Need help understanding question regarding Bell states

In summary, the conversation is about a homework question asking the individual to show elementary properties of bell states and to find a quantum circuit that performs a Bell measurement in terms of single qubit unitary gates, CNOT gates, and single qubit measurements in the {|0> , |1> } basis. The individual is unsure about what is being asked and is seeking clarification. They have already been able to show the orthonormal basis and express the states in terms of the usual basis. They are wondering if they simply need to add a single qubit measurement gate to each wire or if there is more to the question.
  • #1
Ocifer
32
0

Homework Statement


Basically, in a homework question, I'm presented with the definition of bell states and asked to show some elementary properties. I've been able to show they form an orthonormal basis, and express them in terms of the usual basis, |00>, |01> |10> |11>.

I am then asked,

"Find a quantum circuit that performs the Bell measurement (measurement of two qubits
in the Bell basis) in terms of single qubit unitary gates, CNOT gates, and single qubit
measurements in the {|0> , |1> } basis."

Homework Equations



[itex] | \psi_{xy} \rangle = CNOT_{12}H_1 | xy \rangle [/itex]

The Attempt at a Solution



I don't understand what is being asked of me. I can figure out a circuit which encodes any of the normal basis states |00>, |01> |10> |11> into its corresponding Bell basis, state. This is a circuit with only two wires (since it's a two qubit space), but do I simply then add a single qubit "M" (measurement) gate to each wire? Is that all that is being asked, or is there more I'm not understanding?
 
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  • #2
I'm not asking for the answer, but if someone could explain what the question is actually asking of me, I'd really appreciate it. Thanks.
 

Related to Need help understanding question regarding Bell states

1. What are Bell states?

Bell states, also known as EPR pairs or entangled states, are quantum states that exist in a two-qubit system. They are characterized by a special type of correlation between the two qubits, known as quantum entanglement.

2. How are Bell states used in quantum communication?

Bell states are important in quantum communication because they allow for the secure transmission of information. By measuring one qubit in a Bell state, the state of the other qubit is instantly known, even if they are separated by large distances. This allows for secure communication without the risk of interception or eavesdropping.

3. What is the significance of Bell states in quantum computing?

Bell states are a crucial resource in quantum computing, as they are used to perform operations such as quantum teleportation and entanglement swapping. These operations are essential for creating more complex quantum algorithms and for achieving quantum computational speedup.

4. How are Bell states created in a quantum system?

Bell states can be created through a variety of methods, such as using quantum gates or through measurements on entangled particles. The most common method is to use a controlled-NOT (CNOT) gate to entangle two qubits and create a Bell state.

5. Are Bell states only limited to two qubits?

No, Bell states can exist in systems with more than two qubits. In fact, the concept of Bell states can be extended to a larger number of qubits, known as n-qubit Bell states. These states are important for more complex quantum computing tasks and for studying quantum entanglement in larger systems.

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