用“teleportation”这个词来指代量子隐形传态？

Charles Bennett:

在科幻故事里，这个词经常被用来表示一种神秘的科幻过程，即一个物体或一个人在一个地方被摧毁，然后被传输到另一个地方，再被完整无缺地重建起来。所以他们仍然拥有原来的思想，他们的计划仍然在如初进行。这是一种极具想象力的梦幻般的交通媒介。当我们研究出这种操纵量子比特的方式时，我们觉得我们对量子态进行的操作就像“teleportation”。

提问2：您对于给中学生准备报告的感受是什么？

Charles Bennett:

几个月前我就做了一件类似的事情，参加一个叫做“科学碗”的活动。参加这个活动的都是来自美国各地、想要从事科学领域工作的中学生。其中一个学生问我，我应该进入哪个科学领域？我应该学习什么？最活跃最令人兴奋的科学领域是什么？然后我告诉他，他不应该这样去思考这个问题。你在这个房间里说明大概率你是真正对科学感兴趣的，如果你真的是这种人，你一直在思考跟科学相关的事，那么没有比继续思考科学更好的准备方式了。然后我说，我可以给你举个例子，告诉你昨晚发生在我身上的一件事，我自己就一直是那样的人。我当时正在马路上散步，而前几天刚下过雨，街道下面有很大的水流经过雨水管的声音。我走向一个雨水管，听它发出的声音，但是它发出的声音并不是稳定不变的，并不是（模仿稳定水流的声音）而是（模仿变化水流的声音），然后我想，怎么会发生这样的事情呢？我通过栅栏向下看。那里有一根水管，其中的水流正不快不慢地上涨，我知道这个上涨的水流源自何处，——因为由雨水形成的径流，正在渗透进土壤里。然后我听到了另一根雨水管发出的声音，就在坡上离这根十米或二十米的地方。所以我走上去，往里面看。果然，在那里我看到了一根水管，水流在其中正以稳定的速度流过，就像一道稳定输入的声浪。然后我说，我来自一个音乐世家，这就像是一件乐器。当你不吹奏时，长笛是不会发出任何声响的。但当你吹奏它的时候，它会以一个特定的频率振动。如果你像这样地，用科学的思维去思考生活中发生的每一件事，那么你将会成为一个很棒的科学家。

提问3：如何避免窃听者进行窃听？

Gilles Brassard:

窃听者试图对Alice发送给Bob的信号进行的任何测量行为，都会产生扰动。所以量子密钥建立方案要求通信双方——Alice和Bob，能够发现这种扰动。一个很简短的回答是，任意企图的窃听行为都会带来扰动，并且这种扰动是无法避免且无法逆转的，只要接收方发现信号受到了扰动，他就会发现有人在窃听。

Charles Bennett:

我可以做一些补充。这个问题还可以这么问：是否可以阻止窃听者对信号产生扰动？结果是你无法阻止。如果窃听者猛力进行窃听，这会阻碍Alice和Bob建立密钥。但如果窃听者只进行少量窃听，窃听者可能会掌握密钥的信息。但是Alice和Bob会丢弃这个密钥，永远不会用这个密钥来发送有用的信息。

提问4：请问您们对薛定谔的猫有什么见解？

Gilles Brassard:

我认为薛定谔创作这个故事是为了说明这不会发生——你不会有一只又死又活的猫。但以我对物理的理解，这确实是会发生的。与“不是这个就是那个会以一定概率发生”相比，我事实上更能接受它们会同时发生这个观点。量子物理中，所有可能会发生的事都会同时发生。因此，从这个角度来看，薛定谔的猫确实是既死又活的。我十分赞同这一点。

Artur Ekert:

我想要补充一点回答。显然，这是关于我们如何理解量子物理的问题，但不是通过方程式来理解。因为我们都认为对于预测来说，没有比写方程式更好的方式。但当你问一个物理学家、计算机科学家或一个数学家，这到底是代表什么意思？你说的叠加态是什么意思？它背后代表的真实事物是什么？我认为方程式对应了一些真实存在的东西。

