22
votes
Accepted
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 ...
- 20.7k
18
votes
Accepted
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 ...
- 8,705
13
votes
Accepted
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 ...
- 4,048
11
votes
Accepted
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
$$|\psi⟩|\psi⟩=(\alpha|0⟩+\beta|1⟩)(\alpha|0⟩+\beta|1⟩)=\alpha^2|00⟩+\alpha\beta|01⟩+\beta\alpha|10⟩+\...
- 166
9
votes
Accepted
No-cloning theorem does not seem precise
The no-cloning theorem itself can be stated very precisely.
Given an unknown pure state $|\psi\rangle$ that is drawn from a distribution
$\{p_i,|\phi_i\rangle\}$ (known to the counterfeiter), it ...
- 55.7k
9
votes
What do they mean by "qubit can't be copied"?
As already mentioned in the other answers, the crucial point is that copying means implicitly that the state of the original qubit is unknown, i.e. given a qubit in an unknown state, you want to ...
- 191
9
votes
Accepted
Is effective quantum cloning possible, given that any classical function can be implemented as a quantum circuit?
No-cloning theorem suggests no such thing. A closer look at the theorem's proof reveals a loophole for orthonormal states. The theorem says that there is no unitary $U$ such that
$$
U|\psi\rangle|0\...
- 20.7k
8
votes
Accepted
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 ...
- 33.2k
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 ...
- 33.2k
8
votes
Accepted
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 ...
- 55.7k
7
votes
Accepted
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|)(|\...
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 ...
- 3,613
6
votes
Accepted
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 ...
- 10.7k
6
votes
Accepted
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\...
- 55.7k
6
votes
Accepted
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.
...
- 20.7k
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 ...
- 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 ...
- 51
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 ...
- 1,626
5
votes
Accepted
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 ...
- 5,324
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 ...
- 8,705
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 ...
- 55.7k
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 ...
- 55.7k
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
$$
...
- 6,108
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\...
- 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\...
- 55.7k
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....
- 17.2k
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 ...
- 55.7k
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\...
- 6,711
3
votes
Accepted
Can all kinds of pure non-entangled states be cloned?
It's not the non-entangled part that's important in your statement. The important part is that any mutually orthogonal states can be cloned (provided you know what the set of states is).
- 55.7k
3
votes
Accepted
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 ...
- 33.2k
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