# 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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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: $$\frac{1}{\sqrt{2}} \begin{bmatrix} \... 5 votes 2 answers 128 views ### Is it true that if U sends computational basis states to product states, then it sends product states to product states? Let U be a unitary such that for all n-qubit computational basis states |x\rangle, the state U |x\rangle is a product state. I am trying to prove that for all n-qubit product states |w\... 1 vote 1 answer 48 views ### Matrix representation for biproduct mixed states Nielsen and Chuang [10e, p. 74] introduce the Kronecker product A\otimes_K B as a matrix representation of the tensor product A\otimes B of the operators A and B (for clarity I use a subscript ... 0 votes 0 answers 28 views ### Figuring out which experiment is being performed from the results of the experiment Consider two different experiments involving qubits. In Experiment 1, a qubit is prepared in the mixed state I/2, where I is the 2 × 2 identity matrix. Alice then chooses an orthonormal basis B... 1 vote 3 answers 141 views ### How to show that the QFT satisfies \frac1{\sqrt N}\sum_j\prod_le^{2\pi i j_l k/2^l}|j_1...j_n⟩=\bigotimes_l \frac1{\sqrt2}(|0⟩+e^{2\pi i k/2^l}|1⟩)? I'm reading Ronald de Wolf's lecture notes, and in chapter 4.5 he writes that$$ \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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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\...