Questions tagged [density-matrix]
For questions about density matrices and related concepts and ideas, e.g. procedures for computing properties of quantum states from their density matrices.
354
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Finding the eigenvalues of a qutrit state
I am interested in the state:
$\frac{1}{\sqrt{2}} (\left|11\right> + \left|22\right>)$
If I find the density matrix of this, I find the $9 \times 9$ matrix $\rho$.
If I want to find the reduced ...
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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?
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Is possible to write a separable state as a finite or countable infinite sum of product states?
Let us consider the tensor product of two finite Hilbert spaces $\mathcal{H}_1\otimes \mathcal{H}_1$.
According to Watrous book, the set of separable states is the convex hull of the set of product ...
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QISKIT: ValueError: too many subscripts in einsum DensityMatrix()
I am trying to compute the entanglement entropy of a partition of a quantum system on qiskit. To do this, I call the function DensityMatrix(). If I go above 10 sites (e.g. 12), I get an error like:
...
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Derivation of Choi-Jamiolkowski isomorphism
I'm following the course Mathematical Methods of Quantum Information Theory by Reinhard Werner. In lecture 6, he gave a derivation of Choi-Jamiolkowski isomorphism, and I'm struggling to understand ...
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How to get the Kraus operator $M_0=\sqrt{1-p}\, I$ for the depolarizing channel, from its isometric representation?
I am confused as to how we get $M_{0} = \sqrt{1-p} I$ and the following $M_{1}, M_{2}, M_{3}$.
The above notes say that we should partially trace over the environment in the $|{0}\rangle, |{1}\rangle, ...
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Why is a density matrix an orthogonal projector?
Suppose I have a density matrix like $\rho = \frac{1}{2}[I + \hat{n}\vec{\sigma}]$.
The claim is that $\rho$ is an orthogonal projector for the state $|+\rangle$ in an arbitrary direction $\hat{n}$.
...
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I have two Choi matrix I suspect be equivalent. Can I manipulate them?
I am performing a process tomography over a protocol I suspect to be equivalent to the $CS$ gate.
To compare basic operators I usually compute the Choi matrix of the target gate -- which in this case ...
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Can we use a Werner state for quantum teleportation? [duplicate]
Some background:
The quantum teleportation protocol requires first that Alice and Bob share an entangled state, say a Bell state $|\psi^{+}\rangle_{AB}$.
There is another state $|\psi\rangle_{A'}$ to ...
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How is Pauli twirling so powerful?
So the Pauli twirling approximation gives us a quantum channel $\Phi$ that transforms a density matrix $\rho$ to:
$\Phi(\rho)\mapsto\sum_{i=0}^3 \sigma^i \rho \sigma^i,$
where $\sigma^0 = \mathbb{I}, \...
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General Bell state expression: What condition for mixture of Bell states to be entangled?
Convention: $|qubit_{A}, qubit_{B}\rangle$
The general Bell state equation: $|\beta(a,b)\rangle = \frac{1}{\sqrt{2}}\sum_{k=0}^{1}(-1)^{ka}|k, k\oplus b\rangle = \frac{1}{\sqrt{2}}[|0,0 \oplus b\...
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Finding entanglement in matrix that is a sum of 4 Bell states
A general Bell state:
$|\beta(a,b)\rangle = \frac{1}{\sqrt{2}}[|0,0 \oplus b\rangle + (-1)^{a}|1,1 \oplus b \rangle]$
$|\beta(0,0)\rangle = \frac{1}{2}[|00\rangle \langle 00| + |00\rangle \langle 11| +...
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Does separability of a matrix implies the matrix is a density matrix?
Suppose I have a matrix that is unknown whether it is a density matrix and assume that finding the eigenvalues of it is difficult because the matrix is expressed generally.
However, suppose that this ...
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Define a traceless part of $\rho$ [closed]
I saw in a paper: $|\bar{\rho}\rangle\rangle=|\rho\rangle\rangle-|\hat{I}\rangle\rangle / 2^{n / 2}$ for the $4^n$-dimensional vector representing the traceless part of $\rho$. https://arxiv.org/abs/...
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calculate the reduced density matrix of a 2 qubit state and compare the eigenvalues
So I have the exercise to apply a Cz gate to the following 2 Qubit state
$|a\rangle \otimes |b\rangle = (a_0 |0\rangle + a_1 |1\rangle) \otimes (b_0 |0\rangle + b_1 |1\rangle)\\\\$
Afterwards, I ...
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Moments of Pauli coefficients of Haar-random states
I want to evaluate the quantity $\sum_{P\in \rm{P}^n}\text{Tr}^{\alpha}(\rho P)$, where $P$ is an element of n-qubit Pauli group $\rm{P}^n$ and $\rho$ is a density matrix of a Haar random state. It is ...
