# Quantum definition of information

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• lostinspace1999
In summary: If you put an ice cube on a hot metal plate, it will predictably melt into a puddle of water. So your equations allow you to compute the future state from the past state. On the other hand, if you start with a plate holding a puddle of water, you can't figure out that it used to be an ice cube. Hot water cooling off leads to the same final state as ice melting. So melting seems irreversible. But in classical physics, at least, the microscopic details--the positions and momenta of the water molecules--will be different depending on whether it was once an ice cube. The information about the past was not truly lost, it just became inaccessible--it's stored in the details of the motions of microscopic

#### lostinspace1999

Watching a physics documentary I heard the following statement 'If an object falls into a black hole, what happens to its information'.

I have a problem understanding the definition of information

Is this. Information we could have gained through study? Or, Information governing particles at an quantum level?

Sorry if it sounds like a dumb question, just confused me, not difficult these days

Information is not a well-defined physical concept. It is an informal, more intuitive but subjective, way of talking about the objective physical (and statistical) concept of entropy.

lostinspace1999 said:
Watching a physics documentary I heard the following statement 'If an object falls into a black hole, what happens to its information'.

I have a problem understanding the definition of information

Is this. Information we could have gained through study? Or, Information governing particles at an quantum level?

Sorry if it sounds like a dumb question, just confused me, not difficult these days

There is a technical definition of "information", but I don't think that you actually need that technical definition to understand this issue.

In both classical mechanics and quantum mechanics, physics is reversible at the microscopic level. For our purposes, that just means that distinct initial states lead to distinct final states. If at time $t_1$ you know that a system is in state $A$, then the equations of physics will allow you (in principle) to compute the state it will be in at a later time, $t_2$. Call that state $B$. Reversibility just means that you run the equations backwards: If you know that the system was in state $B$ at time $t_2$, then you can (again, in principle) use the equations of physics to compute the state at the earlier time, $t_1$. So this is the intuitive sense in which information is never lost: in principle, you can always recover any information about the past.

In practice, it seems like things are not reversible. If you put an ice cube on a hot metal plate, it will predictably melt into a puddle of water. So your equations allow you to compute the future state from the past state. On the other hand, if you start with a plate holding a puddle of water, you can't figure out that it used to be an ice cube. Hot water cooling off leads to the same final state as ice melting. So melting seems irreversible. But in classical physics, at least, the microscopic details--the positions and momenta of the water molecules--will be different depending on whether it was once an ice cube. The information about the past was not truly lost, it just became inaccessible--it's stored in the details of the motions of microscopic particles.

Now, for black holes radiating through Hawking radiation, it seems irreversible. You can throw anything into a black hole--a car, a potted plant, etc., the final state of the black hole is unchanged. When the black hole radiates away, there seems to be no record left, even at the microscopic level, of what went into the black hole. Since all the physics involved in black hole radiation---General Relativity, quantum mechanics---are reversible at the microscopic level, it's a puzzle how you can have irreversible processes arise from reversible processes. So the question is: Is black hole formation and evaporation really irreversible? If so, how did irreversibility arise from reversible laws of physics? If not, then where did the information go when the black hole evaporated?

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Thanks for the answers, I'm no student, just find modern science amazing, maybe one day it will sink in.

Loved the analogy with the ice cube, made it seem so much easier to comprehend.

## 1. What is the definition of quantum information?

The definition of quantum information refers to the encoding and processing of information using quantum systems, such as qubits, which can exist in multiple states simultaneously. This allows for the storage and manipulation of significantly more information than traditional binary systems, leading to potentially more efficient and powerful computing.

## 2. How is quantum information different from classical information?

Classical information is based on binary digits (0s and 1s), whereas quantum information is based on qubits, which can exist in superposition states of both 0 and 1 simultaneously. This allows for a greater amount of information to be stored and processed in a single quantum system.

## 3. What is the significance of quantum information?

The significance of quantum information lies in its potential to revolutionize computing and communication. Quantum computers have the ability to solve certain problems significantly faster than classical computers, and quantum communication allows for secure transmission of information through quantum cryptography.

## 4. How is quantum information related to quantum mechanics?

Quantum information is closely related to quantum mechanics, as it utilizes the principles of superposition and entanglement to encode and process information. Quantum mechanics provides the mathematical framework for understanding and manipulating quantum information.

## 5. What are some practical applications of quantum information?

Some practical applications of quantum information include quantum cryptography for secure communication, quantum simulation for solving complex problems in chemistry and physics, and quantum machine learning for more efficient data analysis. Quantum information also has potential uses in fields such as finance, logistics, and drug discovery.

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