Can we find a quantum analogue of the Bertrand paradox?

In summary, the conversation discusses a quantum version of the Monty Hall problem where the initial state is divided into three possibilities. The probabilities for different outcomes are computed, leading to a discussion on the quantum analogues of classical probability paradoxes. These include the Tuesday paradox and the Bertrand paradox. The conversation also explores the manipulation of quantum states in the game.
  • #1
jk22
729
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I considered a quantum version of the problem

There is one winning position so the initial state is |100>+|010>+|001> divided by sqrt3

Suppose the presentator opens door 3 the intermediate state is then a mixture

Cos a|100>+sin a|010>

We suppose finally the player chooses door 2 hence the end state were |010>

Going through those steps we can compute the probabilities pi*pf=(cos a+sin a)^2/3*sin^2 a

We find the extremas to be .06 up to .48

How to interprete those probabilities ? Does it mean that the game can be won only 48% of the time and hence it would be a lucrative game for the presentator ?
 
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  • #2
jk22 said:
Suppose the presentator opens door 3
What does that mean quantum mechanically?

jk22 said:
the intermediate state is then a mixture

Cos a|100>+sin a|010>
Where do the cos and sin come from?
 
  • #3
It probably means that now we have the knowledge its 1 in door 1 or 2 hence the first two superposed states.

The cos and sin are unknown coefficient that will be found afterwards for the presentator to choose where to put the 1 ?
 
  • #4
jk22 said:
It probably means that now we have the knowledge its 1 in door 1 or 2 hence the first two superposed states.
I don't understand how you can do that. What measurement are you doing?

jk22 said:
The cos and sin are unknown coefficient that will be found afterwards for the presentator to choose where to put the 1 ?
Again, how do you do that? What kind of manipulation are you making on the quantum state?
 
  • #6
Last edited:

1. What is the Quantum Monty Hall problem?

The Quantum Monty Hall problem is a variation of the classic Monty Hall problem, which is a famous probability puzzle. In this variation, there is an additional quantum element, where the player is allowed to choose both doors at the same time, and the host can open both doors at once.

2. How does the Quantum Monty Hall problem differ from the classic Monty Hall problem?

In the classic Monty Hall problem, the player is only allowed to choose one door, and the host can only open one door. The Quantum Monty Hall problem adds the element of quantum superposition, where both doors can be chosen and opened simultaneously.

3. What is the solution to the Quantum Monty Hall problem?

The solution to the Quantum Monty Hall problem is that the player should switch their initial choice of doors. This is different from the classic Monty Hall problem, where the player should always switch. In the Quantum Monty Hall problem, the player has a 50% chance of winning if they switch, whereas they have a 33.3% chance of winning if they stick with their initial choice.

4. How does quantum mechanics play a role in the Quantum Monty Hall problem?

Quantum mechanics plays a role in the Quantum Monty Hall problem because it allows for the concept of quantum superposition, where multiple states can exist simultaneously. In this problem, the player's choice of doors and the host's opening of doors can exist in multiple states at once, making it different from the classic Monty Hall problem.

5. Are there any real-life applications of the Quantum Monty Hall problem?

The Quantum Monty Hall problem has real-life applications in quantum computing and cryptography. It can also be used as a teaching tool to help people understand the concepts of quantum mechanics and probability. Additionally, it has been studied in fields such as psychology and decision-making to understand how people make choices in situations with uncertainty and multiple possible outcomes.

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