Questions tagged [schmidt-decomposition]
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For tetrapartite state, and another way of decomposition, is the Schmidt basis separable?
Consider two tetrapartite quantum states $|\phi\rangle^{AA^\prime BB^\prime}$ and $|\psi_1\rangle^{AA^\prime}|\psi_2\rangle^{BB^\prime}$ in a finite dimentional Hilbert space $\mathcal{H}^A\otimes\...
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Does proximity of two bipartite states in a norm force high overlap between the elements of the Schmidt bases?
I want to know that there is a relation between the distance of two vectors and the corresponding elements of the Schmidt bases.
We assume that two bipartite vectors $|\phi\rangle^{AB}$ and $|\psi\...
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1
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Prove that there are infinitely many entanglement classes under LU
Dur, 2000 states that
(...)But even in the simplest systems, $|\psi\rangle$ and $|\phi\rangle$ are typically not related by LU, and continuous parameters are needed to label all equivalence classes.
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SWAPing Schmidt vectors
Can anything be said about the inner product of a bipartite entangled state with itself but with the Schmidt vectors swapped? That is, if the Schmidt decomposition of a state is given by
$$\vert \psi \...
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2
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Truncating the bond dimension of an MPS -- how good is the approximation?
$\newcommand{\complex}{\mathbb{C}}\newcommand{\ket}[1]{|#1\rangle}$ Let $\ket{\psi}\in(\complex^d)^{\otimes n}$ be a pure quantum state. It is well-known that $\ket{\psi}$ is a matrix product state ...
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How to check if a $n$-qubit unitary is the tensor product of single-qubit unitaries
Let's assume I give you the expression of a unitary matrix acting on two qubits that is:
$$U=\sum_{i} A_i \otimes B_i$$
for some operators $A_i$ and $B_i$.
Is there a simple criterion allowing you to ...
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6
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Schmidt decomposition for tripartite system $ABC$ with vanishing mutual information between $A$ and $C$
Suppose I have a tripartite system $ABC$ in a pure state $|\psi_{ABC}\rangle$ with mutual information $I(A:C)=0$. This implies that the reduced density matrix $\rho_{AC}$ factorizes as $\rho_{AC} = \...
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