# What does |0> mean? ie what does the | > mean/do?

• Lee
In summary, The notation "Bra and ket" (| >) is not arbitrary and is used to represent the ground state for a quantum system. The vertical line and angle symbolize a "ket" vector.
Lee
What does |0> mean? ie what does the | > mean/do?

| > is just a decoration; it makes something look different. It's no different than when you put a little arrow over your vectors, or little hats over your unit vectors.

Ah, right. I thought it was maybe linked to < > meaning expectation value.

Lee said:
Ah, right. I thought it was maybe linked to < > meaning expectation value.

Well when you take the inner product of <x| with |x> you get <x|x>, which is a number and can be thought of as an expecttion. So the notation ("Bra and ket") isn't entirely arbitrary.

Lee said:
What does |0> mean? ie what does the | > mean/do?

$|0\rangle$ stands for the ground state for a quantum system (the state with the minimum possible energy). The $|\rangle$ with "something" in between the vertical line and the angle means that the "something" is a "ket" vector.

Daniel.

## 1. What does the |0> notation represent in science?

The |0> notation, also known as the "ket" notation, is used in quantum mechanics to represent a specific state of a quantum system. In this notation, the vertical bar represents a quantum state and the number or symbol inside the bracket indicates the specific state. The |0> state is known as the ground state or the lowest energy state of a quantum system.

## 2. How is the |0> notation used in quantum computing?

In quantum computing, the |0> notation is used to represent the qubit in the zero state. This is the starting point for any quantum computation and is essential for creating superposition and entanglement between qubits. The |0> state is also used as a reference point for measuring the state of a qubit during a computation.

## 3. What is the significance of the |0> state in quantum mechanics?

The |0> state is significant because it represents the lowest possible energy state of a quantum system. This state is important for understanding and manipulating the behavior of quantum systems, as it serves as a reference point for measuring and comparing other states. Additionally, the |0> state is used as a starting point for many quantum algorithms and computations.

## 4. How does the |0> state differ from the |1> state?

The |0> state and the |1> state are known as the basis states in quantum mechanics, representing the two possible states of a qubit. The main difference between these two states is the direction of the spin or the orientation of the qubit. The |0> state has a spin or orientation in the positive direction, while the |1> state has a spin or orientation in the negative direction.

## 5. Can the |0> state be changed or manipulated?

Yes, the |0> state can be changed or manipulated through quantum operations and measurements. In quantum computing, operations such as the Hadamard gate can change the state of a qubit from |0> to a superposition state, which is a combination of |0> and |1>. Additionally, measurements can collapse the state of a qubit from superposition to either |0> or |1>, depending on the outcome. This allows for the manipulation and control of quantum states for various applications.

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