Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [w-state]

For questions regarding the W state, which is a quantum state generally defined as a superposition of three qubits. The W state can be thought of as a uniform superposition of the three qubits wherein precisely one of the qubits is in one state (say "up"), while the other two are in the other state (say "down").

11 questions
8
votes
1 answer

What is the stabilizer rank of the W state?

The $ n $ qubit $ W $ state is defined here https://en.wikipedia.org/wiki/W_state The stabilizer rank of a quantum state $|\psi\rangle$ is the minimal $r$ such that \begin{equation} |{\psi}\rangle = \sum_{j=1}^{r} c_j |φ_{j}\rangle. \end{equation}…
Ian Gershon Teixeira
  • 5,062
  • 6
  • 30
8
votes
1 answer

What is the minimum number of non-Clifford gates does it take to prepare a superposition over all "two-hot" basis vectors?

The generalized W state: $$W_n=\frac{1}{\sqrt{n}}(|100\cdots 0\rangle + |010\cdots 0\rangle + \ldots + |00\cdots 01\rangle)$$ is often thought of as the uniform superposition over all "one-hot" basis vectors, as each such vector has a single qubit…
Mark Spinelli
  • 15,378
  • 3
  • 26
  • 83
6
votes
2 answers

How to implement Grover's diffusion operator when starting with a W state?

In the general form of Grover's algorithm, we start with the uniform superposition of n qubits. Now, suppose instead that we start with a generic state, for example the W state, and the oracle only inverts the phase of one of the basis. To make it…
tigerjack
  • 568
  • 3
  • 17
4
votes
1 answer

What is the general form for GHZ and W class states?

I am reading the following paper on mixed three-qubit states. It states that any three–qubit pure state can be written as (equation 1 of the paper) $|\psi_{GHZ}\rangle=\lambda_0 |000\rangle+\lambda_1 e^{i\theta} |100\rangle+\lambda_2…
Anindita Sarkar
  • 443
  • 1
  • 7
4
votes
2 answers

Entanglement distribution of W-State over different locations

I would like to create a quantum system with the gates for a W state where each qubit is at a different location. Entanglement distribution has been proven in several research articles. I'm new to this space and interested: if three qubits W-state…
TimW
  • 53
  • 4
3
votes
2 answers

How to implement a circuit preparing the three-qubit W state?

I'm trying to implement a circuit wich prepare this three qubits state : $\frac{1}{\sqrt{3}}(|100\rangle + |010\rangle + |001\rangle)$ It seems that the three qubits W-state can produce this state, and I found this code. But I have seen a simple…
user12910
  • 471
  • 1
  • 4
  • 9
2
votes
1 answer

What does the graph of a W state look like?

Consider the blow four-qubit W state $\frac12(\left| 1000 \right>+\left| 0100 \right>+\left| 0010 \right>+\left| 0001 \right>)$ I know if we remove any qubit the rest state stay entangled. So if we remove arbitrary two qubits, the rest two qubits…
reza
  • 817
  • 3
  • 9
1
vote
1 answer

Is entanglement distillation possible between states of different fidelities?

I am looking for an algorithm that allows me to perform distillation from a pair of W-states of different fidelities. All the algorithms I found so far are focused on distilling identical states, which in practice may not be the case. Is there an…
AlexW
  • 11
  • 1
1
vote
0 answers

W state Entanglement Breaks During $X$-Basis Measurement

I'm encountering a problem in my Qiskit simulation involving W-state entanglement. The issue arises when attempting to measure all three qubits in the $X$ measurement basis. Surprisingly, the entanglement breaks, and this behavior is consistent even…
Rayhan Kabir
  • 11
  • 2
1
vote
1 answer

How to find density matrix of 3 qubit W state?

Given a state in bra-ket notation as $|\psi\rangle=\frac{1}{\sqrt{3}}(|001\rangle+|010\rangle+|100\rangle)$. What is the density matrix of this state written using Pauli's spin operator?
Jatin Ghildiyal
  • 19
  • 2
1
vote
2 answers

How to perform the measurements on a quantum circuit in W state basis?

I need to perform the measurements on a quantum circuit in the basis $\{ \eta^\pm,\zeta^\pm \} $. Where $ \eta^\pm,\zeta^\pm $ are given as follows: $$\eta^\pm = \frac{1}{2}|001\rangle + \frac{1}{2}|010\rangle \pm \frac{1}{\sqrt{2}}|100\rangle…
Devesh
  • 63
  • 6