Suppose we have some quantum system with sub-systems A and B. It could be, for example, two qubits or groups of qubits. Is it fair to say that tracing out the sub-system A is always akin discarding any information about the sub-system A? So, if our information comes only from the measurement of t...

While reading Aaronson's Barbados lectures (PDF) I found myself interested in the Firewall problem and the Harlow-Hayden decoding task. The problem is, coming from the engineering side I don't really know anything about, say Hawking radiation or quantum field theory claiming that "there are Bell ...

To make the partial transpose a complete positive and therefore physical map, one has to mix it with enough of the maximally mixed state to offset the negative eigenvalues. The most negative eigenvalue is obtained when partial transpose is applied on the maximally entangled state which is $-\fr...

Suppose we are given the Hamiltonian $$H=f \frac{\text{Tr}\sigma_x \rho}{\text{Tr}\rho}\sigma_x,$$ where $\rho$ is the density matrix, and $\sigma_x$ is the Pauli matrix $$ \sigma_x= \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}, $$ and $f$ is a coupling constant. The time evolution of the de...

This question is about Lemma $7.1.2$ in Kaye, Laflamme, and Mosca's textbook: Let $\omega = \frac{x}{2^n} = 0.x_1x_2\ldots x_n$ be some fixed number. The phase estimation algorithm applied to the input state $|\psi\rangle = \frac{1}{\sqrt{2^n}}\sum_{y=0}^{2^n-1}e^{2\pi i \omega y}|y\rangle$ o...

While reading the Quantum algorithm Wikipedia entry, I noticed that the sentence "A quantum circuit consists of simple quantum gates which act on at most a fixed number of qubits", was annotated with a "why?".

I have a state $$ |\tilde{\Phi_2}\rangle =\dfrac{1}{2^{3l/2}}\sum_{x=0}^{2^l-1}\sum_{y=0}^{2^l-1}\sum_{z=0}^{2^l-1}|0\rangle^{\otimes q}\otimes |x\rangle^{\otimes l}\otimes |y\rangle^{\otimes l}\otimes |z\rangle^{\otimes l} $$ Now i want to change the state $|z\rangle$ by the states $|x\rangle$ ...

Following the AMPS paper, the Hawking radiation can be divided into an early and late part, decomposed as follows: $$ |\Psi\rangle=\sum_{i}|\psi_{i}\rangle_{E}\otimes |i\rangle_{L},$$ where $\lbrace|i\rangle_{L}\rbrace $ are an orthonormal basis for the late radiation. Further on, we expand $|\...

I was on the Wikipedia page for Nitrogen-Vacancy Center and in the first paragraph the following statement is made: An individual N-V center can be viewed as a basic unit of a quantum computer, and it has potential applications in novel, more efficient fields of electronics and computational ...