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Results tagged with quantum-information
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user 43987
Quantum information is the study of the informational content of quantum states. The most common object of study is the "qubit", the information in a two-state quantum system such as spin-1/2 or photon polarization.
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What is the expression of the state after $n$ parallel hadamard gate on $n$ $\left|1\right>$...
The state you get after applying $n$ Hadamard gates on $|1 \rangle$ is
$$\left( \dfrac{|0 \rangle - |1 \rangle}{\sqrt{2}} \right)^{\otimes n} \, .$$
This can be written as
$$\frac{1}{\sqrt{2^n}}\sum_{ …
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Why when we have GHZ, then we cannot send a qubit using teleportation technique?
No-cloning theorem says that you cannot "clone" the state. As in there is no way to make perfect copies of a quantum state. In the simple teleportation case with two parties the Alice's state is tran …
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How does a superposition work with the cNOT quantum gate?
Quantum operations are linear. So if you know how CNOT acts on the basis vectors then you can work out any case. Specifically in the usual $1/0$ basis, CNOT adds the control qubit to the target qubi …
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Checking correctness of partial trace
I am doing some simulations that requires me to take partial trace over a three qubit density matrix $\rho_{ABC}$. I find the mixed state density matrix of one qubit by tracing out the other two,
$ …
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Accepted
Prove that the elements of the dual frame of an IC POVM cannot be positive
Suppose $D_k \geq 0$ for all $k$. Notice that all the $D$ operators have unit trace.
For two PSD matrices it holds that, $Tr(AB) \leq Tr(A)Tr(B)$.
This implies that, $Tr(N_k D_k) \leq Tr(N_k)$ for all …
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Simulation probabilistic classical computation on quantum computers
{Edit: I found a much easier way to do this without resorting to linear system solving. I have included both methods in the answer}
Finding such a $U$ certainly seems possible as with the enlarged Hi …
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Accepted
How to tell if a density matrix is separable?
For 2×2 (which is your case) and 2×3 dimensional bipartite systems the PPT condition can be used to check for separability. For higher dimensions separability testing has been proven to be a computat …
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Accepted
Question about tunneling diagram in adiabatic quantum computation
) The cost function is the spectrum of the final Hamiltonian. In fact the final Hamiltonian is often designed to solve some NP-hard problem like TSP or 3-SAT.
) This requires some explanation. The …
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Physical meaning of $Tr(\rho ^2)$
If $\rho$ is the density matrix of a system then $Tr(\rho ^2) \leq 1$. If the equality holds the system is in a pure state and it is in a mixed state otherwise. But, what is the physical meaning of $T …
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Two definitions of the density matrix?
There seems to be two different definitions of definitions of density matrices in Physics.
In Quantum Information we define a the density matrix associated with a wave function $ | \psi \rangle$ as …
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Accepted
Understanding amplitude amplification in quantum computing
I won't explain the complete algorithm here. You can find a good explanation in Wikipedia or Nielsen and Chuang
The aim of Grover search is to find some "marked" items ($|x_t\rangle$) in an unstruct …
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Two qubits system in polar co-ordinates
Yes. We can do this for any number of qubits using N dimensional spherical coordinates. For two qubits we can write a general density matrix as a linear combination of direct products of Pauli mat …
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