Questions tagged [quantum-state]

Questions about or related to quantum states. Consider using the density-matrix tag when relevant.

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Evolution of a state vector: Why is the action of $N$ equivalent to the action of $UNU^{†}$?

There is another question asked on this on stack exchange but I did not find any answers there that fully answered the question. In Gottesman's paper "The Heisenberg Representation of Quantum ...
am567's user avatar
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I would like to understand the meaning of applying permutation to a unitary matrix

$$U = \frac{1}{2} \begin{pmatrix} -1 & -1 & 1 & 1 \\\\ 1 & -1 & 1 & -1 \\\\ 1 & -1 & -1 & 1 \\\\ 1 & -1 & 1 & 1 \end{pmatrix}$$ $$P = \frac{1}{...
junghyunHa's user avatar
1 vote
1 answer
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Affine transformation of the Bloch sphere to Kraus representation of qubit channels

It is known that qubit channels can be written in the form: $$ \begin{align} \Phi(\rho) = \frac{1}{2}\left(I+(T\vec{r}+\vec{t})\cdot\sigma\right)\ \end{align} $$ where $\vec{r}$ is the Bloch vector ...
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What does it mean that the elements of a generalized measurement are operators?

I have a very simple question on Generalized measurements. The definition I was given is the one below: A set of operator $\left \{ M_{\alpha} \right \}$ is called generalized measurements for an ...
OffHakhol's user avatar
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How to compare the output of statevector_simulator and qasm_simulator in Qiskit

I am stuck with a very difficult problem. Suppose, I execute a circuit on statevector_simulator, and I get all the values negative. Suppose, now i execute the same ...
Manu's user avatar
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Measuring one register of the state $\frac{1}{2^{m}} \sum_{x}\sum_{k} (-1) ^ {x\cdot k} |k\rangle |f(x)\rangle$

I'm reading the article which contains lemma 1. Its proof contains the statement, that probability of getting $|0\rangle$ (denote it as $\text{Pr}\left[|0\rangle\right]$) after measuring the first ...
Georgy Firsov's user avatar
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What happens to $|y\rangle \sum_{x}|x\rangle|f(x) + g(y)\rangle$ when we throw away the first register?

Let's suppose, that applying $\mathbf{H}$ (Hadamard operator) to the first register of the state $c \cdot \sum_{x}|x\rangle|f(x)\rangle$ ($f$ is a permutation, $c$ is a normalization factor), and ...
Georgy Firsov's user avatar
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1 answer
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What is the meaning of complex expected values?

Introduction I am using BQSKIT to compile an approximation of a Toffoli gate (for testing purposes) and output to a QISKIT QuantumCircuit. I want to find the expected value of this approximation to ...
Shadow43375's user avatar
2 votes
1 answer
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How to find a quantum circuit to generate a target state?

I am starting in Quantum Computing, but I am pretty lost, sorry... let's say I need to design a quantum circuit to generate some given quantum states in Dirac's notation, as in the following example, ...
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confusion on the LCU method regarding the normalization

Let $A = \sum_{k} a_k U_k$ where $a_k$ are real, positive coefficients $U_k$ are unitary matrices. I have realized that $\sigma = A \rho A$ can be implemented on a quantum computer by using the LCU ...
Hailey Han's user avatar
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How would I write the equation for this circuit?

Would the equation for this circuit be: $$(H \otimes H) \cdot \text{CNOT} \cdot (H \otimes H)$$
Daniel Vandormael de Oliveira's user avatar
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1 answer
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Simplification of a generic quantum state

We are given a generic 2-qubit density matrix $$\rho=\frac{1}{4}\left[I_4+\Sigma_i a_i \sigma_i \otimes I_2 + \Sigma_i b_i I_2 \otimes \sigma_i + \Sigma_{i,j} c_{ij} \sigma_i \otimes \sigma_j\right]$$ ...
Anindita Sarkar's user avatar
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Can a generic 2-qubit state be unitarily converted into one of the form $I_2\otimes I_2+\lambda\sigma_z\otimes\sigma_z$?

Suppose I have a general 2-qubit state written in a basis consisting of tensor products of Pauli matrices: $\rho=\frac{1}{4}\left[I_2\otimes I_2+\Sigma_{i} a_i \sigma_i\otimes I_2+\Sigma_{i} b_i I_2\...
Anindita Sarkar's user avatar
1 vote
1 answer
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Two qubit Pauli expectation value of $\underset{U}{\mathbb{E}}[U^{\otimes 2} (P_1 \otimes P_2)^{\otimes 2} U^{*\otimes 2}]$

I want to find a value for the expression: $$\underset{U}{\mathbb{E}}[U^{\otimes 2} (P_1 \otimes P_2)^{\otimes 2} U^{*\otimes 2}],$$ where $U$ is a two-qubit unitary operator chosen Haar randomly, $...
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How to amplify amplitudes above some threshold, given additional information about the state

Given a quantum state $\left|\Psi\right> = \sum_{i=0}^{2^n-1} \alpha_i\left|i \right>$, for which I know that the probabilities ($|\alpha_i|^2$) follow a sine/cosine like distribution as in the ...
D.D.'s user avatar
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Expected trace distance between two types of random ensembles

