Unanswered Questions
152 questions with no upvoted or accepted answers
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What is the difference between "entanglement distillation" and "entanglement purification"?
To my understanding, entanglement distillations is transformation of several copies of weakly entangled states into fewer copies of more strongly entangled states using local operations and classical ...
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Reduced Density Matrix Equation of Motion to describe an Ellipse
Given a pure two qubit state $|\psi_{AB}\rangle$. If we trace out system $B$, the remaining density matrix $\rho_A = Tr_B|\psi_{AB}\rangle\langle\psi_{AB}|$, can be represented as a point lying ...
glS♦
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Finding a class $C$ of bipartite PPT states such that entanglement of $\rho \in C$ implies entanglement of $\rho + \rho^{\Gamma}$
Consider an entangled bipartite quantum state $\rho \in \mathcal{M}_d(\mathbb{C}) \otimes \mathcal{M}_{d'}(\mathbb{C})$ which is positive under partial transposition, i.e., $\rho^\Gamma \geq 0$. As ...
glS♦
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What proportions of certain sets of PPT-two-retrit states are bound entangled or separable?
For two particular (twelve-and thirteen-dimensional) sets of two-retrit states (corresponding to 9 x 9 density matrices with real off-diagonal entries), I have been able to calculate the Hilbert-...
glS♦
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Are X-state separability and PPT- probabilities the same for the two-qubit, qubit-qutrit, two-qutrit, etc. states?
On p. 3 of "Separability Probability Formulas and Their Proofs for Generalized Two-Qubit X-Matrices Endowed with Hilbert-Schmidt and Induced Measures" (https://arxiv.org/abs/1501.02289), it is ...
glS♦
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What is the minimum number of separable states (not necessarily pure) needed to decompose arbitrary separable states?
For a bipartite separable quantum state $\rho$ acting on Hilbert space $H\otimes H'$ with $\dim H=D$ and $\dim
H'=D'$, what is the minimum number of separable state needed for a decomposition? That ...
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Can Alice and Bob convince the cops that they don't share any entanglement?
Suppose Alice and Bob are arrested for killing Eve, and are taken to two different interrogation rooms. The police quiz Alice and separately Bob, asking them a bunch of different questions along the ...
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What are good pedagogical introductions to entanglement distillation?
I have a basic understanding of what entanglement distillation entails, up to the typical subspace projection protocol described in Nielsen & Chuang, and I would like to read more on the subject. ...
glS♦
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Quantum entanglement as topological entanglement
According with Aravind:
the Hopf link, L2a1, corresponds to the Bell state $\frac{1}{\sqrt 2}\big (|00\rangle+|11\rangle\big )$,
the Borromean link (L6a4) can be considered as GHZ state $\frac{1}{\...
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Is it ever beneficial to communicate qubits that aren't EPR pairs?
When Alice wants to send a qubit $q$ to Bob, she doesn't have to send $q$ itself. She can instead generate an EPR pair $(a, b)$, send $b$ to Bob, and teleport $q$ to Bob by consuming $(a,b)$ and ...
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Must two separable states that are $\epsilon$-close in trace distance admit close separable decompositions?
$\newcommand{\complex}{\mathbb{C}}$ Let $n$ and $m$ be positive integers. Does there exist a continuous function $f: [0,1] \rightarrow [0,1]$ such that $f(0)=0$, and whenever two separable density ...
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Relation between geometric and discrete circuit complexity
Geometric complexity of a unitary, as introduced for example here https://arxiv.org/abs/quant-ph/0502070, measures the length of a geodesic connecting the identity matrix and a given unitary in the ...
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Volume law spread after Hamiltonian evolution
Start with an $n \times n$ lattice, with each qubit initialized to the state $|0\rangle$. Then, apply the Hadamard gate on each qubit. Then, evolve the system under the Hamiltonian
\begin{equation}
...
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260
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How to show that Werner states produce correlations explainable via local hidden variable models?
Werner states can be written as
$$\rho_W=
p\frac{\Pi_+}{\binom{n+1}{2}}
+(1-p)\frac{\Pi_-}{\binom{n}{2}},
$$
with $\Pi_\pm\equiv\frac12(I\pm\mathrm{SWAP})$ projectors onto the $\pm1$ eigenspaces of ...
glS♦
- 26.9k
4
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Can changing reference frames generate entanglement in identical particles?
Suppose we have a pair of qubits, physically realised as two spin-half particles in some separable pure state $|\psi\rangle$, separated by a distance '$l$', large enough to be regarded as ...
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