有一种看待这些方程式的角度，这是一种独特的看待量子物理的理论，这个理论被称为 Everett诠释，又被称作“多世界诠释”。根据“多世界诠释”，在一些世界中，猫是活的。事实上我很喜欢这个诠释，因为它听起来很疯狂。第一次听到它时，你会说，哇，这么多世界，这一定很疯狂。但事实上，当你更多地思考这个理论时，你会发现它实际上并没有大家以为的那么疯狂。因为它并没有对一些非物理的现象做出神秘的假设，例如波函数的坍塌等。所以，针对你的问题的回答是，我相信在那些世界里，猫是既死又活的。

提问5：现在你打开盒子看到一只活猫。如果你回到五秒前重新打开盒子，会看到什么？

Gilles Brassard:

我想我理解了你的问题，下面我会间接地回答它。相信“多世界诠释”的人是这样看待这个问题的，Artur和我都相信多世界诠释，盒子中的猫在同一时刻是又死又活的。当你打开盒子的时候，你是同时看到猫活着和猫死了这两种状态的。所以，通过打开盒子，你分解成两个世界的你，在其中一个世界你看到猫是死的，对于这个世界中的你来说，猫是死的。而在另一个世界中，你会看到猫是活的。所以这跟是否回到过去并没有关系。在盒子打开前，分裂在盒子内部发生。当盒子打开后，分裂从盒子内部扩散到盒子外部。你将会同时看到猫死了和猫活着两种状态。

Charles Bennett:

另外，关于回到过去这个问题，你必须说清楚是如何回到过去的，你真的回到了你现在所处的这个世界的过去了吗？

Artur Ekert:

是的，你是否回到了现在的你所处的世界的过去，还是去了另一个世界的过去？

Charles Bennett:

另外，还取决于你是否撤销了你现在（对盒子中的猫）的观察。你可以用一个简单的半波片来撤销分裂，这个实验叫做量子擦除实验。如果一个物体，并不像猫一样拥有那么多原子，而是仅仅有一个或两个原子，撤销对它的观察是完全可行的。因为并没有那么多的状态需要进行重组。所以在这个问题上，我也跟很多其他人一样，认为这是一个定量和实操上的差别，也就是说你无法撤销一个量子观察，不是因为它在本质上是无法逆转的，而是跟你无法将炒鸡蛋回复原状一个原因，即使你可以恢复一个或两个原子的位置。

Artur Ekert:

是的。所以实际上，用更专业的术语来讲……

Charles Bennett:

在炒鸡蛋的问题上，如何更专业呢？

Artur Ekert:

首先，我会尽可能利用我的实验技能来炒鸡蛋。如果你们对量子物理稍微有一点专业的了解的话，你们将会知道这就像逆转幺正变换。这个过程是可以被逆转的。所以这是一种可逆的想法。多世界诠释认为所有事物都可以用方程表示，包括你。幺正变换被作用在猫身上，你的身上，就像对所有事物的观察。诸如此类，这些过程都是可以被逆转的。但很显然，从专业角度来看，就像Charlie指出的那样，这就像试图将炒鸡蛋恢复原状。所以宇宙就像是你在计算中选择一个基矢。在这个特定的例子中，从单宇宙的角度来看，并不是这样的。但是从多元宇宙的角度来看就是这样的。

Gilles Brassard:

