All Questions
Tagged with textbook-and-exercises entanglement
49
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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 ...
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1
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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.
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Possible post - measurement states for Bell state $\frac{1}{\sqrt{2}}[|00\rangle + |11\rangle]$
This is in reference to page 241 of Introduction to classical and quantum computing by Thomas.G Wong.
The author starts off with a Bell state $\frac{1}{\sqrt{2}}[|00\rangle + |11\rangle]$.
In trying ...
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Is the balanced superposition of all three-qubit computational basis states entangled?
I am reading the "An introduction to quantum computing for non-physicists" by Rieffel and Polak. In page 308, they define an entangled state as a state that "cannot be described in ...
3
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1
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Proof of Nielsen's theorem (Theorem 12.15) given in Nielsen-Chuang (assumption of invertibility)
Theorem 12.15 of Nielsen and Chuang's 10th anniversary edition is Nielsen's Theorem (1999). In particular, it says,
Theorem 12.15: A bipartite pure state $\mid \psi \rangle$ may be transformed to ...
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1
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How to compute the maximum possible coherence of a two-particle Bell state?
I am reading through some notes and am stuck on a bit of math that shows the max possible coherence. Our wave function is $|\psi\rangle =\frac{|01\rangle+|10\rangle}{2}$ and doing $|\psi\rangle \...
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Do unitary matrices acting on entangled states always give a quantum state?
I'm trying to understand what happens when Alice(Bob) apply a unitary to her(his) part of an entangled state. Let us consider the following unitary transformations:
$$U_1 = \frac{1}{\sqrt{2}}
\...
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Understanding Controlled Operation
while reading an article on phase kickback, I came across this paragraph.
When you apply a controlled operation on a target qubit that is in an eigenstate of the unitary, what’s essentially happening ...
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What is the difference between "maximally entangled" and "entangled" states?
when we talk about bell state we say that these states are maximally entangled. so just wanted to understand is there any difference between just entangled and maximally entangled ?
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Show that any two product states of the same dimension are LU-equivalent
States $|Ψ \rangle$, $|Φ\rangle$ on $C_d⊗C_{d′}$ are said to be equivalent up to Local Unitarities (LU-equivalent) if there exist unitaries $U : C_d → C_d$ and $V : C_{d′} → C_{d′}$
such that:
$|Ψ \...
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Prove whether the state $|0\rangle\otimes|0\rangle+|1\rangle\otimes|+\rangle$ is entangled
I'm trying to figure out whether or not the following state is entangling:
$$|Ψ⟩ = 1/\sqrt2 (|0⟩ ⊗ |0⟩ + |1⟩ ⊗ |+⟩)$$
Expanding it out I get:
$$1/\sqrt2 (|0⟩ ⊗ |0⟩ + 1/\sqrt 2(|1⟩ ⊗ |1⟩ + |1⟩ ⊗ |0⟩))$$...
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Write in seperable form [closed]
Consider the two-qubit state $$𝜌 =
1/4
\{(|00⟩ + |11⟩) (⟨00| + ⟨11|) + (|01⟩ + |10⟩) (⟨01| +
⟨10|)\}.$$ Though looks like an entangled state, it is in fact a separable one. Write it down in the
...
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Show by example that a linear combination of entangled states is not necessarily entangled
$\newcommand{\bra}[1]{\langle#1\rvert} % Bra
\newcommand{\ket}[1]{\lvert#1\rangle} % Ket
\newcommand{\qprod}[2]{ \langle #1 | #2 \rangle} %Inner Product
\newcommand{\braopket}[3]{\langle #1 | #2 | #3\...
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Are the first and second qubits of the state $| 111 \rangle + | 010 \rangle + | 101 \rangle + | 000 \rangle$ entangled with each another?
State of qubits:
$\frac{1}{2} (| 111 \rangle + | 010 \rangle + | 101 \rangle + | 000 \rangle)$
Are the first and second qubits of this register entangled with each another?
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What conditions on the coefficients of a bipartite pure state imply it being entangled?
With $\{ |e\rangle_j \}_{j=1}^{dim. \mathcal{H}_A}$ for $\mathcal{H}_A$ and $\{|f\rangle_j \}_{j=1}^{dim. \mathcal{H}_B}$ for $\mathcal{H}_B$, the product state reads
\begin{equation}
|u\rangle \...
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