系统可存储信息所需的粒子数量及临界点是什么？

Great question—this dives right into the sweet spot between quantum behavior, information theory, and practical storage reliability, which is such a fascinating area to unpack. Let’s break this down clearly:

1. How many particles do you need to store information? #

There’s no universal fixed number—it all depends on what kind of information you’re storing, how long you need to keep it, and the environment the system lives in. But let’s tie this to the constraint you mentioned: single subatomic particles or nuclei can’t reliably store information. Here’s why, and how adding particles changes things:

• For classical information (the 0s and 1s in your hard drive, for example), you need a system that can hold two distinct, stable states. A single particle’s state (like an electron’s spin up/down) is way too fragile—thermal noise, stray electromagnetic fields, or even quantum tunneling will flip it in microseconds, making it impossible to trust the stored data. To fix this, you need a group of particles whose collective state resists these disturbances:
  • A magnetic domain in a hard drive uses millions of aligned atoms, but even a smaller cluster (hundreds to thousands of atoms) could act as a stable bit if shielded properly—because the odds of all those atoms flipping randomly at once are astronomically low.
  • Put simply: more particles mean more redundancy against random noise.
• For quantum information (quantum bits/qubits), the math gets trickier. A single particle can act as a qubit in theory, but quantum states are even more fragile than classical ones. To store a quantum bit reliably, you need error-correcting codes that use multiple physical particles to protect one logical qubit. Depending on the code (like surface codes), this could require 50–100+ physical particles to keep a single logical qubit stable long enough to use.

2. What’s the "critical threshold" when adding particles makes information storage possible? #

This threshold isn’t a rigid number—it’s the point where the system shifts from being too fragile to hold information to being reliably usable. It’s defined by three key, interconnected factors:

• Stability against noise: Below the threshold, random environmental disturbances (heat, radiation, etc.) can easily flip or scramble the system’s state. Above it, the collective behavior of the particles averages out these tiny disruptions. For example, a single atom’s spin might flip in microseconds, but a cluster of 100 aligned atoms will stay that way for minutes or hours, even at room temperature.
• Distinct, measurable states: Below the threshold, the system’s possible states blur together (either because the energy difference between states is too small, or noise makes them indistinguishable). Above the threshold, the collective state creates clear, separate "bins" (like 0 and 1) that we can measure without ambiguity.
• Practical operability: Below the threshold, trying to write or read information would disrupt the system entirely (you can’t measure a single particle’s state without changing it, for example). Above the threshold, we can interact with the system’s collective state (using magnetic fields, lasers, etc.) to encode or retrieve data without destroying the stored information.

It’s also worth noting this threshold is flexible: cool the system to near absolute zero (reducing thermal noise) and you can get away with far fewer particles. If you only need to store information for a fraction of a second, even a small cluster might work. But for long-term, room-temperature storage, you need enough particles to beat the odds of random noise wiping out your data.

内容的提问来源于stack exchange，提问作者DannyH