有一个网站，在这个网站上，你花三美元九十五美分就可以买到一个宇宙，我是很严肃地在说这件事，但我不确定他们是否是严肃的。这个网站的操作方式是这样的：比方说你现在必须要做一个重要的决定，是去散个步还是洗个澡？你无法下决心应该怎么做，但是你意识到不管你选择做哪一件事，你都无法做另一件。并且很有可能你没有做的那件事会带给你名望和财富。现在你无法决定做哪一件事。所以这个网站提供了一个方法，让你通过掷一个量子硬币来决定做什么。首先，你要跟自己约定：如果硬币正面朝上，你就去洗澡；如果硬币反面朝上，你就去散步。你向自己保证将会按照掷硬币的结果去做。然后你抛这个量子硬币，并根据这个硬币的结果来行动。如果你相信量子力学，在抛硬币的时刻，宇宙分裂了，所以两件事你都会去做。如果你选择做的这件事最后导致了很糟糕的结果，至少你会因为也干了另一件事而感到些许安慰。尽管这并不会帮助你特别多。

Charles Bennett:

我觉得如果他们是以诚实的态度经营这个网站，并且你想要撤销你的购买的话，他们应该把钱还给你。

Gilles Brassard:

他们甚至提供会员服务。我记得花二十美元你就可以每个月分裂宇宙一次。所以花二十美元你就可以创造出四千零九十六个宇宙。他们还会给你一件T恤。但有个问题是，他们是在你开始前还是在最后才给你T恤？如果他们是在最后给你T恤，他们应该给你四千零九十六件T恤。

提问6：我们是否可以通过量子隐形传态将一个生命体传输到另一个地方？生命体中存在量子纠缠现象吗？

Artur Ekert:

我认为你的问题包含两个不同的问题。说到第一个问题，即我们是否可以分解一个复杂物体。我们都认为这在理论上是可行的，但实际上我们认为永远都无法做到这一点。如果人体在数量级上包含十的二十三次方个原子，你需要执行非常复杂的贝尔态测量操作。所以我认为不仅是如今的科技无法实现这点，未来的科技也同样无法实现。

现在我们来谈论一下第二个问题。我想你可能会知道生命体中已被发现存在固有的量子相干现象。例如，我们知道有些细菌居住在不太见光的湖底，并且它们通过光合作用来获得能量。所以每个到达这个细菌的光子都非常非常的宝贵。因此，从细菌中的光捕获单元到化学反应中心的能量转移必须十分高效。科学家对这个过程进行研究后发现，量子叠加可以使得这个过程更加高效。所以如今我们可以说，在生命体中存在不平凡的量子现象。

提问7：还需要多少年我们能够造出破解基于RSA算法或椭圆曲线算法保密系统的量子计算机？比如比特币是基于椭圆曲线算法的，那么多久之后经典加密算法无法再被应用在商业上？

Gilles Brassard:

事实上这个很难预测。但这方面的发展比我原来以为的快多了，还需要多少年才会发生呢？大概至少十年吧。然而，就像我之前所解释的，一旦量子计算机出现，过去的所有秘密都会被摧毁。所以将没有任何秘密，不仅是RSA被破解之后的信息，而是你自出生后发送的所有信息，你曾相信被RSA算法或椭圆曲线算法保障了安全性的所有信息。这些信息以加密形式被其他人储存了起来。一旦他们拥有了量子计算机，他们就会打开所有的旧秘密。所以这是一个十足的灾难。

Artur Ekert：

我感觉你是在担心比特币的安全性。因为比特币建立在两个特征上，而这两个特征可以——或者说某种程度上——可以被量子计算机破解。一个可被破解的地方存在于区块链。你需要数字签名，而数字签名基于椭圆曲线算法，椭圆曲线算法在量子攻击面前是脆弱的。另一个可被破解的地方存在于挖矿的过程中。你在挖矿时会进行广泛的搜寻，而这一点会遭受算法的影响。尽管我认为第一个可破解点，数字签名的破解，对比特币来说是更危险的。但就像Gilles在他的报告中所指出的，量子计算机的出现并不意味着经典公钥密码系统的终点。因为你能够很容易地想到，可以通过给比特币协议加一层来提升它的性能。例如，可以将数字签名建立在格密码上，那将会在未来保护系统的完整性。所以是有方法可以解决比特币的问题的。在现有的形式下，比特币显然在量子攻击面前是脆弱的。对大家来说这是一个很好的课题，关于如何提升比特币使其可以抵抗量子攻击。

