Questions tagged [product-states]
Having to do with problems which are primarily concerned with some state, which is a tensor product of states on each of its smallest subsystems, and where this represents a significant restriction on the problem (e.g., if it would be more common to consider an arbitrary state).
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Simple proof that entangled pure states are not separable
I am trying to understand more about the notion of separable states. For clarity, I will only use the word entangled for pure states, even if a non-separable state is sometimes called entangled too.
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Calculate the product state/quantum register back into its tensor product
So let's asume I have a product state/quantum register as a result of a tensor product of two qubits.
Lets take a "hard" product state matrix like:
$$\frac{1}{\sqrt{2}}
\begin{bmatrix}
\...
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Is it true that if $U$ sends computational basis states to product states, then it sends product states to product states?
Let $U$ be a unitary such that for all $n$-qubit computational basis states $|x\rangle$, the state $U |x\rangle$ is a product state. I am trying to prove that for all $n$-qubit product states $|w\...
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Matrix representation for biproduct mixed states
Nielsen and Chuang [10e, p. 74] introduce the Kronecker product $A\otimes_K B$ as a matrix representation of the tensor product $A\otimes B$ of the operators $A$ and $B$ (for clarity I use a subscript ...
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Figuring out which experiment is being performed from the results of the experiment
Consider two different experiments involving qubits. In Experiment 1, a qubit is prepared in the mixed state $I/2$, where $I$ is the $2 × 2$ identity matrix. Alice then chooses an
orthonormal basis $B$...
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How to show that the QFT satisfies $\frac1{\sqrt N}\sum_j\prod_le^{2\pi i j_l k/2^l}|j_1...j_n⟩=\bigotimes_l \frac1{\sqrt2}(|0⟩+e^{2\pi i k/2^l}|1⟩)$?
I'm reading Ronald de Wolf's lecture notes, and in chapter 4.5 he writes that
$$
\frac{1}{\sqrt N}\sum\limits_{j=0}^{N-1}\prod\limits_{l=1}^{n}e^{2\pi i j_l k / 2^l}|j_1...j_n\rangle =
\bigotimes\...
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For bipartite mixed state, if one part is pure, then the global mixed state is a product state?
In Nielsen and Chuang, the chapter about Schmidt decomposition, there is an interesting result states that for a bipartite pure state $|\psi\rangle_{AB}$, if part A is a pure state, then $|\psi\...
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Is factoring of a product state unique?
Suppose I have a product state of two qubits (i.e. a vector of size 4x1). Given it is separable (no entanglement), is this separation unique?
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