All Questions
Tagged with quantum-computer density-operator
15 questions
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How to find stabilizer generators of a subsystem from a known set of generators?
$\newcommand{\ket}[1]{\left|#1\right>}$
I am working on a problem and would appreciate some help. I'm working with a multi-qubit state defined by a set of stabilizer generators, ie $\ket{\psi} \in ...
- 45
1
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47
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Is it enough to recovery density matrix for error correction in quantum computing?
When we discuss error correction, we always talk about the recovery of the density matrix of a single qubit. But somehow I feel that this is not enough. Consider a circuit that contains more than 1 ...
- 181
-1
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2
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471
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How can a dephasing channel be formally represented by a unitary operation?
The dephasing channel is often represented as
$$\mathcal{E}\left(\rho\right)=p_0\rho+(1-p_0)\sigma_z\rho\sigma_z$$ that acts on a single qubit.
Another way of writing it down is by using Kraus-...
- 456
0
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192
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Truncated Completely Positive Trace Preserving (CPTP) maps
Let us consider the the Liouville equation of a level $N$-system with density matrix $\rho$ together with its standard properties (positive semi-definite, unit trace, etc). The evolution of the system ...
- 2,218
1
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2
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382
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Reconstructing state from density matrix (and implications for Grover search)
If I am given a density matrix $\rho$ that I know corresponds to a pure state (i.e., $\rho = |\psi\rangle\langle\psi|$ for some $|\psi\rangle$), then is it possible for me to infer the state $|\psi\...
- 367
3
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1
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58
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How do I prove the identity for ${\rm tr}_p [e^{-iS\Delta t}(\rho\otimes\sigma)e^{iS\Delta t}]$ in Seth Lloyd's 2014 Quantum PCA Paper?
Equation (1) in Seth Lloyd's paper on Quantum PCA says:
$\text{tr}_{p}\text{e}^{-iS\Delta t} \rho \otimes \sigma \text{e}^{iS\Delta t} = \cos^2(\Delta t)\sigma + \sin^2(\Delta t) \rho - i \sin(\Delta ...
- 33
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202
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Simplification in operator-sum representation (Nielsen and Chuang)
First remark: there is a similar question: Operator-sum representation of a quantum operation with different input and output spaces which helped more generally, but I am still stuck on a part unasked ...
- 245
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1
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For what $\lambda$ is the channel $\mathcal E(\rho)=\lambda \rho^T + \frac{1-\lambda}{d}I$ CPT? [closed]
Consider the following channel:
$\mathcal{E}(\rho) = \lambda\rho^T + \frac{1-\lambda}{d}I $
Which $\rho^T$ means transpose and $d$ is the dimension of the Hilbert space.
My question is, for what ...
- 71
0
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2
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466
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Rank of a density matix
I was just trying to understand the meaning of rank of a density matrix. I came across the following post, which says that the rank of density matrix is the number of non-zero eigenvalues. And for a ...
user214336
2
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354
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von Neumann measurement model of a qubit with continuous detector
I have a two state qubit system with initial state $|\psi_s\rangle_i = a|0\rangle+b|1\rangle$ and a detector with initial state
$$|\psi_d\rangle_i = \int_{-\infty}^{\infty}\left(N \exp[-\frac{q^2}{2\...
- 61
-2
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1
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206
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Why is the partial trace of this subsystem equal to this? [closed]
I am doing my bachelors dissertation based on an article by David Deutsch. He defines the action of a quantum gate as:
$$
U = \sum_{x, y \in \mathcal{Z}_{2}} |x \dot{+}y\rangle|y\rangle\langle x|\...
- 33
11
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0
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407
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What's the physical meaning of the eigenvalues of the spin-flipped density matrix?
In the computation of the entanglement of formation(EoF) of a 2 qubits mixed state, $\rho$, according to Wooters, we need to compute the concurrence of the state by computing the eigen values $\{\...
- 1,578
2
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3
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445
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Two qubits system in polar co-ordinates
I know that I can write a single qubit state in terms of polar co-ordinates $(r,\theta,\phi)$ on a Bloch sphere.
\begin{equation}
\rho =
\begin{pmatrix}
\frac{1+r \cos\theta}{2} &\frac{r \exp(-i\...
0
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3
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Why is a two-qubit state described by a point in a 15-dimensional space?
While trying to understand the basics of how quantum computers work, I recently read this statement.
"...consider that single-qubit states can be represented by a point inside a sphere in 3-...
16
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2
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37k
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Trace of an operator matrix (Quantum computation and quantum information)
I'm reading the book Quantum computation and quantum information by Mike & Ike and I'm stuck at 2.60/2.61. There, the author says that, given the operator $A|ψ⟩⟨ψ|$, its trace is:
$${\rm tr}(A|\...
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