Gilles Brassard:

我不同意你的说法，我认为比特币是我们现有科技下最糟糕的发明。因为比特是基于大量的计算，而这种计算毫无用处。比特币的挖矿没有任何目的，除了能让一部分人变得富有。所有的这些计算都需要耗费大量的能量，这些能量是被浪费掉的。那些浪费掉的能量变成温室气体排放到大气中，正在加速气候变化，而且比特币是造成气候变化灾难的主要因素之一。所以对我来说，比特币是一个怪兽，如果量子计算机可以摧毁比特币，我并不希望它被其他的密码系统拯救。

Artur Ekert:

我也想发表点不同意见。即使我们在比特币的问题持不同意见，它仍然是一种加密货币。它仍然包含了很有趣的区块链的概念，不管你挖矿还是不挖矿。在比特币这个例子中，它使用了分布式账本的概念。我认为它是一种设计精巧的加密货币。不管我们是否喜欢它，这也是一种很有趣的概念，并且最终会被接受。到了某个时刻，量子界肯定将会占据一个位置。

Charles Bennett:

以前我也跟 Gilles一样，认为比特币具有危害性。后来我改变了我的想法，因为我想，是谁在付电费呢？为什么他们愿意为此付钱？他们愿意为此付费是因为对他们来说，相比较其他的转移货币或保持账本完整性的方式，分布式账本和通过比特币来转移货币花费更少。所以如果对生意有帮助的话，他们是不会愿意多付电费的，后来需要额外付的费用变成了矿工的挖矿津贴。这时，相比较其他处理账本的方式，比特币对他们来说是一个更糟糕的选择。这是一种不完备的经济学思考。就像有些人会说，让我们只吃本地生产的食物吧，但这可能意味着在冬天你需要为温室中的照明消耗大量电力，那么将食物从西班牙装上船运来，会更加节省能源。那么我会说，通过运输来获得食物更好。

Gilles Brassard:

我的观点是，有些人会说，为什么我需要在乎这些？如果我可以变得富有的话，那就破坏环境好了。

Charles Bennett:

哎呀，我知道有些人就是这样的。

提问8：量子物理中是否也使用了洛伦兹变换？

Charles Bennett:

是的。量子物理中也用了洛伦兹变换。比方说，我们有一位已故同事做了一些工作，研究处于相对运动的参考系中物体间的量子通信，就是说物体间的相互运动会对量子通信产生影响，但是这种影响现在已经研究得很透彻了。

Artur Ekert:

当然已经存在相对论量子物理。我们在这里讨论的基本上都在非相对论范畴。有趣的是，狭义相对论和量子理论，尽管产生于不同的思维方式，但让人惊奇地是，它们彼此相容。这实际上是非常有趣的。所以这实际上或许表明了这并不太令人惊奇，因为这两个理论都描述了现实的本质。但是这也展现了关于自然如何运转，我们仍有不完全清楚的地方。所以要去努力，特别是进入广义相对论后。要努力去理解量子引力和这些联系，这些都是物理学的前沿问题。希望你们中的一个可以将它进一步发展。

提问9：有将广义相对论和量子力学结合在一起的理论吗？

Artur Ekert:

如今有很多研究量子引力的方法。但是我觉得如今我们还没有一个很明确的量子引力理论。这个领域已经存在很多现象学模型。例如，你可以问某种量子现象在引力场中是怎样的？所以已经存在很多现象学模型，但是目前还没有一个很自洽的量子引力理论。

提问10：在遇到一些十分难懂的数学概念时，我们应该怎么做？

Gilles Brassard:

关于这个问题爱因斯坦曾经给过一个很出名的回答，一个小女孩告诉他她在数学上遇到了麻烦。爱因斯坦回答，相信我，我在数学上遇到的问题比你大。换句话说，数学从来都不是容易。但是数学很重要，很美。所以你需要努力学习数学并且不要感到气馁。

英文

Problem 1

Why did you use the word “teleportation”?

