Questions tagged [no-cloning-theorem]
In physics, the no-cloning theorem states that it is impossible to create an identical copy of an arbitrary unknown quantum state. (Wikipedia)
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Can a quantum gate send $|a,b\rangle$ to $|0,a\rangle+|1,b\rangle$?
I am looking for a quantum gate (or a circuit) that operates on two quantum registers of equal size and in states $|a \rangle$ and $| b \rangle$, respectively, and prepares the state: $\frac{1}{\sqrt{...
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Do no-cloning and no-deletion theorems follow one from the other?
I am very new to Quantum Information. I had the following question on two no-go theorems:
The No cloning theorem states there is no unitary operator $U$ such that $U|\psi\rangle|0\rangle=|\psi\rangle|\...
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How Does the Transformation $|x \rangle | 0 \rangle \rightarrow | x \rangle | Hx \rangle $ Avoid Violating the No-Cloning Theorem?
This question relates to Nielsen & Chuang, Exercise 10.26, which says
Suppose $H$ is a parity check matrix. Explain how to compute the transformation $|x \rangle | 0 \rangle \rightarrow | x \...
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How comes the notion of an ensemble of identical states (e.g. in quantum tomography) does not contradict the no-cloning theorem?
The no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state. How does that fit together with Quantum tomography, a process by ...
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Can teleportation violate the no-cloning theorem with 3 entangled qubits?
I saw the How to prove teleportation does not violate no-cloning theorem? question.
But I want to address this issue from a different angle.
What if instead of entangling 2 qubits, we would have ...
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What are the best algorithms to achieve probabilistic quantum cloning?
I am aware that there are algorithms that can clone states with unit fidelity but with a positive probability of failure. What would be the best known algorithms to create a perfect clone of an ...
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How to check if a mapping is unitary?
In the case of the No-cloning theorem, it is argued that a unitary $U$ that is capable of performing coping does not exist. Specifically, for any two unknown states $|\psi_1\rangle$ and $|\psi_2\...
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Could "no cloning" be used as a defence for quantum encryption?
If I've understood correctly, no-cloning theorem prevents copying qubit states during the computation. Could this be used to defend against quantum computers breaking encryption that can run with ...
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Cloning for error correction by preparing state multiple times
In quantum error correction, we start with the fact that no-cloning theorem doesn't allow cloning of unknown states, hence we need to come up with other strategies.
But often we know the circuit that ...
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Is effective quantum cloning possible, given that any classical function can be implemented as a quantum circuit?
As in Compiling a classical function to a quantum circuit in practice, as far as my understanding goes, it is known that any classical function can be implemented as a quantum circuit. So given $f(x)=...
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No clonning states that one cannot clone any arbitrary given state. But can we have a device that can create same superposition state repetatively?
No clonning states that one cannot clone any arbitrary given state. But can we have a device that can create same superposition state repetatively
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Applications that support low fidelity qubits generated by UQCM
I am studying Universal quantum cloning machines. I have found that two imperfect clones can be generated with fidelity of 83.33%. Where can we use these imperfect clones in quantum worlds? Can we use ...
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Copying |0⟩, |1⟩ Qubits will break the no-cloning theorem?
I am trying to create a bit string of |0⟩'s and |1⟩'s in order to create an array.
Would this still break the no-cloning theorem since we do know their state: they are |0⟩'s and |1⟩'s.
If possible, ...
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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)?
I am currently trying to implement circuit (in Qiskit if that is relevant) to approximate a state of a qubit without measuring it (basically I want to "attach it" to a qubit and have some ...
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How can classical bits be copied if qubits cannot be copied?
The no-cloning theorem of quantum mechanics tells us there can be no general quantum circuit that can copy arbitrary qubit states, i.e. a quantum gate or circuit cannot send $|0\rangle |\psi\rangle\...
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No-cloning theorem and distinguishing between two non-orthogonal quantum states revisited
There are a couple of posts on this question, but I think they are not satisfactory. The question is Nielsen and Chuang's QCQI, Exercise 1.2, page 57, which asks "Explain how a device which, upon ...
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Using distinguishability of non-orthogonal states to create a cloning device
Consider the following problem from Nielsen and Chuang's Quantum Computation and Quantum Information:
Explain how a device which, upon input of one of two non-orthogonal quantum states $\left|\psi\...
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Can all kinds of pure non-entangled states be cloned?
Is it correct to say that for an $n$-qubit system, we can clone all kinds of pure non-entangled states, without violating the no-cloning theorem?
That is, is the correct interpretation for the proof ...
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Approximate Cloning
Question
Consider two single qubit states $\left\{|\alpha_0\rangle,|\alpha_1\rangle\right\}$ which are not orthogonal or parallel, i.e. $\left|\langle\alpha_0|\alpha_1\rangle\right|\ne0,1$. ...
