# Probability of an entanglement state

• phyky
In summary, when two systems are entangled, with states |A> and |B> = (|0_B{}>+|1_B{}>)/√2, the entangled state |AB> has a probability of 1/2 to be found in the states |0_A{}0_B{}> and |1_A{}1_B{}>. This is still true even with the rephrased question of |U> = (|0a>|0b> + |1a>|1b>)/root 2, where the probability to find |0a> and |1b> is also 1/2. This follows from the Born rule trace formula, as shown by the equation trace
phyky
given two system is entangled, |A>=(|$0_{A}$>+|$1_{A}$>)/√2, |B>=(|$0_B{}$>+|$1_B{}$>)/√2. entangle state |AB>what is the probability to find |$0_A{}$$0_B{}$> and |$1_A{}$$1_B{}$>. are there still 1/2 just like normal inner product formulation?

Last edited:
phyky said:
|AB>=(|0a>+|1b>)/√2, what is the probability to find |0a> and |1b>. are there still 1/2?

You need to rephrase that - states with two particles have terms of the form |a>|b>.

Thanks
Bill

Well your rephrased question would be |U> = (|0a>|0b> + |1a>|1b>)/root 2. If you have an observation |0a>|0b> or |1a>|1b> then one or the other will be detected with probability 1/2. This is directly from the Born rule trace formula eg trace (|U><U| |1a>|1b>) = 1/2.

Thanks
Bill

## What is the definition of probability of an entanglement state?

The probability of an entanglement state refers to the likelihood that two or more quantum particles are in a correlated or "entangled" state. This means that their quantum properties are linked in a way that cannot be explained by classical physics.

## How is the probability of an entanglement state calculated?

The probability of an entanglement state is calculated using mathematical equations and principles from quantum mechanics. Specifically, it involves calculating the inner product of the two quantum states that are entangled.

## What factors can affect the probability of an entanglement state?

The probability of an entanglement state can be affected by various factors, such as the initial state of the quantum particles, the strength of the entangling interaction between the particles, and external influences such as interactions with their environment.

## Is it possible to have a probability of an entanglement state of 100%?

No, it is not possible to have a probability of an entanglement state of 100%. This is because entanglement is a probabilistic phenomenon and there is always a degree of uncertainty involved in quantum systems.

## What is the significance of the probability of an entanglement state in quantum computing?

The probability of an entanglement state is crucial in quantum computing as it determines the success rate of performing quantum operations on entangled qubits. Higher probabilities of entanglement can lead to more accurate and efficient quantum computations.

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