Charles Bennett

Well, in science fiction, teleportation is often used to mean a mysterious science fiction process, where an object or a person is destroyed in one place, and transported to another place, intact. So that they have their thought, and their plans are all there. It's a fancy medium of transportation. And so it seemed to us when we worked out this way of handling qubits, that what we were doing to the quantum state was like teleportation. We were disembodying it in one place, and recreating it exactly in another place.

Problem 2

What is your feeling about preparing a talk for middle school students?

Charles Bennett

Because I actually did this a few months ago. And it was something they called The Science Bowl, which was (attended by) secondary school students from all over the united states who were especially going into science. And one of them asked me, what field of science should I go into? What should I study? What's the most active or exciting field of science? And I said that was the wrong way to think about it.

If you were the kind of person that you probably are if you're in this room, you think about science all the time, and there's no better preparation than continuing to do that. Then I said I could give you an example of what happened to me last night. Not last night now, but last night from then. Because I was always that kind of person.

I knew I wanted to be a scientist since I was three years old. And I was walking up and down the street, and it had rained a couple of days earlier. And there was a lot of sound of the water running under the streets through the storm sewers. And I walked up to a storm sewer and I listened to it. And the sound was not steady, wasn't……But was…..So I said, well, why can that be happening? And I look down under the grid. And there was a pipe, and water was coming in at an intermediate rate. But I know where was the water coming in from, because the runoff from the rain was all just percolating through the soil. And I saw there was another storm sewer, just about ten or twenty metres up the hill from this one. So I walked up and looked in there. And there I saw a pipe, and water was running in at a steady rate. But the water in the tank of the sewer, I mean this little meter square space under the street, that you could look down through, was sloshing back and forth, was like a wave that was being driven by the steady input. And I said, well, I come from a musical family. I said, this is just like a musical instrument. A flute doesn't make any sound when you don't blow on it. But when you blow on it, it oscillates at a particular frequency.

So I said if you go through life thinking that way about everything, then you'll be a good scientist.

Problem 3

How to avoid eavesdropping from eavesdroppers?

Gilles Brassard

Well, the eavesdropper and any attempt by the eavesdropper to measure the signal from Alice to Bob, Will create a disturbance. So the protocol for quantum key establishment requires the two parties, Alice and Bob, to notice that disturbance. And the detail how this is done, was one of the slides of Charlie Bennett. But he did not go through the detail. I'm not sure how much detail I should give. But the very short answer is that, because any attempted eavesdropping creates a disturbance, that’s unavoidable and irreversible. As long as the receiving party can notice that the signal has been disturbed, he will know that there was eavesdropping.

Charles Bennett

I can add to that, maybe. The question might have meant, can you prevent the eavesdropper from disturbing the signal? No, you can't. If the eavesdropper eavesdrops vigorously, then that will prevent Alice and Bob from establishing a key. But if the eavesdropper eavesdrops a little bit, the eavesdropper might learn about the key. But Alice and Bob will reject it, and never use it for sending a meaningful message.

Problem 4

Is renormalization a mathematical technique, or an objective existence in physics?

Charles Bennett

I think it means something different in condensed matter theory and field theory. There is a renormalization that we do in quantum information, which is when a measurement occurs, the term in the superposition, instead of having a coefficient of the square root of a half, the one that happens gets a coefficient of one, and the other one gets a coefficient of zero.

Problem 5

What are your views on Schrodinger’s cat?

