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23 votes
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How can classical bits be copied if qubits cannot be copied?

TL;DR: The ban on copying is not nearly as universal as it might seem. No-cloning theorem actually allows copying as long as it is limited to orthogonal states. Classical information is the type of ...
Adam Zalcman's user avatar
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18 votes
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Why isn't there a contradiction between the existence of CNOT gate/entanglement and the no-cloning theorem?

The cloning theorem requires that the result of the cloning is two independent copies of the starting qubit, i.e., the state of the system in the end should be $\big(\alpha |0\rangle + \beta |1\rangle ...
Mariia Mykhailova's user avatar
13 votes
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What do they mean by "qubit can't be copied"?

All operations on quantum states are unitary operations. We don't make the rules, this is just how nature seems to work. So if you want to define an operation that copies a qbit, it has to be a ...
ahelwer's user avatar
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11 votes
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How is the no-cloning theorem compatible with the fact that fan-out gates work?

By "copying a quantum state", we mean that we cannot take $$|\psi⟩|0⟩=\alpha|00⟩+\beta|10⟩$$ into $$|\psi⟩|\psi⟩=(\alpha|0⟩+\beta|1⟩)(\alpha|0⟩+\beta|1⟩)=\alpha^2|00⟩+\alpha\beta|01⟩+\beta\alpha|10⟩+\...
haoyu's user avatar
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9 votes
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No-cloning theorem does not seem precise

The no-cloning theorem itself can be stated very precisely. Given an unknown pure state $|\psi\rangle$ that is drawn from a distribution $\{p_i,|\phi_i\rangle\}$ (known to the counterfeiter), it ...
DaftWullie's user avatar
  • 59.8k
9 votes

What do they mean by "qubit can't be copied"?

As already mentioned in the other answers, the crucial point is that copying means implicitly that the state of the original qubit is unknown, i.e. given a qubit in an unknown state, you want to ...
user1587520's user avatar
9 votes
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No-cloning theorem and distinguishing between two non-orthogonal quantum states

That's the way that I would initially go about answering the question. There are, however, a few tweaks you could make. Definitive Answer As you point out, the annoying feature is that you can ...
DaftWullie's user avatar
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9 votes
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Is effective quantum cloning possible, given that any classical function can be implemented as a quantum circuit?

No-cloning theorem suggests no such thing. A closer look at the theorem's proof reveals a loophole for orthonormal states. The theorem says that there is no unitary $U$ such that $$ U|\psi\rangle|0\...
Adam Zalcman's user avatar
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8 votes
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Premise of the proof of the No-Cloning Theorem

The proof does not seem to rule out the case that there exists a specific U that can clone only the specific state |ψ⟩. That's because you can clone specific states. Cloning is only impossible if the ...
Craig Gidney's user avatar
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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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7 votes
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Proof of no-cloning

For step (116), the equivalence between both of them is proved by \begin{equation} (\langle\psi_1|\otimes\langle0|)C^\dagger C(|\psi_2\rangle\otimes|0\rangle) = (\langle\psi_1|\otimes\langle0|)(|\...
Josu Etxezarreta Martinez's user avatar
6 votes

No-cloning theorem does not seem precise

To keep the problem small, let's say 1 qubit. In the original statement $| \psi \rangle$ could be any state $\alpha | 0 \rangle + \beta | 1 \rangle$ for whatever $\alpha$ and $\beta$ produce a well ...
AHusain's user avatar
  • 3,663
6 votes
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Has Blockchain made Quantum Money obsolete?

I propose the following advantages to quantum money, over and above blockchain-based cryptocurrencies. The security of Nakomoto-style cryptocurrencies (read, Bitcoin) is based on computational ...
Mark Spinelli's user avatar
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
  • 59.8k
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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5 votes

In what ways can qubits be used for applications that do not require entanglement?