Consider a Haar random state on $n$ qubits, and denote it by $|\psi\rangle$. Now consider the following state $$|\phi\rangle = \frac{1}{\sqrt{k}} \sum_{i=1}^{k} |\phi_{1, i} \rangle \otimes |\phi_{2, ...
BlackHat18's user avatar
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Cite sources for development of hardware and software for quantum computers

I have written a paper on Quantum K map and my professor has asked me as the next step to cite sources from creditable science journals on the issue of hardware and software development for quantum ...
Root Groves's user avatar
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1 answer
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Run a circuit on "simulator_statevector" of the IBM Quantum Platforms

I would like to obtain the statevector of a QuantumCircuit using the simulator_statevector (and Qiskit) of the IBM Quantum ...
stopper's user avatar
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Entangled qubit systems always maximally entangled?

For a bibpartite system $A,B$ with $A\in\mathcal{H}_A$ and $B\in\mathcal{H}_B$, the Schmidt decomposition of its state $| \psi \rangle_{AB}$ is : \begin{equation} | \psi \rangle_{AB}= \sum_{i=0}^{\min ...
deb2014's user avatar
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Initial state preparation in Quspin

Say we want to prepare an initial state for a one-dimensional Heisenberg spin-$\frac{1}{2}$ chain, with all spins pointing along the $+x$ direction using Quspin. In the Quspin, one can define the ...
felix's user avatar
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Which qubit has the highest $|1\rangle$ amplitude?

Suppose I can prepare $n$ qubits each in an unknown independent state (not entangled). If needed, you can assume that each qubit is in a state $a_i |0\rangle + b_i |1\rangle$ for real numbers $a$ and $...
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1 answer
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How do quantum computers encode a string?

New to quantum computing. How do quantum computers represent a string at the hardware level? For example, if Classical computers wanted to encode "Hello world!", they would use UTF-8 to ...
chickenj0's user avatar
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1 answer
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Why this QC probability drop to $|01⟩$ and $|11⟩$ instead of $|10⟩$ and $|11⟩$? [duplicate]

I have QC like this The final state before measure should be $|1⟩ ⊗ |-⟩$, and it will be $\frac{1}{\sqrt{2}}(|10⟩ - |11⟩)$, so the probability of this QC should be a half is $|10⟩$ and other half is $...
Joe_LL's user avatar
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2 answers
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Why are quantum states represented by Bloch or Q-Spheres?

I'm new to quantum computing. Why are quantum states/qubits represented on spheres: either as Bloch spheres or as Q-Spheres. Is it just a convenient graphical representation, or is there something ...
chickenj0's user avatar
2 votes
1 answer
181 views

How to find the eigenvectors and eigenvalues of a hermitian operator?

While reading Theoretical Minimum by Leonard Susskind, I came across the exercise 3.4 where he asked to find the eigenvalues and the eigenvectors of the matrix that represents the $\sigma_{n}$ ...
zizaaooo's user avatar
3 votes
1 answer
104 views

Asymptotic purity from the spectrum of the Choi matrix?

I have a completely positive map $T$ and a sequence of $d\times d$ states $S_1,S_2,\ldots$ obtained by applying $T$ repeatedly to the identity matrix. I'm interested in quantifying what happens to ...
Yaroslav Bulatov's user avatar
4 votes
1 answer
126 views

What mathematical object is the set of quantum states of a qudit? How should one write this?

It is tempting to write $|\psi\rangle \in \mathbb{C}^d$ for a qudit state, but this isn't very precise because of global phases. What's a better notation for the set of states of a qudit?
shashvat's user avatar
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How to find $p_x$ and $p_y$ components on the Bloch sphere?

Consider an arbitrary state: $$|\psi\rangle = a|0\rangle+b|1\rangle,$$ where $a=\cos\left(\frac{\theta}{2}\right), b=\sin\left(\frac{\theta}{2}\right)e^{i\phi}$ (neglecting global phase), $\phi$ is ...
Curious's user avatar
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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 ...
Rayhan Kabir's user avatar
-2 votes
1 answer
124 views

Disentanglement of qubits from output of CNOT gate

Suppose we have a control qubit with initial state $\binom{a}{b}$ and a target qubit with initial state $\binom{c}{d}$.What a CNOT does is transform the state of the target qubit into: $\begin{pmatrix}...
Root Groves's user avatar
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1 answer
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IBM quantum composer possible bug?(state amplitudes of quantum circuit)

I have this quantum circuit: and from the IBM quantum composer I get this state amplitudes: I wanted to flip the target qubit and keep only its pure state however this is not what I am getting.I am ...
Root Groves's user avatar
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1 answer
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State of qubit after gate and measurement

Suppose we have a gate with 1 control qubit and 1 target qubit: Lets say the state of the control qubit initially was $\begin{pmatrix} a\\ b \end{pmatrix}$ and the state of the target qubit was ...
Root Groves's user avatar
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1 answer
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Calculate of theoretical probabilities for the outcomes

I have a $|+\rangle$ state qubit and I measure it in a random basis. The random basis is made with random $\theta$, $\varphi$ and $\lambda$ of $U3$ gate. How can I calculate the theoretical ...
hdsa's user avatar
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-1 votes
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Do quantum computing principles have a theoretical or hypothetical potential to solve factorial time problems?

