# Tagged Questions

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### Reduce density matrix for given eigenfunction [closed]

My question is about how to find reduce density matrix for partition of given eigenfunction. Full question is just in image.
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### Inner products containing the tensor product of two operators

The book Nielsen & Chuang "Quantum Computation and Quantum Information" presents the concept of tensor products as follows. Suppose we have the vectors $|v\rangle$ and $|w\rangle$ which exist in ...
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### Coarse-graining on a second channel decreases mutual information?

Let $X_1,B_1,X_2,B_2$ and $Y_1,A_1,Y_2,A_2$ and $C_1$ and $C_2$ be binary random variables. Suppose: $I(X_2:B_2|C_2=0)+I(Y_2:A_2|C_2=1) \leq 1$. This can be thought of as a bound on the capacity ...
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### Heisenberg XXX time evolution operator for three qubits

I've a problem to reproduce the result in equation (4) on page three of this paper: http://arxiv.org/abs/0802.2588. So far I've understood that they apply a Heisenberg XXX interaction between ...
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### How do I simulate this simple quantum circuit in MATLAB

I want to simulate a circuit similar to the one below in MATLAB. If you have a state matrix describing the state of 3 qubits, I understand that you could apply a CNOT matrix tensored with and identity ...
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### Is the reduction map completely positive? [duplicate]

I am struggling with proving the complete positivity of a general map ( granted it is CP ). The reduction map is defined as $$\rho \rightarrow \mathrm{Tr}(\rho)I - \rho$$ It is a trivial job to ...
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### What is the Reduced Density Matrix?

The difference between pure and mixed states is the difference in their density matrix structure. For density matrix $\rho$ of mixed state the trace of $\rho^{2}$ should be less than 1. For pure ...
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### Tensor product of Hadamard Operators

The Hadamard Operator on one qubit is: \begin{align*} H = \tfrac{1}{\sqrt{2}}\left[\,\left(\color{darkgreen}{|0\rangle + |1\rangle}\right)\color{darkblue}{\langle ...
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### A tensor product of two spin-1 particles

I'm rather confused, and I was hoping if someone could help me figure out this (probably rather elementary) issue. I have two particles with spin 1, whose state I describe by $m_S$ and $m_I$ ...
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Is there any rule or technique so that one can design quantum gate operator from matrix operator? Suppose, what will be the quantum gate operator for this matrix operator : $$\left( \begin{array}{c ... 1answer 87 views ### Super-dense coding protocol with a key I have this assignment: Show that super-dense coding protocol with the key in the state \frac{|00⟩⟨00|+|11⟩⟨11|}{2} is equivalent (in a sense of transmission rate and security) with ... 2answers 128 views ### Smallest number of quantum gates to simulate other gates? What is the smallest number of Fredkin gates needed to simulate a Toffoli gate? What is the smallest number of Toffoli gates needed to simulate a Fredkin gate? Where the Toffoli's gate is the CCNOT ... 1answer 55 views ### Sinusoidaly Driven Two-Level System (TLS) I'm trying to solve the driven Two-Level System (TLS or qubit) question using a Fourier transform of the Schrodinger equation (SHE), but I'm getting stuck on solving the equation. Given Hamiltonian ... 0answers 118 views ### Definition of a 'tunneling lifetime' I'm given a one-dimensional potential with two wells, one local minimum at some higher energy and one deep global minimum next to it, separated by a barrier of own shape and height (phase qubit). I ... 0answers 212 views ### Invariance of states under local unitary transformations [closed] How can I show explicitly that the bell state$$|\psi^{-}>=\frac{1}{\sqrt{2}}(|0>|1>-|1>|0>)$$is invariant under local unitary transformations U_{1}\otimes U_{2} ? 2answers 128 views ### Grover algorithm R_D Circuit I need sketch two circuits to understand Grover algorithm. The first is the operator R_f and another is the operator R_D = H^{\otimes n}(2|0\rangle\langle0|-I)H^{\otimes n}. I get the first ... 1answer 81 views ### Statistical sum of physical quantities in a quantum system Let C = A + B (statistical sum, so \mathbb{E}[C] = \mathbb{E}[A] + \mathbb{E}[B]), and let p(A = a) = 1. Are the following true? \mathbb{E}[C^2] = a^2 + 2a\mathbb{E}[B] + \mathbb{E}[B^2] ... 1answer 54 views ### Violation of the Normalization Constraint? Say we have two qubits |a\rangle and |b\rangle both initialized to |0\rangle. We then apply the rotation gate R_{x}(\frac{\pi}{2}) of matrix representation \left( \begin{array}{} ... 1answer 177 views ### Question on hadamard gate and cnot gate circuit tables I'm trying to solve this problem for homework: Now show that if the CNOT gate is applied in the Hadamard basis - i.e. apply the Hadamard gate to the inputs and outputs of the CNOT gate - then ... 1answer 292 views ### Bloch sphere representation Suppose you know that a qubit is either is in state |+\rangle with probability p or in state |-\rangle with probability 1-p. If this is the best you know about the qubit's state, where in the ... 2answers 1k views ### How to apply a Hadamard gate? How to apply a Hadamard gate to 3 qubits? by example how to apply H to (1/\sqrt{2})(\left|000\right> + \left|111\right>)? 1answer 352 views ### Two Qubit problem A two-qubit system was originally in the state  \frac{3}{4}|00\rangle-\frac{\sqrt{5}}{4}|01\rangle+\frac{1}{4}|10\rangle-\frac{1}{4}|11\rangle  , and then we measured the first qubit to ... 1answer 389 views ### Quantum Circuit, example of the Bernstein-Vazirani problem This question is regarding the quantum circuit in the picture below. Suppose we have the set up below, where U performs the operation U:\mid x \rangle \mid y \rangle \rightarrow \mid x \rangle\mid y ... 0answers 243 views ### Computing with qubits [closed] We have a qubit in the state |\psi \rangle= √3/2 |0\rangle + 1/2 |1\rangle, which we want to measure in the cos \theta\ |\theta\rangle + sin \theta |1\rangle, sin \theta |\theta\rangle - cos θ ... 2answers 146 views ### Bell State, if Bob applies a Pauli Gate? After Alice and Bob share a Bell state, Bob applies a Pauli gate to his qubit. What will be the situation of the Bell state? What happens? Then Alice applies the same gate to her qubit – again, what ... 1answer 117 views ### How to deterministically distinguish the following quantum states? (1) How to deterministically distinguish the following quantum states:$$\frac{1}{\sqrt{2}}[|+0\rangle|0\rangle+|-1\rangle|1\rangle$$,$$\frac{1}{\sqrt{2}}|-0\rangle|0\rangle+|+1\rangle|1\rangle, ...
I think this question is a bit low brow for the forum. I want to take a state vector $\alpha |0\rangle + \beta |1\rangle$ to the two bloch angles. What's the best way? I tried to just factor out ...