Gilles Brassard

Well, I think that he’s doing very well. Seriously, Schrodinger invented this story, I think, to say that this would not really happen, that you would not have a cat as both dead and alive. But my view of physics is that it does happen. And in fact I am perfectly comfortable with the idea. (Compared with) all these things that standard quantum theory tell you, that either this or that happen with some probabilities, (that) it’s random, one or the other would happen, I’m much more comfortable with the view that they both happen, actually. And that everything that could happen in quantum physics does happen, all at the same time. And therefore, seen that way, the Schrodinger’s cat is indeed both dead and alive. And I have no problem with that.

Chen Yu'ao：

Artur, do you want to add some?

Artur Ekert：

Well, yes. It’s a question, of course, how we understand quantum physics, not necessarily in terms of equations. Because when you write down equations, we tend to agree that there's no better matter of this agreement when it comes to predictions, writing equations. But when you ask a physicist, all computer scientists or a mathematician, what do you really mean by that? What is this superposition that you have? Is there a real thing behind it? Then some people say, yeah, you know, it's just a question of interpretation.

It's not a realistic thing. I'm a realist. I think that the equation correspond to something that is really out there. And there's one way of looking at it. It is a particular way of looking at quantum physics. It is to take equations of quantum physics very seriously. And it's called the Everett interpretation, where you also know as the many-worlds interpretation, where you can say, in some worlds, the cat is alive, in some others, it is dead. And I'm actually quite happy with this interpretation, because it sounds crazy. First time you hear about it, you say, wow, so many worlds, it must be crazy. You have one of those wacky scientist, right? But actually the more you think about it, you realize that it is actually less crazy than people think. Because it doesn't make some mystical assumption about some unphysical phenomena, like a collapse of the wave function, and so forth.

So, to answer your question, I believe the cat is really both dead and alive in some of those worlds.

Problem 6

Now you open the box and see an alive cat. If you travel back to five seconds ago to reopen the box, what will you see?

Gilles Brassard

I think I understand your question and I will not answer it directly. But tell me, if my answer doesn't answer your question. The way that people who believe in the many-worlds interpretation see things, Artur and I are among them, is that the cat in the box is simultaneously both dead and alive. When you open the box, you simultaneously see both things. So you, by opening the box, you split between one of you who sees the cat dead, and the cat is dead for you. And in a different universe, you see the cat being alive. It is alive. So it's not a matter of going back in time. The splitting occurs inside the box until the box is open. When the box opens, and then the splitting goes out. And you see the cat both dead and alive.

Chen Yu'ao

So you would believe in the interpretation of the multiverse？

Charles Bennett

And also, going back in time, you have to say how you do it.Do you go back?

Artur Ekert

Yeah, whether you go to the same universe, or the other one.

Charles Bennett

Also, whether you undo your observation of (the cat inside the box).When I said you could undo this splitting with a simple half-wave plate, this is a quantum eraser experiment. So for a thing that instead of having as many atoms as a cat, has one atom or two atoms. undoing it is perfectly possible, because there are not that many states to recombine. So I think I would agree with the other people that it's a quantitative and practical difference, that you can't undo a quantum measurement, not because it's intrinsically irreversible, but for the same reason that you can't unscramble an egg, even though you can unscramble the position of one or two atoms.

Artur Ekert

Yeah. So actually, in more technical terms…

Charles Bennett

How could you be more technical on scrambling an egg?

Artur Ekert

Well, it goes as far as my experimental abilities, to scramble them in the first place.But (for) those of you who are familiar a little bit with the technical side of quantum physics, it's like reversing unitary operation. It can be reversed. Right? So it's a reversible think. And the many-worlds (interpretation) takes the view that everything goes into the equation, you included. So this unitary operation is performed on the cat, on you, as the observation on everything. And as such, it is reversible. But of course, technically, as Charlie pointed out, it's like unscrambling the egg.

Artur Ekert

Yeah. So the universe is like, picking up the bases in your computation.In this particular case, from the perspective of one universe, it is not. But from the perspective of the multiverse, it is.