One (obvious) application is the generation as True Random Number Generators, e.g. IDQ, or you can download some here Free True Random Numbers (please do not use these for security relevant ...
Fleeep's user avatar
  • 374
5 votes

Has Blockchain made Quantum Money obsolete?

This work (which I'm a co-author) discusses the properties that different forms of money have. The paper discusses cryptocurrencies such as Bitcoin, and public quantum money. The following figure is ...
Or Sattath's user avatar
5 votes

Copying |0⟩, |1⟩ Qubits will break the no-cloning theorem?

Would this still break the no-cloning theorem since we do know their state The No-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown ...
Victory Omole's user avatar
5 votes
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Could "no cloning" be used as a defence for quantum encryption?

The no-cloning theorem states that being given a state $|\psi\rangle$ on which one has no information whatsoever, it is not possible to create a second register $|\psi\rangle$ while leaving the first ...
Tristan Nemoz's user avatar
  • 6,897
4 votes

What do they mean by "qubit can't be copied"?

To answer the first part of the question (whether unitary matrix $U$ operates on $|\psi_A \rangle$ only): A unitary matrix can operate on an arbitrary number of qubits. Single-qubit gates, like Pauli ...
Mariia Mykhailova's user avatar
4 votes

In what ways can qubits be used for applications that do not require entanglement?

Certainly not exhaustive, but to get the ball rolling... One possible application is blind quantum computation. In this, there is a user who wants to complete a computation, but only has the ...
DaftWullie's user avatar
  • 59.8k
4 votes

Using distinguishability of non-orthogonal states to create a cloning device

I think you've maybe missed some of the reasoning in the premise. If you are trying to clone an unknown qubit, but you know it to be one of two states $|\psi\rangle$ or $|\phi\rangle$, then the point ...
DaftWullie's user avatar
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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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4 votes

Is effective quantum cloning possible, given that any classical function can be implemented as a quantum circuit?

Just to complement the other answer, the operation $Q_f$ does certainly exist and is sometimes called a transversal CNOT: Given an arbitrary $n$-qubit state expressed in the computational basis as $$ ...
forky40's user avatar
  • 7,213
4 votes

Do no-cloning and no-deletion theorems follow one from the other?

Yes! Your reasoning is correct about applying $U^*$ to both sides, since $U^*U=I$. You can derive $U|\psi\rangle|0\rangle = |\psi\rangle|\psi\rangle$ from $U|\psi\rangle|\psi\rangle = |\psi\rangle|0\...
user34722's user avatar
  • 421
4 votes

Do no-cloning and no-deletion theorems follow one from the other?

The no cloning and no-deletion theorems are a much stronger claim than you've stated. For example, the no-cloning theorem states that there does not exist any quantum operation that takes $|\psi\...
DaftWullie's user avatar
  • 59.8k
3 votes

How is the no-cloning theorem compatible with the fact that fan-out gates work?

As a complement to haoyu's answer, it is also worth noting that the no-cloning theorem does not forbid ANY cloning. Instead, cloning some states is ok. In other words, what the no-cloning theorem says ...
Godfly666's user avatar
3 votes

How to prove teleportation does not violate no-cloning theorem?

Firstly, carefully read through the formal presentation of the protocol as described on Wikipedia. Secondly, there's nothing to prove as such here. It is evident from the teleportation protocol itself....
Sanchayan Dutta's user avatar
3 votes

What does it mean that copying a state is impossible but creating a copy of by entangling is possible?

The no cloning theorem can be stated in the form: If you are given an unknown state $|\psi\rangle$, which is promised to be one of a set of distinct states $\{|\phi_i\rangle\}$, it is impossible to ...
DaftWullie's user avatar
  • 59.8k
3 votes

How to prove teleportation does not violate no-cloning theorem?

Cloning means the generation of $|q\rangle|q\rangle$ from $|q\rangle|0\rangle$. This is not what happens in teleportation. Teleportation is kind of a swap operation, i.e. something like $|q\rangle|0\...
Danylo Y's user avatar
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