I neither have a background in QC, higher mathematics (calculus) and nor have I gone through the literature about the field. As a layman what catches my attention is that people say that quantum ...
lousycoder's user avatar
1 vote
1 answer
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qiskit statevector ordering issue

I am currently studying Qiskit. I don't understand the two pictures below while studying. When I apply circuit.x(1), the X gate should be applied to the second qubit, resulting in the state |01>. ...
junghyunHa's user avatar
2 votes
1 answer
213 views

is a mixed states really a statistical mixture?

$\DeclareMathOperator{\Tr}{Tr}\newcommand{\ket}[1]{|#1\rangle}\newcommand{\bra}[1]{\langle#1|}$Let consider the pure state $$ \ket{\psi_{1}}=\dfrac{\ket{0}+\ket{1}}{\sqrt{2}} $$ whose density matrix ...
yosh's user avatar
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0 answers
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Measuring an entangled quantum state

I have this exercise to solve, but I can't figure out how to proceed. First, I don't think the state proposed is valid (the probabilities don't sum up to 1). 'Secondly, given that it should be an ...
Giulia's user avatar
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How to determine the single-qubit phase?

In some works it is suggested to find the qubit phase by the following method: Apply $X/2$ (or $Y/2$) gate - preparing the qubit in superposition. Detune the qubit by flux pulse, for example here ...
Curious's user avatar
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2 answers
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Does the $\text{CNOT}$ gate activate if the control qubit is $-|1⟩?$

I understand how the $\text{CNOT}$ gate works intuitively: However, say we have a circuit where the $Z$ gate is applied to $|1⟩$, which turns $|1⟩ \to -|1⟩$. Then, there is a $\text{CNOT}$ gate with ...
Spike Spiegel's user avatar
1 vote
1 answer
40 views

References for mapping qudit gates to qubits equivalent

Let's assume that I'm modelling a d-levels qudit as a set of n qubits, where $d = 2^n$. I would need to map the application of quantum gates on the qudit to a set of operations of the relative qubits ...
Frank's user avatar
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2 votes
2 answers
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How to estimate the negative amplitude of multiple qubits?

The probability of measurement is the square of amplitude. After measurement, how to guess the original amplitude of state?? For example, in linear problem, we would like to know the exact solution, ...
Nyyni's user avatar
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0 votes
1 answer
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In Qiskit, no state vector after measure and reset

The code below doesn't work. I am looking for a workaround. OK, I can save the state vector as numpy array, recreate the whole circuit and initialize it thanks to this array. It works, but any simpler ...
Maurice Clerc's user avatar
2 votes
0 answers
22 views

Specifying the image of a set of states under the action of a channel

I have a generic channel $\mathcal{N}$ acting on a subspace of states defined on a $d$-dimensional Hilbert space $\mathcal{H}$. I am trying to make a statement about the dimension of the image of that ...
forky40's user avatar
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1 vote
1 answer
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Measuring one qubit in an entangled pair in another basis?

Qubits are usually measured in the computational basis, but we can change the basis by a unitary $U$ to measure in the basis formed by the columns of $U$. For example, if $| \psi \rangle = | 0 \rangle$...
Andrew Baker's user avatar
3 votes
1 answer
90 views

What is the difference between classical-quantum and completely classical states?

States that are completly classical : $$ \begin{aligned} \tilde\rho_{A B} & =\sum_{x \in \mathcal{X}} \sum_{y \in \mathcal{Y}} p_{X, Y}(x, y)(|x\rangle \otimes|y\rangle)(\langle x| \otimes\langle ...
IamKnull's user avatar
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2 votes
1 answer
140 views

Finding the "dual" basis of an overcomplete basis for Quantum State Tomography

This question is related to this stack exchange post: What does the POVM corresponding to single-qubit state tomography look like? From what I understand, when we are interested in reconstructing a ...
junoswrld's user avatar
2 votes
0 answers
99 views

Mutual information of shared state is larger than expectation values

Im trying to prove the following identity for a special case: Alice and Bob share the Bell state \begin{align*} |\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle+|11\rangle). \end{align*} Consider the ...
user27450's user avatar
0 votes
1 answer
62 views

Matrices size of n-qubit controlled gates and n+2 states qubit?

Operations on many qubits at the same time is the same as operation of qubits with many states. For example the CNOT gate matrix with 1 control qubit will be the same of a "gate" acting on ...
Root Groves's user avatar
0 votes
1 answer
78 views

How to show that the GHZ state is absolutely maximally entangled?

A multipartite state is called absolutely maximally entangled if for its any bipartition the reduced density matrix of smaller part is maximally mixed. Show that GHZ state has this property.
user27383's user avatar
2 votes
1 answer
118 views

How does this measurement in the Hadamard basis look like?

I am reading this paper by Mahadev. In going from (19) to (20) the author does a Hadamard measurement on two registers. I don't understand what exactly the Hadamard measurement does. The (simplified) ...
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