Questions tagged [partial-transpose]
For questions about partial transpose, i.e. the transpose limited to a subsystem of a composite system.
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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
$$
\...
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If $\rho_{AB}$ is a separable then the partial transpose w.r.t to A is PSD
Def: The partial transpose of a linear operator $\rho_{AB}$ over a Hilbert space $H_A \otimes H_B$ w.r.t A is defined for a linear operator $\rho_{AB}=\rho_A \otimes\rho_B$ as $\rho^{T_A}_{AB}=\rho_A^...
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General Bell state expression: What condition for mixture of Bell states to be entangled?
Convention: $|qubit_{A}, qubit_{B}\rangle$
The general Bell state equation: $|\beta(a,b)\rangle = \frac{1}{\sqrt{2}}\sum_{k=0}^{1}(-1)^{ka}|k, k\oplus b\rangle = \frac{1}{\sqrt{2}}[|0,0 \oplus b\...
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Finding entanglement in matrix that is a sum of 4 Bell states
A general Bell state:
$|\beta(a,b)\rangle = \frac{1}{\sqrt{2}}[|0,0 \oplus b\rangle + (-1)^{a}|1,1 \oplus b \rangle]$
$|\beta(0,0)\rangle = \frac{1}{2}[|00\rangle \langle 00| + |00\rangle \langle 11| +...
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how to obtain partial transpose of a Tripartite operator?
i know for a bipartite system with elements
|ij><kl|
elements of its partial transpose are
|kj><il|
now suppose a ...
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Does a partial transpose always have real eigenvalues?
I am working with a tripartite system, but when I partially transpose the $8\times 8$ density matrix I get two complex eigenvalues. I know the criteria for the positive and negative eigenvalues, but ...
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Is there an identity for the partial transpose of a product of operators?
The partial transpose of an operator $M$ with respect to subsystem $A$ is given by
$$
M^{T_A} := \left(\sum_{abcd} M^{ab}_{cd} \underbrace{|a\rangle \langle b| }_{A}\otimes \underbrace{|c \rangle \...
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What are examples of zero capacity quantum channels with Choi rank less than $d$?
All the currently known examples of quantum channels with zero quantum capacity are either PPT or anti-degradable. These notions can be conveniently defined in terms of the Choi matrix of the given ...
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Is there an easy way to calculate the eigenvalues of the partial transpose of a given matrix? [duplicate]
Consider the state
$$|\psi\rangle=(\cos\theta_A|0\rangle+\sin\theta_A|1\rangle)\otimes(\cos\theta_B|0\rangle+e^{i\phi_B}\sin\theta_B|1\rangle).$$
To calculate the $\rho^{T_B}$ I first calculate the $\...
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How can one argue that the partial transpose $\rho^{T_B}$ of a general separable state is positive?
How can one argue that the partial transpose $\rho^{T_B}$ of a general separable state is positive?
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How do I calculate the eigenvalues of the positive partial transpose of this two-qubit state?
How can I calculate the eigenvalues of $\rho^{T_{B}}$ (PPT) of the following 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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Defining dimension of an operator in qutip
My main question: Can someone please explain to me how the list of array is used to define the dimension in qutip?
Context:
If I have my density operator ...
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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 ...
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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 ...
glS♦
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