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How do I show that a reduced density matrix of $1$ is $\rho_{12}^{1} = Tr_{2}[\rho_{12}] = \sum_{i}\langle i_{2} | \rho | i_{2} \rangle$?
Let the system be a 2 - qubit system and let $\rho_{12}$ be a density matrix of some state for this 2 - qubit system.
How do I show that a reduced density matrix of $1$ is $\rho_{12}^{1} = Tr_{2}[\...
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How do I find the reduced density matrix of a system where two people share one qubit and have one qubit of their own?
I have the following problem and have attempted to find a solution to it, but to no avail.
Alice and Bob have one qubit each, say $|\psi\rangle$ with Alice and $|\phi\rangle$ with Bob. They also share ...
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Given that for every valid density matrix $\rho$, $\text{Tr}(M\rho) = 1$; what can we conclude about matrix $M$?
My intuition says that $M$ has to be the identity matrix, but I am not able to show it rigorously. I tried playing around using spectral decomposition. If
$$
\rho = \sum_i \lambda_i |\lambda_i \rangle ...
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How to compute marginal probabilities of Alice's qubit (in density operator language)?
Let $| \psi \rangle = \frac{1}{\sqrt{2}}|00\rangle + \frac{1}{2}|01\rangle + \frac{\sqrt{3}}{4} |10\rangle + \frac{1}{4}|11\rangle$ be a state vector describing a closed quantum mechanical system.
...
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Statevector from Density matrix of non-pure state
I have a state vector of a 16 qubit system. I want to get the wave function (in the form of a state vector) for half and quarter of this system. When I try to make a ...
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0
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What does the product of two density matrices represent physically?
A quantum state, pure or mixed, can be described by a density matrix that encodes the Bloch vector $\hat{m}$ analog of a quantum state like
$\rho = \frac{1}{2}[\mathbb{I} + \hat{m}.\vec{\sigma}]$.
Let ...
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Prove the fidelity equals $F( \rho , \sigma) = |\langle \psi_{\rho} | \psi_{\sigma}\rangle|^2$ for pure states
I am trying to learn by myself quantum computing and information and I have a very simple question concerning the demonstration of the following equality: $F( \rho , \sigma) = |\langle \psi_{\rho} | \...
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How to compute the partial trace of the state $|\psi\rangle = \sum_{k}c_k |k\rangle\otimes|k\rangle\otimes |k\rangle$?
Suppose we have a quantum system defined on a Hilbert space of $H=H_A\otimes H_B\otimes H_C$, and there is a state defined in $H$ of the form:
\begin{eqnarray}
|\psi\rangle = \sum_{k}c_k |k\rangle\...
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Density matrix and State vector give different result in mesolve in QuTiP
qutip mesolve gives me different population evolve depending on that initial state is state vector or density matrix. And, in some situation, it gives me negative population. It doesn't make sense...
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Create qnode with density matrix on pennylane
I'm using pennylane.
What I want to do is
Create a qnode with the 2*2 density matrix of a single qubit one. It has the parameter as phi
Given density matrix:
$$\...
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How many dimensions does an n-qubit system have?
How many dimensions does an $n$-qubit system have?
What is definition of dimension for a quantum state? Is it related to the number of rows and columns of a density matrix?
My guess is that it has $2^...
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Can a density operator be written equivalently as $\rho=\sum_i p_i|\psi_i〉\!\langle\psi_i|$ and $\rho=\sum_i\lambda_i|\psi_i\rangle\!\langle\psi_i|$?
My doubt arises from page 99, 101 of the book Quantum Computation and Quantum Information by Michael A.Nielson and Issac L.Chung.
Let {${p_{i}, | \psi_{i} \rangle }$} be an ensemble of pure states.
...
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Induced measure on the set of density matrices defined through the Ginibre ensemble
I am defining a density matrix via
$\rho = \frac{X^\dagger X}{\textrm{tr}(X^\dagger X)}$, where $X$ belongs to the Ginibre ensemble. This results in an induced distribution on the set of density ...
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What is the probability of a state $|0\rangle$ being in another state $\alpha|0\rangle+\beta|1\rangle$?
I am trying to calculate the probability of a state (density matrix) being in a specific other state.
Lets say I have a 2-dimensional state with the states given by the orthonormal basis states $|0\...
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Can density matrices of multipartite systems always be written as product states?
suppose the density matrix $\rho_{ABC}$ with the subsystems {A,B,C}
can we write $\rho_{ABC}$ as below?
$\rho_{ABC}=\rho_A \otimes \rho_B \otimes \rho_C $
if the answer is yes please share a ...
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How to perform a state density modification for a single targeted state only?
I have a question about single target state modification... Suppose we have a 3 qubit state density distribution as follows (prenormalized):
$$\begin{bmatrix} |000\rangle & 3 \\ |001\rangle & ...
