# Questions tagged [quantum-state]

Quantum systems can mathematically be described by their 'quantum state'. When the system is closed/isolated, the state is 'pure' and can be written as a sum (i.e. 'superposition') of basis vectors. When the system is a subsystem of an open system, the state is instead usually 'mixed' and cannot be written as a pure state, so has to be written as a density matrix. Consider using the density-matrix tag when relevant

1,002 questions
Filter by
Sorted by
Tagged with
49 views

### Are X-state separability and PPT- probabilities the same for the two-qubit, qubit-qutrit, two-qutrit, etc. states?

On p. 3 of "Separability Probability Formulas and Their Proofs for Generalized Two-Qubit X-Matrices Endowed with Hilbert-Schmidt and Induced Measures" (https://arxiv.org/abs/1501.02289), it is ...
52 views

### QuTiP VS RK45: Which one gives the correct results for time-dependent systems?

I am writing a code for a quantum thermal machine which includes both coherent and dissipative time evolutions in its different stages of operation. However, evolving the system with "mesolve&...
59 views

### How to create superposition of states with fixed parity with a quantum circuit?

I'm searching for a circuit to generate, starting from the $|00\, ...\,0\rangle$ state, an arbitrary superposition of all states with either even or odd parity. The gate choice is irrelevant for now, ...
543 views

### Understanding quantum circuit diagrams: a circuit that compares two states $|YX\rangle$ and $|AB\rangle$

I have a quantum circuit which I would like to understand, which compares two standard basis states $|YX\rangle$ and $|AB\rangle$. It operates on the corresponding bits in each of the two states: i.e.,...
426 views

### Connection between the definitions of concurrence for a two-qubit states

The concurrence for a state $\rho$ as defined here is \begin{equation} C(\rho) = {\rm max}\{0, \lambda_1-\lambda_2-\lambda_3-\lambda_4\}. \end{equation} Where $\lambda_i$ are the eigenvalues of matrix ...
72 views

321 views

### Is the set of classical-quantum states convex?

I read about the classical-quantum states in the textbook by Mark Wilde and there is an exercise that asks to show the set of classical-quantum states is not a convex set. But I have an argument to ...
399 views

### What is the largest number of stabilizers a pure state can have?

What is the largest number of stabilizers a pure state can have? Elaborately put: Let $P(n)$ denote the Pauli group. Given an arbitrary pure state $|\psi\rangle$, what is the upper limit on how many ...
150 views

### How can I print out a state vector of a specific wire?

Suppose we start from 2 wires (q0 and q1) and through some quantum gates, suppose we measure q1 wire only. As we measure the q1 wire, the state vector of this quantum state would be determined ...
41 views

45 views

### Show that the trace of squared density matrix gives ${\rm tr}(\rho^2)=\frac12(1+\|\mathbf n\|^2)$ [duplicate]

Equation 7.7 is given below: $$\hat\rho = \frac12(I +n_x(\hat X)+n_y(\hat Y)+n_z(\hat Z))$$ Where $I$ is the identity matrix and $\hat X,\hat Y,\hat Z$ are Pauli matrices. Now my attempt of this was ...
150 views

In the paper by Stamatopoulos et al., the authors say that it is possible to load a distribution on a three qubit state to obtain: In Qiskit finance this is performed using the uncertainty model ...
66 views

59 views

### How to tranfer given superposition to quantum circuit?

Let's say I have a superposition of qubit defined as $\frac{1}{2} (| 000 \rangle + | 001 \rangle + | 111 \rangle + | 110 \rangle)$ (as given in the answer here: Explanation of output produced by the ...
2k views

238 views

62 views

### Random quantum states and Schur-Weyl duality

Consider the following density matrix over $n$ qubits, with $C$ being a single qubit operator: $$\rho_{n} = \int_{C \sim \text{Haar}} \big(C|0\rangle\langle0|C^\dagger\big)^{\otimes n} dC.$$ Let's ...
49 views

### Weak Schur sampling and state distinguishability

Consider the task of distinguishing between the following two $n$ qubit quantum states. $$\rho = \frac{\mathbb{I}}{2^{n}}.$$  \sigma = \frac{1}{2^{n/2}}\sum_{x \in \{0, 1\}^{n/2}} |x\rangle\langle ...
$\renewcommand{ket}{\left| #1 \right\rangle}$ $\renewcommand{bra}{\left\langle #1 \right|}$Suppose we have to qubits both in the state $\ket{+ }= \frac{1}{\sqrt{2}}(\ket{0}+\ket{1})$, and we ...
### Why can the most general state of a qubit be written as $|\Psi\rangle=\cos(\frac\theta2)|0\rangle+e^{i\phi}\sin(\frac\theta2)|1\rangle$?
Why we can express a most general qubit as $|\Psi\rangle = \cos{\left(\frac{\theta}{2}\right)}|0\rangle + e^{i \phi} \sin{\left(\frac{\theta}{2}\right)} |1\rangle$? Is there any formal proof for this?