# 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

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### Eigenvalues of a quantum state after partial tracing

I am interested in the smallest nonzero eigenvalue of a quantum state. Does this eigenvalue always increasing after a partial trace i.e. the smallest nonzero eigenvalue of $\rho_A$ is always larger ...
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### XX and YY and ZZ Hamiltonians in vqe

I'm trying to implement a vqe in cirq and I have sort of a brain knot. I have a 4 qubit chain with periodic boundary condition. So in fact a 2x2 qubit grid. Now 2 of them each are coupled. How do I ...
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### How to get state vector probabilities in Q#

Is there a similare function in Q# like Statevector.probabilities in Qiskit to get state vector probability, for example, if my circuit contains one qubit with one $H$ gate, the function returns ...
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### $N(\frac{1}{2},2)=3$ for vectors in a Hilbert Space

Came across This question regarding the maximum number of almost orthogonal vectors one can embed in a Hilbert space. They state that $N(\frac{1}{2},2)=3$, and that explicit construction of the ...
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### Terminology: what do $|i\rangle$ and $|\mbox{-}i\rangle$ represent?

$|0⟩$ and $|1⟩$ are usually referred as the computational basis. $|+⟩$ and $|-⟩$, the polar basis. What about $|i\rangle$ and $|\mbox{-}i\rangle$? And collectively? Orthonormal states? References are ...
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### Defining dimension of an operator in qutip

My main question: Can someone please explain to me how the list of array is used to define the dimension in qutip ? context: If I have my density operator ...
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### Is there a proof or example to show that a noiseless subsystem is not necessarily closed under addition?

In a text (section 3.6 page 92) about noiseless subsystems by D. Lidar, it is mentioned:'A subsystem is a tensor factor in a tensor product, and this does not have to be a subspace (e.g., in general ...
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### Why does full state reconstruction require at least $N+1$ MUBs?

Consider an $N$-dimensional space $\mathcal H$. Two orthonormal bases $\newcommand{\ket}{\lvert #1\rangle}\{\ket{u_j}\}_{j=1}^N,\{\ket{v_j}\}_{j=1}^N\subset\mathcal H$ are said to be Mutually ...
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### What is the right way to prepare a specific qubit state in Qiskit / Q#?

There are two possibilities to prepare a qubit in a particular state like $| - \rangle$ in Qiskit. The first approach is using the initialize function: ...
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### Is spontaneous excitation possible?

I know the $|1\rangle$ state can relax spontaneously to the $|0\rangle$ state, but can the opposite also happen?
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### Qiskit: Initializing n qubits with binary values (0s and 1s)

Is there a way in Qiskit to initialize $n$ qubits with binary values (0s and 1s)? For example, how can I initialize two qubits in the state $|11\rangle$? Here is a code snippet: ...
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### How do you CNOT between qubits faraway from each other?

I'm just curious. Say I have 3 qubits on a straight line 0-1-2. How do you guys (on the IBMQ or Rigetti team for example, or anyone who actually works on quantum computer) entangle 0-2 if I, say, am ...
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### How does noise affect the implementation of quantum gates?

I am trying to think about quantum noise visually here. If, for example, one wants to implement an X-gate to perform a 180-degree rotation around the Bloch Sphere. In a perfect world, the X-gate will ...
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### Quantum Ising model correlation function query

In this paper on quantum Ising model dynamics, they consider the Hamiltonian $$\mathcal{H} = \sum_{j < k} J_{jk} \hat{\sigma}_{j}^{z}\hat{\sigma}_{k}^{z}$$ and the correlation function \mathcal{G}...
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### What is the matrix for measuring a superposition of general number of qubits in standard basis?

Let's say I have the state of the system of 2 qubits: $\frac{1}{\sqrt{3}}|00\rangle+\frac{2}{\sqrt{3}}|10\rangle$, and I want to measure it in the standard basis. How would I write it mathematically? ...
### How can the Holevo bound be used to show that $n$ qubits cannot transmit more than $n$ classical bits?
The inequality $\chi \le H(X)$ gives the upper bound on accessible information. This much is clear to me. However, what isn't clear is how this tells me I cannot transmit more than $n$ bits of ...