What is the sy – state and how is it different from the Bell state?
The sy-state, also known as the singlet-y state, is one of the four maximally entangled Bell states in quantum information. It is an important concept in the study of quantum entanglement, specifically in relation to the rotational invariance of the Bell state.
To understand the sy-state, let's first discuss the Bell state. The Bell state is a two-qubit state that represents the maximum amount of entanglement between two quantum systems. It is named after physicist John Bell, who first introduced the concept. The Bell state is expressed as:
|Ψ⟩ = 1/√2 (|00⟩ + |11⟩)
In this state, the two qubits are entangled in such a way that their measurement outcomes are perfectly correlated. For example, if one qubit is measured and found to be in the state |0⟩, the other qubit will be found in the state |0⟩ as well. Similarly, if one qubit is measured and found to be in the state |1⟩, the other qubit will also be found in the state |1⟩. This correlation holds true regardless of the distance between the qubits.
Now, let's move on to the sy-state. The sy-state is a specific variation of the Bell state, obtained by applying a rotation operation to the original Bell state. This rotation operation is known as the σy gate, which is a quantum gate that applies a Pauli Y matrix to a qubit. The sy-state is expressed as:
|Ψ⟩ = 1/√2 (|01⟩ – |10⟩)
In the sy-state, the measurement outcomes of the two qubits are still perfectly correlated, but they are now correlated in a different way compared to the original Bell state. For example, if one qubit is measured and found to be in the state |0⟩, the other qubit will be found in the state |1⟩. Conversely, if one qubit is measured and found to be in the state |1⟩, the other qubit will be found in the state |0⟩. Again, this correlation holds true regardless of the distance between the qubits.
The key difference between the sy-state and the Bell state lies in their rotational invariance properties. While the Bell state is invariant under rotations around the z-axis, the sy-state is invariant under rotations around the y-axis. This means that if the sy-state is rotated by any angle around the y-axis, it will remain the same sy-state. This property is not shared by the Bell state.
The sy-state is a specific variation of the Bell state obtained by applying a rotation operation known as the σy gate. It exhibits a different correlation pattern between the measurement outcomes of the two qubits compared to the original Bell state. The sy-state is also distinguished by its rotational invariance property around the y-axis.
Other recent questions and answers regarding EITC/QI/QIF Quantum Information Fundamentals:
- Are amplitudes of quantum states always real numbers?
- How the quantum negation gate (quantum NOT or Pauli-X gate) operates?
- Why is the Hadamard gate self-reversible?
- If measure the 1st qubit of the Bell state in a certain basis and then measure the 2nd qubit in a basis rotated by a certain angle theta, the probability that you will obtain projection to the corresponding vector is equal to the square of sine of theta?
- How many bits of classical information would be required to describe the state of an arbitrary qubit superposition?
- How many dimensions has a space of 3 qubits?
- Will the measurement of a qubit destroy its quantum superposition?
- Can quantum gates have more inputs than outputs similarily as classical gates?
- Does the universal family of quantum gates include the CNOT gate and the Hadamard gate?
- What is a double-slit experiment?
View more questions and answers in EITC/QI/QIF Quantum Information Fundamentals