Questions tagged [entanglement-negativity]

For questions about the entanglement measure derived from the PPT separability criterion.

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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 $$ \...
Anindita Sarkar's user avatar
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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 ...
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What is the maximum and minimum value of logarithmic negativity measured for bi-party entanglement?

I have calculated logrithmic negativity for my biparty entangled system in a superconducting circuit. The negativity gives a sine curve where maximum value comes out to be 4 and minimum 0.5. Now, how ...
Syed Shahmir Kazmi's user avatar
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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 \...
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What is the logarithmic Negativity of the Werner state? [closed]

What is the Logarithmic Negativity of the Werner state $$\rho_w = p|\Psi^-\rangle\langle\Psi^-|+\frac{1-p}{4}I_4$$ where $|\Psi^-\rangle = \frac{1}{\sqrt{2}}(|10\rangle-|01\rangle)$?
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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| $
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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 ...
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What is the deep physical reason behind the existence of bound entanglement? [closed]

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 ...
Devjyoti Tripathy's user avatar
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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 ...
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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 ...
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