你好，量子世界！/ Hello, Quantum World!

你举着一支裹着糖霜的草莓冰棍站在夏天的太阳底下，还没咬上一口，就发现甜筒的尖尖已经开始往下滴水了。你顺手把口袋里的条形磁铁放在装满回形针的铁盒子上，晃了晃盒子，上百个回形针噼里啪啦全被吸到了磁铁底部。这时候你有没有过这样的疑惑：为什么冰棍会自己融化？为什么磁铁能隔着盒子吸住回形针？

You hold a sugar-coated strawberry ice lollipop under the summer sun, and before you take a bite, you notice the tip of the cone is already dripping. You casually place the bar magnet from your pocket on a box full of paper clips, shake the box a little, and hundreds of paper clips clatter onto the bottom of the magnet. Have you ever wondered at this moment: why does the ice lollipop melt on its own? Why can the magnet attract paper clips through the box?

这些我们天天见到的现象，都遵守宏观世界的规则：冰棍的温度比周围高，热量就会从温度高的地方往温度低的地方跑，直到冰棍和周围温度一样，就融化完了；磁铁周围有看不见的磁场，铁做的回形针会被磁场吸引，哪怕中间隔了个纸盒子。宏观世界的东西，你扔出一个球，它要么在空中飞，要么落在地上，不可能同时既在天上又在地上；你家里的灯要么开着，要么关着，不可能同时既亮又灭。我们把这种“非此即彼”的状态叫经典状态，你每天接触的几乎所有东西，都是经典状态的。

These daily phenomena all follow the rules of the macroscopic world: the ice lollipop is hotter than its surroundings, so heat transfers from the hotter place to the cooler one until the lollipop reaches the same temperature as its surroundings and finishes melting; there is an invisible magnetic field around the magnet, and iron paper clips are attracted by the magnetic field, even if there is a paper box in between. Objects in the macroscopic world: if you throw a ball, it is either flying in the air or on the ground, and it cannot be in both places at the same time; the light in your home is either on or off, and it cannot be both bright and off at the same time. We call this "either/or" state a classical state. Almost everything you come into contact with every day is in a classical state.

但如果把你的眼睛放大一亿倍，小到能看到原子、电子这些微观粒子的时候，你会发现世界的规则完全变了：电子可以同时出现在好几个地方，光子可以同时走两条路，两个离得特别远的粒子还能“心电感应”，一个动了另一个瞬间就变。这个比原子还小的微观世界，就是量子世界，它的规则和我们日常见到的世界完全不一样，看起来就像魔法一样。

But if you magnify your eyes by 100 million times, small enough to see microscopic particles like atoms and electrons, you will find that the rules of the world are completely different: electrons can appear in multiple places at the same time, photons can travel two paths at the same time, and two particles that are very far apart can have "telepathy", when one moves, the other changes instantly. This microscopic world smaller than atoms is the quantum world, its rules are completely different from the world we see every day, and it looks like magic.

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1.1 量子世界的三大魔法 / Three Magical Rules of the Quantum World

> 📌 小博士提示（Sidebar: Little Scientist's Tip）：量子（Quantum）这个词来自拉丁语，意思是“有多少”，因为物理学家发现微观粒子的能量不是连续的，而是一份一份的，比如光的能量就是一份一份的光子，所以用量子来描述微观世界的最小单位。 > 📌 Little Scientist's Tip: The word "quantum" comes from Latin, meaning "how much". Physicists found that the energy of microscopic particles is not continuous, but quantized, for example, the energy of light is one photon at a time, so "quantum" is used to describe the smallest unit of the microscopic world.

1.1.1 魔法一： superposition / Magic 1: Superposition

宏观世界里，一个东西的状态是确定的：你面前的杯子要么在桌子上，要么在地板上，不可能同时在两个地方。但量子世界里的粒子不一样，它可以同时处于多个状态的叠加，这就是量子叠加态。

In the macroscopic world, the state of an object is certain: the cup in front of you is either on the table or on the floor, and it cannot be in two places at the same time. But particles in the quantum world are different, they can be in a superposition of multiple states at the same time, this is called quantum superposition.

你可以把量子叠加想象成一个永远转不停的陀螺：宏观的陀螺停下来的时候，要么尖朝前，要么尖朝后，状态是确定的；但量子的“陀螺”可以同时尖朝前又尖朝后，直到你伸手按一下它，它才会“选”一个状态停下来。你按的这个动作，在量子力学里叫测量，测量会让叠加态“坍缩”成确定的经典状态。

You can think of quantum superposition as a top that never stops spinning: a macroscopic top, when it stops, either points forward or backward, and its state is certain; but a quantum "top" can point both forward and backward at the same time, until you reach out and press it, it will "choose" a state to stop. The action of you pressing it is called measurement in quantum mechanics, and measurement will make the superposition state "collapse" into a certain classical state.

