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17 votes
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Toffoli gate as FANOUT

To simplify the question consider CNOT gate instead of Toffoli gate; CNOT is also fanout because \begin{align} |0\rangle|0\rangle \rightarrow |0\rangle|0\rangle\\ |1\rangle|0\rangle \rightarrow |1\...
kludg's user avatar
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15 votes

Advances on imperfect quantum copying

Numerous papers on quantum cloning have been written since 1996, including both theoretical and experimentally focused papers. The following survey paper is a good place to start if you want to learn ...
John Watrous's user avatar
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11 votes

Advances on imperfect quantum copying

Regarding the optimality of the results of your linked article [1],$\def\ket#1{\lvert#1\rangle}\def\bra#1{\!\langle#1\rvert}$ we find in Section III A that on input $\ket{\phi}$, the states ...
Niel de Beaudrap's user avatar
8 votes

Cloning classical data encoded into qubits

The no cloning theorem only applies when quantum information is in an unknown superposition. If you know a basis in which the state of some qubits is not under superposition, then you can make all the ...
Craig Gidney's user avatar
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8 votes

Toffoli gate as FANOUT

The no cloning theorem says that there is no circuit which creates independent copies of all quantum states. Mathematically, no cloning states that: $$\forall C: \exists a,b: C \cdot \Big( (a|0\...
Craig Gidney's user avatar
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7 votes

Toffoli gate as FANOUT

The answer is that the no-cloning theorem states that you cannot clone an arbitrary unknown state. This circuit does not violate the no-cloning theorem, because let's look at what it does when the ...
user1271772 No more free time's user avatar
6 votes
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No-cloning theorem and distinguishing between two non-orthogonal quantum states revisited

TL;DR: The assumption of non-orthogonality is implicitly used by the linked answer. It is needed due to a "loophole" in the no-cloning theorem that allows cloning of known orthogonal states. ...
Adam Zalcman's user avatar
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6 votes
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Approximate Cloning

Given the constraints you impose (why those are appropriate constraints is perhaps another discussion), I think you're over-complicating things. Without loss of generality, you can assume $$ |\alpha_0\...
DaftWullie's user avatar
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5 votes

Advances on imperfect quantum copying

As John Watrous said, the Rev. Mod. Phys. article is an excellent starting point. If you want to know the sort of thing that's been looked at since, then in a shameless bit of self-promotion, you ...
DaftWullie's user avatar
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5 votes
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Shared entanglement to copy orthogonal states

Assume this works. Then, nothing prevents Alice from applying the same protocol to a quantum state that is known to her, such as $|0\rangle$ or $|1\rangle$. This way, she could send information to Bob ...
Norbert Schuch's user avatar
4 votes

Is their a way to perfectly clone coherent state and squeezed states?

The no-cloning theorem states that an unknown quantum state cannot be copied exactly --- so this rules out any algorithm that attempts to produce perfect copies of an arbitrary quantum state (...
Josh Izaac's user avatar
4 votes
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does there exist a quantum approximate cloning method that does not modify the initial qubit (the one whose state we want to clone)?

It's not possible to make an approximate clone of a qubit without ever affecting that qubit. Otherwise you could just keep approximate-cloning, do tomography on the clones to confidently learn the ...
Craig Gidney's user avatar
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3 votes

Advances on imperfect quantum copying

There are many interesting variants of quantum cloning, one of which I will mention here since no one else has specifically mentioned it yet. Quantum telecloning combines (approximate) quantum cloning ...
Elijah Pelofske's user avatar
3 votes

Advances on imperfect quantum copying

You may also want to check for: state dependent deterministic cloners which clone with a better fidelity when input state comes from a known ensemble. Ref: Bruss et al., PRA 57, 2368 (1997) ...
user5392's user avatar
3 votes

Compute the output of this Approximate Quantum Cloning three-qubit circuit

The fastest way to check is with a simulator: You can tell 00 has twice the amplitude of 11 (and 10) because their probabilities have a $2^2:1$ proportion. You can tell the phases are right because ...
Craig Gidney's user avatar
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3 votes

Is there a non-deterministic protocol for entanglement generation between distant parties?

No. By definition, the set of states that you can produce under LOCC are the separable states. This includes all possible measurements, post-selection on certain outcomes etc. The whole point of ...
DaftWullie's user avatar
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2 votes

Classical and quantum limits to classical copying?

You seem to be mixing two very different concepts here. Quantum cloning is talking about the absolute limits of what is theoretically possible in a perfect world. In this absolute theoretical limit, ...
DaftWullie's user avatar
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2 votes
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Is there a non-deterministic protocol for entanglement generation between distant parties?

No, any such protocol would violate the holevo bound (1 bit of communication per 1 sent qubit, including qubits sent during preparation). You could just keep repeating the process until it gave you ...
Craig Gidney's user avatar
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2 votes
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How to show that BB84 is safe against imperfect cloning?

If you impose that $U|\psi\rangle|0\rangle=|\psi\rangle|\psi'\rangle$ for all $|\psi\rangle$ (or at least for a pair of non-orthogonal states), then you'll be able to prove that $|\psi'\rangle$ must ...
DaftWullie's user avatar
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1 vote

No-cloning theorem and distinguishing between two non-orthogonal quantum states revisited revisited

I think what you asking about is the following setting: you are given a qubit which is either $|\psi\rangle$ or $|\psi'\rangle$ with are not orthogonal. You know what those two possible states are, ...
DaftWullie's user avatar
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1 vote

Does a noiseless quantum channel violate no-cloning theorem?

No. Quantum channels typically represent evolutions of open quantum systems. The input is a state at a time $t_1$ and the output is a state at a latter time $t_2>t_1$. Having a state $\rho$ at time ...
Adam Zalcman's user avatar
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1 vote

Compute the output of this Approximate Quantum Cloning three-qubit circuit

One way to do this is simply working through the quantum circuit one step at a time. Note that your preparation circuit for the state $|\phi\rangle$ can be written as: The initial state is $|00\...
KAJ226's user avatar
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