Gilles Brassard

There is a website called cheap universes dot com and there on that website, you can buy a universe for only three dollars, ninety-five cents. I'm totally serious. I'm not sure if they are. But the way it works is that…Let's say that you must make an important decision, either go to take a walk or take your bath. And you can't decide which you should do. But you realize that whichever you do, you don't do the other. And perhaps the one that you don't do would bring you fame and fortune. And you just cannot decide which to do. So first, you commit to yourself. If the coin turns up heads, you take a bath. If it turns up tails, you go for a walk, you completely commit to yourself that you will do that. Then you flip the quantum coin, and you do what a coin tells you. If you believe in quantum mechanics, and even if you don't actually, and if you are sincere about doing what you're committed to do, then you actually do both. At the moment when the coin is flipped, the universe is split, and yet you will do both things.at least you can be content to know that you have also done the other. Although it doesn't help you much.

Charles Bennett

Well, I think that if they really want to be honest about that site, and you do want to undo it, they should give you your money back.

Gilles Brassard

Well, they even sell you a subscription. And I think, for twenty dollars, you get to split the universe once per month. So you get to create four thousand ninety-six universes for twenty dollars. And they even give you a t-shirt. So the question is, do they give you a t-shirt before you start or at the end? If they you give it to you at the end then (that) you get four thousand ninety-six t-shirts is much better.

Problem 7

Can we transfer a living organism to another place through teleportation? Does the phenomenon of quantum entanglement exist in living organisms?

Artur Ekert

Well, I think there are two different questions in your question. One is (a question that) you already understand correctly. One is can we transfer a complex object such as a human being, via for example teleportation using entanglement to some other place?

And the other question that you asked, which is a very interesting one, is whether there is a quantum phenomenon, such as entanglement, or perhaps superposition in the living quantum system. When it comes to the first question, we had a wonderful interview this morning. And one of the interviewer who were from sort of a secondary school asked the same question whether you can tear apart a complex object, to which we all agree that, in principle it’s possible, but practically we don't think we will ever be able to do it. If you have ten to twenty three atoms in a human being of the order of magnitude, you have to perform a very complicated Bell measurement. So it's just beyond technology not even now, but in the future. When it comes to the second question though…I think you may know that there are inherently coherent quantum phenomena being discovered in living organisms. For example, we know that some bacteria live at the bottom of lakes where there's very little light, and they use photosynthesis to get energy. So every single photon that comes to this bacteria is very, very precious. And therefore, the energy transfer between light-harvesting units in the bacteria to a chemical reaction center has to be very efficient. And it turns out that in this process, quantum superposition helps to make this process more efficient.

So these days we can say that we can see that there are nontrivial quantum phenomena in living systems.

Problem 8

How many years it will take to build a quantum computer that can break commercial cryptosystems that are based on the RSA algorithm or the elliptic curve algorithm?

Gilles Brassard

Well, this is very hard to predict. But I say that the progress has been really much faster than I would have thought, if you had asked me ten or twenty years ago. So I don't have any serious doubts. It will happen. How many years? Is that clear? Probably at least ten. However, as I explained, as soon as it happens, all secrets from the past are destroyed. So there's no secrecy whatsoever, not only from the time RSA is broken, but everything that you have sent since you were born, believing it was secured by RSA or elliptic curves. All of that has been taken down by an encrypted form by someone or other. And they can come back as soon as they have a quantum computer, and open up all the old secrets. So it's a complete disaster. Now I did not understand why you mentioned bitcoin, or block chain.

Artur Ekert

So I’m in the sense that you are concerned about the security of the bitcoin. Because it relies on two features that can be broken by, or to some extent, can be broken by quantum computers. One is in the block chain. You need the digital signature, which is based on elliptic curves, which we know are vulnerable, as you explained, to quantum attacks. And the other part is in the mining process. You use extensive search. And this, again, can be affected by the Grover’s algorithm. Even though I think the first one, the breaking of the digital signature is much more dangerous in this case.