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Shifting amplitude from one basis to another with a control qubit
I was reading a forum where people were talking about a proposed quantum algorithm that solves an NP-complete problem in polynomial time. The algorithm appears to have flaws (after all, none of you ...
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Has Blockchain made Quantum Money obsolete?
Quantum Money is an old proposal that solves the forgeability problem of traditional banknotes, by leveraging the No-Cloning Theorem.
Recently, blockchains solved the Double-Spending problem ...
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How is the no-cloning theorem compatible with the fact that fan-out gates work?
I have some difficulty with understanding no-cloning theorem. Simply speaking, according to the theorem, it is not possible to copy a quantum state.
On the other hand, CNOT gate can be used as so-...
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Can Eve perform this operation?
I am a beginner in quantum computing. Please consider the following scenario:
Suppose Alice wants to send
$\frac{1}{\sqrt{N}}\sum_{j=0,1,2,..N-1} |j\rangle$ to Bob.
Eve has intercepted the state ...
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Premise of the proof of the No-Cloning Theorem
I have seen two similar proofs of the no-cloning theorem. They assume (to the contrary) that there exists a unitary operator $U$ such that $U |\psi\rangle |0 \rangle = | \psi \rangle | \psi \rangle$, ...
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Bounding advantage of a 'no cloning theorem' counterfeiter
No cloning theorem states that if a counterfeiter is given a state $|\psi\big>$ picked from a bunch of non-orthogonal states, then he cannot clone the state perfectly.
But this seems far from ...
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In what ways can qubits be used for applications that do not require entanglement?
Many good questions on this site have explored how entanglement lies at the boundary between the quantum world and the classical. For example in computational speedups, or teleportation or superdense ...
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Why isn't there a contradiction between the existence of CNOT gate/entanglement and the no-cloning theorem?
Of course I am not implying that I am right and the no cloning theorem is wrong, but I am trying to figure out what is wrong with my reasoning and yet I couldn't find the mistake.
Based on Wikipedia
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No-cloning theorem does not seem precise
As per wikipedia, no-cloning theorem states that it is impossible to create an identical copy of an arbitrary unknown quantum state.
But from which distribution is this unknown quantum state sampled ...
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When can a fanout be used without violating the no-cloning theorem?
This is related to this but a little different, so bear with me.
When is a fanout not violating the no-cloning theorem? It seems accepted that a fanout (or at least what seems to be one in my novice ...
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Why can't a fanout be made with a CNOT gate?
I know this question has been answered here, but the answers leave some things confusing to me. When broken down (and used to calculate), the idea that the states are entangled doesn't seem to be ...
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Classical and quantum limits to classical copying?
The no-cloning theorem can be sharpened to give quantitative bounds on the fidelity with which an arbitrary quantum state can be copied. Is there a similar picture available for classical copying? ...
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Cloning quantum states with a device that distinguishes between two non-orthogonal quantum states
I'm aware that this is basically a duplicate question, but I don't have any rep in this community so I can't comment on it, and I don't think I should "answer" that question with my own question:
No-...
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What role do Hecke operators and ideal classes perform in “Quantum Money from Modular Forms?”
Cross-posted on MO
The original ideas from the 70's/80's - that begat the [BB84] quantum key distribution - concerned quantum money that is unforgeable by virtue of the no-cloning theorem. A ...
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What does it mean that copying a state is impossible but creating a copy of by entangling is possible?
Why is it that copying an unknown qubit is impossible but creating a copy of the standard computational basis is possible by entangling it to existing qubits? And why one is possible and the other isn'...
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How to prove teleportation does not violate no-cloning theorem?
For a given teleportation process as depicted in the figure, how one can say that teleporting the qubit state $|q\rangle$ has not cloned at the end of Bob's measurement?
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Proof of no-cloning
I was reading a proof of No-cloning theorem, there are a couple of steps that are not clear to me, but the book does not give explanation for them. So here it is:
Theorem: It is impossible to create ...
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What do they mean by "qubit can't be copied"?
What does it mean by ''qubit can't be copied'' ?
In a note, it is saying that:
Copying a qubit means $$U|\psi\rangle_A|0\rangle_B=|\psi\rangle_A|\psi\rangle_B$$
i.e; applying a unitary transformation ...
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Cloning classical data encoded into qubits
How is it possible to maintain classical data encoded into qubits, which often contains copies of information, given that the no cloning theorem prevents cloning information?
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No-cloning theorem and distinguishing between two non-orthogonal quantum states
I'm currently reading Nielsen and Chuang's Quantum Computation and Quantum Information and I'm not sure if I correctly understand this exercise (on page 57) :
Exercise 1.2: Explain how a device which,...
