For questions about the entanglement measure derived from the PPT separability criterion.
Questions tagged [entanglement-negativity]
13 questions
6
votes
2 answers
Why do completely positive maps satisfy ${\rm Tr}[\Psi(\rho)_++\Psi(-\rho)_+]\leq{\rm Tr}[\Psi(\rho_+)]+{\rm Tr}[\Psi((-\rho)_+)]$?
I am studying a paper of M. Plenio, "Logarithmic Negativity: A Full Entanglement Monotone That is not Convex", PRL 2005 [arXiv:quant-ph/0505071].
In the paper, I do not fully understand the Eq.$(7)$. He said that
Employing linearity of operation…
Acpil
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3
votes
0 answers
Relationship Between Knill-Laflamme Conditions and Negativity
Given an error channel $\mathcal{E}$, one can state the Knill-Laflamme conditions in terms of a condition on the coherent information, e.g., this post.
Is there a version of the Knill-Laflamme conditions in terms of negativity of the logical system…
zeroknowledgeprover
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3
votes
1 answer
Entanglement Negativity and Reduced Density Matrices
The negativity of a density matrix is defined as
$$
\mathcal{N}(\rho_{AB}) = \frac{1}{2} \bigl(\|\rho_{AB}^{T_A}\|_1 - 1\bigr),
$$
where $\rho_{AB}$ is a density matrix on the bipartite system $A \otimes B$,
$T_A$ denotes the partial transpose with…
zeroknowledgeprover
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3
votes
1 answer
Is there an identity for the partial transpose of a product of operators?
The partial transpose of an operator $M$ with respect to subsystem $A$ is given by
$$
M^{T_A} := \left(\sum_{abcd} M^{ab}_{cd} \underbrace{|a\rangle \langle b| }_{A}\otimes \underbrace{|c \rangle \langle d|}_B\right)= \left(\sum_{abcd} M^{ab}_{cd} …
FriendlyLagrangian
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3
votes
1 answer
How do I calculate Logarithmic Negativity for the given bipartite state?
How can I calculate Logarithmic Negativity for the given state?
$\rho = \frac{1}{2} |0\rangle \langle0| \otimes |+\rangle \langle+| +\frac{1}{2} |+\rangle \langle+| \otimes |1\rangle \langle1| $
user14749
2
votes
1 answer
How is the expression $\frac{\|\rho^{T_B}\|-1}{2}$ obtained from the definition of negativity?
In quantum information theory, negativity is defined as summation of the absolute values of negative eigenvalues of the partial transposed density matrix. The expression of negativity is given as
$$
\mathcal{N}\left(\rho_{AB}\right)=\frac{||…
Anindita Sarkar
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2
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Are there quantum algorithms to estimate the partial transpose?
The entanglement negativity and the positive partial-transpose criteria play important roles in quantifying the amount of entanglement for mixed states. Yet, because these measures generally involve partial transposing the density matrix w.r.t. some…
ironmanaudi
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In a bipartite system $AB$, why does the entanglement negativity $\mathcal{N}(\rho^{T_A})$ measure the entanglement between $A$ and $B$?
Consider a system composed of two subsystems $A$ and $B$ living in $\mathcal{H}=\mathcal{H}_A \otimes \mathcal{H}_B$. The density matrix of the system $AB$ is defined to be $\rho$. The entanglement negativity of $\rho$, defined…
FriendlyLagrangian
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1
vote
1 answer
What is the logarithmic Negativity of the Werner state?
What is the Logarithmic Negativity of the Werner state
$$\rho_w = p|\Psi^-\rangle\langle\Psi^-|+\frac{1-p}{4}I_4$$
where $|\Psi^-\rangle = \frac{1}{\sqrt{2}}(|10\rangle-|01\rangle)$?
heromano
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vote
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What is the deep physical reason behind the existence of bound entanglement?
In Quantum Information processing, we can extract entanglement from $n$-copies of a weakly entangled state to produce a fully or highly entangled states in $d$-dimensions, using the known distillation protocols.
However, there are states from which…
Devjyoti Tripathy
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votes
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How to calculate Minimum Residual Contangle for Entanglement
I used expectation values of Heisenberg Langevin equations to construct a 6 × 6 covariance matrix between three qubits.
Now, I am confused in the formula for minimum Residual contangle. I have understanding of logarithm negativity but I'm confused…
Syed Shahmir Kazmi
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0
votes
1 answer
Compute the negativity of maximally entangled bipartite states
The entanglement negativity $\mathcal N(\rho)$ of a (bipartite) state $\rho$ is defined as the absolute value of the sum of the negative eigenvalues of the partial transpose of a state, or equivalently, $2\mathcal…
glS
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0
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Why does the entanglement negativity equal (in magnitude) the sum of the negative eigenvalues?
The entanglement negativity, introduced in (Vidal and Werner 2002), is defined as
$$\mathcal N(\rho) \equiv \frac{\|\rho^{T_B}\|_1-1}{2}.$$
It is mentioned there that this equals the sum of the absolute values of the negative values of the…
glS
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