1
vote
0answers
12 views

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 ...
1
vote
1answer
123 views

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 ...
2
votes
1answer
123 views

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 ...
1
vote
0answers
32 views

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 ...
1
vote
2answers
485 views

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 ...
4
votes
2answers
103 views

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 ...
3
votes
1answer
143 views

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 $m_I$ ...
1
vote
2answers
119 views

Quantum Computation

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 ...
2
votes
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 ...
3
votes
2answers
114 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 ...
2
votes
1answer
51 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 ...
0
votes
0answers
37 views

Finding all marked elements using Grover's algorithm

As part of an assignment I am supposed to design a variant of Grover's algorithm that finds all $t$ marked elements. I guess like most people I'm more familiar with classic computation, so the ...
2
votes
0answers
109 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 ...
2
votes
0answers
184 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 $U_{1}\otimes U_{2}$ ?
1
vote
2answers
126 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 ...
2
votes
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? $\mathbb{E}[C^2] = a^2 + 2a\mathbb{E}[B] + \mathbb{E}[B^2]$ ...
0
votes
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}{} ...
0
votes
1answer
157 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 ...
3
votes
1answer
257 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 ...
3
votes
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 $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
1
vote
1answer
325 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 ...
1
vote
1answer
366 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 ...
1
vote
0answers
237 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 ...
1
vote
2answers
144 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 ...
1
vote
1answer
116 views

How to deterministically distinguish the following quantum states?

(1) How to deterministically distinguish the following quantum states: $$\frac{1}{\sqrt{2}}[|+0\rangle|0\rangle+|-1\rangle|1\rangle$$, $$\frac{1}{\sqrt{2}}|-0\rangle|0\rangle+|+1\rangle|1\rangle$$, ...
2
votes
2answers
487 views

Convert state Vectors to Bloch Sphere angles

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 ...
3
votes
2answers
645 views

How do I calculate the position on the Bloch sphere of a quantum gate with a given diagonal matrix?

In quantum computation there are several principal quantum gates that have corresponding matrix representations. One of these is the Z gate, whose matrix is $\left[\begin{smallmatrix} 1 & 0 \\ 0 ...