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Is Klein's inequality due to Klein?
You may be familiar with "Klein's inequality"; one form of it is
$$
-\operatorname{tr}(\rho \log \sigma) + \operatorname{tr}(\rho \log \rho) \ge 0,
$$
stating that relative entropy is ...
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Lifting map and joint probability
How to use lifting map approach to calculate the following joint probability after equation (12) of Quantum-like model of diauxie in Escherichia coli: Operational description of precultivation effect ?...
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how to find a quantum gate matrix from RHO before and RHO after evolve
to evolve a 4x4 density matrix I use this method:
rhoafter = np.dot(np.dot(gate,rhobefore),np.conjugate(gate.T))
And I want to find the gate from rhobefore and ...
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On the probability of agreeing with different density matrices?
Let's say I have a density matrix and I (person $1$) suspect it to be of the form:
$$ \rho_1 = p_1 |\psi \rangle \langle \psi | + p_2 |\phi \rangle \langle \phi |$$
$|\psi \rangle$ and $| \phi \rangle$...
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Prove that $Tr(\chi(\rho_A) \log(\chi(\rho_A)) = Tr(\rho_A \log(\chi(\rho_A))$
I am trying to see how the following statement about trace $Tr$ is true.
$$
Tr(\chi(\rho_A) \log(\chi(\rho_A)) = Tr(\rho_A \log(\chi(\rho_A)),
$$
for some quantum state $\rho_A$, Where,
$$
\chi(.) = \...
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Tf.einsum vs matmul for computing density matrix from a set of Cholesky decomposed matrices
I am trying to construct a density matrix of shape 256x256 from a set of T matrices. These T matrices are all Cholesky-decomposed matrices. But I am not sure if the ...
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Is it possible to apply a quantum gate to a density marix from a partial trace?
To apply a gate(matrix) to a 2 qubit partial trace(4x4 matrix) I have this function:
...
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Operator qubit ordering not matching circuit qubit ordering
I tried constructing a cx gate manually using tensor products and one using QuantumCircuit in qiskit followed by converting it ...
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How to perform below operation in Qiskit?
I want to implement the below equation in Qiskit.
$(A \otimes B).\rho.(B^\dagger \otimes A^\dagger)$ where $\rho$ is a density matrix and $A$ and $B$ are CNOT gates.
$$ A=\begin{bmatrix}
1 & 0 &...
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Compatibility of partial_transpose in Qiskit
I need to calculate the negativity of a density matrix; in doing so on Qiskit I stuck on the problem of computing the partial transpose for a problem of compatibility.
Basically I extract my density ...
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How to Find a circuit that evolves from one density matrix to another(qiskit or cirq)
given two density matrices, dmBefore and dmAfter, I want to generate(find) a circuit in Qiskit or Cirq that starting initaliazed with dmBefore ends with dmAfter after it's execution. Is it possible?.
...
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Observable for Absolute Overall Magnetization of an Ising Model
I am currently following this tutorial for generating a phase transition plot that has been generated in the same tutorial. In this tutorial's magnetization ...
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2
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What is the density matrix of a pure state?
By definition of the density matrix for example the density matrix of $|0\rangle$ state (pure state) is:
$$\rho=|0\rangle \langle 0| =
\begin{pmatrix}
1 & 0 \\
...
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What trace properties are used in the identity ${\rm tr}_A{\rm tr}_B(\rho\Pi)={\rm tr}_A(\rho_A{\rm tr}_B(\rho_B\Pi))$?
To turn the probability of the projection over the Hilbert space $\mathcal H_A \otimes \mathcal H_B$ into the POVM probabilty over $\mathcal H_A$ we we use this equality:
$$tr_Atr_B(ρΠ_i)=tr_A(ρ_Atr_B(...
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Non trace-preserving map in axiomatic approach to quantum operations
In Nielsen and Chuang's Quantum Computation and Quantum information there is an axiomatic definition of the quantum operation (as one of the 3 approaches to quantum operations).
A quantum operation is ...
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How does Qiskit/Qasm simulate the density matrix of up to 30 qubits?
The full density matrix of 30 qubits contain $2^{30}$ states. How does qiskit/qasm implement this without storing and computing the full $2^{30}$ density matrix of possible state coefficients?
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Representation of maximally entangled states of $2n$ qubits with Pauli matrices?
I'm reading this paper while the author states in the eq(A1) that, for a $2n$ qubits maximally entangled state $|\Psi ^+\rangle \langle \Psi ^+|$, we can write it with Pauli operators $P_u\in\left\{ I,...
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what is square root of a density matrix power two?
I know that in algebra for a variable we have
$ \sqrt {x^2} = |x|$
What if $x$ is a density matrix?
Please share resource for your answer.
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