我们用量子比特（Qubit）来描述量子世界的“开关”，经典比特只能是0或者1，但量子比特可以同时是0和1的叠加态。用数学公式来表示的话，量子比特的状态可以写成： We use qubits to describe the "switches" of the quantum world. A classical bit can only be 0 or 1, but a qubit can be in a superposition of both 0 and 1 at the same time. Expressed in a mathematical formula, the state of a qubit can be written as: $$|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$$ 这里的$|0\rangle$和$|1\rangle$是量子比特的两种经典状态，$\alpha$和$\beta$是概率幅，它们的平方和等于1，也就是$|\alpha|^2 + |\beta|^2 = 1$。如果$\alpha$和$\beta$的绝对值都是$\frac{\sqrt{2}}{2}$，那么这个量子比特有50%的概率测量得到0，50%的概率测量得到1。 Here $|0\rangle$ and $|1\rangle$ are the two classical states of the qubit, and $\alpha$ and $\beta$ are probability amplitudes, the sum of their squares is equal to 1, that is $|\alpha|^2 + |\beta|^2 = 1$. If the absolute values of $\alpha$ and $\beta$ are both $\frac{\sqrt{2}}{2}$, then this qubit has a 50% probability of measuring 0 and a 50% probability of measuring 1.

> 📌 趣味小实验（Sidebar: Fun Experiment）：你可以拿一枚硬币来做小实验：把硬币抛到空中，在它落地之前，你可以说它同时是正面和反面（叠加态），等你用手按住它（测量），它就会变成确定的正面或者反面。这就是量子叠加的简化版哦！ > 📌 Fun Experiment: You can do a small experiment with a coin: throw the coin into the air, before it lands, you can say it is both heads and tails (superposition), when you press it with your hand (measurement), it will become a certain heads or tails. This is a simplified version of quantum superposition!

 *漫画1：左边的宏观陀螺停下来只能尖朝前或尖朝后，右边的量子陀螺可以同时朝两个方向，直到被测量* *Comic 1: The macroscopic top on the left can only point forward or backward when it stops, while the quantum top on the right can point in both directions at the same time until it is measured*

1.1.2 魔法二：量子纠缠 / Magic 2: Quantum Entanglement

量子世界还有更神奇的魔法，叫量子纠缠：如果你把两个量子比特“纠缠”在一起，不管它们离得有多远，哪怕一个在地球，一个在月球，只要其中一个的状态变了，另一个的状态会瞬间发生改变，不需要任何时间传递信号。

There is even more magical rule in the quantum world called quantum entanglement: if you "entangle" two qubits together, no matter how far apart they are, even if one is on Earth and the other is on the moon, as long as the state of one changes, the state of the other will change instantly, without any time to transmit the signal.

爱因斯坦把这种现象叫做“幽灵般的超距作用”（Spooky action at a distance），因为他觉得这太不可思议了，怎么可能两个离得那么远的东西能瞬间关联？但后来的实验证明，量子纠缠是真的存在的，它不是科幻，是已经被验证的物理现象。

Einstein called this phenomenon "spooky action at a distance", because he thought it was too incredible, how could two things so far apart be instantly connected? But later experiments proved that quantum entanglement is real, it is not science fiction, it is a physical phenomenon that has been verified.

> ⚠️ 小博士纠错（Sidebar: Correction from Little Scientist）：很多人觉得量子纠缠可以超光速传信息，这是错的哦！因为纠缠粒子的测量结果是完全随机的，你没法控制其中一个粒子变成0还是1，所以没法用它来传递信息，相对论说的“光速是速度上限”还是成立的。 > ⚠️ Correction from Little Scientist: Many people think quantum entanglement can transmit information faster than light, this is wrong! Because the measurement results of entangled particles are completely random, you cannot control whether one particle becomes 0 or 1, so you cannot use it to transmit information, the theory of relativity's statement that "the speed of light is the upper limit of speed" still holds.

你可以把纠缠的量子比特想象成一对手套：你把左手套放在北京，右手套放在上海，你打开北京的盒子发现是左手套，不用看就知道上海的是右手套，不管它们离得多远，状态都是关联的。但量子的纠缠比手套更神奇：手套在放的时候就已经确定哪个是左哪个是右了，但纠缠的量子比特在测量之前，两个都没有确定的状态，一个变成0的瞬间，另一个才会瞬间变成1，哪怕它们之间隔了一光年远。

You can think of entangled qubits as a pair of gloves: you put the left glove in Beijing and the right glove in Shanghai, when you open the box in Beijing and find it is the left glove, you know the one in Shanghai is the right glove without looking, no matter how far apart they are, their states are related. But quantum entanglement is more magical than gloves: when the gloves are placed, it is already determined which is left and which is right, but before measurement, neither of the entangled qubits has a certain state, when one becomes 0 instantly, the other will instantly become 1, even if they are a light-year apart