Gilles again pointed in his talk, that it's not necessarily the end of classical public-key crypto systems, because you can easily imagine improving the bitcoin protocol by adding another layer. For example, the digital signature can be based on a lattice-based crypto. And so that would actually protect the integrity of the system in the future. So there is a way of fixing bitcoin. In the current form, bitcoin certainly is vulnerable to quantum attacks. It's a good project for people actually, How to improve bitcoin to make it immune to quantum attacks.

Gilles Brassard

I beg to disagree, for a different reason. I think that bitcoin is about the most horrible invention of our current technology. Because bitcoin is based on a notion of doing enormous amount of calculation, which is completely useless. Its mining has no purpose, whatsoever, other than getting some people rich. And all of these calculations require a large amount of energy.

That energy is wasted. And that wasted energy goes into green gas effects in the atmosphere. We are precipitating the climate change. And bitcoin is making it one of the major factors in the current disaster of climate change. So to me bitcoin is a monster. And if quantum computers can destroy bitcoin, I don't wish it to be saved with using other cryptography.

Artur Ekert

Well, I beg to disagree here. But even if we disagree about the bitcoin, there's still a crypto currency in general. There's still an interesting concept of the block chain whether you do mining or not mining. In this particular case, it's the distributed ledger. But I think that there's an ingenious cryptographic thing. And whether we like it or not like it, it's an interesting concept that will be adopted. And at some point, quantum community will have to take a position, certainly.

Charles Bennett

Well, after having agreed with Gilles about the perniciousness of bitcoin in the block chain. I changed my mind, because I thought, well, who is paying for this electricity?

Why are they paying for it? They're paying for it because the distributed ledger and the ability to move currency around with bitcoin is for them less costly than other means of moving the money around or maintaining the integrity of the ledger. So if it's useful for businesses, they were not going to pay more in electricity costs, which are then transferred into these mining subsidies for the miners, Then it's worse to themover doing the ledger some other way. It's the same kind of incomplete economic thinking as people who say, let's eat only locally grown food. But if that means that you have to use a lot of electricity to run the lights in your greenhouse, during the winter,and it's cheaper to put it on a boat and bring it from Spain. Then I would say, well, the one that has the transportation is better.

Gilles Brassard

My view is that some of these people would say, why should I care that? I'm just destroying the environment if I'm getting rich from it.

Charles Bennett

Oh, I know there are people like that.

Problem 9

Is Lorentz transformation also used in quantum physics？

Charles Bennett

So yes. And there is like that our late colleague, did a lot of work on quantum communication between parties that are in different reference frames moving relative to one another. And so it does change it, but in a way that has been well worked out.

Artur Ekert

And perhaps I should add a little bit. There is, of course, relativistic quantum physics. What we discussed here was basically in non-relativistic domain. But what is interesting though, is that somehow special theory of relativity and quantum theory, even though they come from sort of a different way of thinking, somehow amazingly they kind of respect each other. It is actually quite interesting. That actually shows maybe it's not so surprising, because both of them describe underlying reality. But it also shows that there's something we don't understand fully about how the nature work. So trying, especially if you go further to general theory of relativity. Trying to understand quantum gravity and those connections, something that is on the frontier of physics. And hopefully one of you will just push it any further.

Problem 10

Is there a theory that combines general relativity and quantum mechanics?

Artur Ekert

Now, there are many approaches to quantum gravity. But I think that at the moment So, this is the area where you can have various phenomenological models. You can, for example, ask questions how certain quantum phenomena will look in gravitational field. So there are phenomenological models, but there's no like one consistent and good theory of quantum gravity at the moment.

Problem 11

What should we do when encountering some mathematical concepts that are very hard to understand?

Gilles Brassard

Well, I think that Einstein famously answered this question to a little girl who was telling him that she had trouble with mathematics. And he answered, believe me, my difficulties with mathematics are far greater than yours. So in other words, math is not always easy. But it's important. And it's beautiful. And you need to work hard on it and not get discouraged.

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