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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What role (if any) does the uncertainty principle play in giving huge quantum speedups?
I really like this Quanta article on the quest to find the source for exponential quantum speedups. Popular descriptions of quantum computers and the advantage they provide usually lean in to (1) ...
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connection between no-cloning theorem and accessible information
In the following paragraph Nielsen and Chuang give proof (with contradiction) that no-cloning theorem about non-orthogonal states lead to accessible information will be less than $H(p)$. BUT no-...
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How to prove the no-cloning theorem for density matrices and quantum channels?
$\newcommand{\ket}[1]{\left|#1\right\rangle} \newcommand{\bra}[1]{\left\langle#1\right|} \newcommand{\ketbra}[1]{\ket{#1}\bra{#1}}$Suppose $\mathcal{E}$ is a trace-preserving quantum channel that ...
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No-cloning theorem and distinguishing between two non-orthogonal quantum states revisited revisited
There are many posts to this question from Nielson and Chuang's Quantum Computation and Quantum Information Exercise 1.2 page 57. It is required to prove that if a hypothetical device exists, which ...
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How to show that BB84 is safe against imperfect cloning?
One of the reasons why BB84 is usually considered safe is due to the no-cloning principle. However, as far as I know imperfect cloning of quantum states is possible. I've been thinking about a ...
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Hypothesis on faster-than-light communication
I'm having a hard time understanding why it is not possible to communicate faster than light with entangled qubits. Now, this is my hypothesis. A and B have a pair of qubits, and 2 synced clocks at 12:...
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Does no-cloning imply zero capacity of antidegradable channels?
I read that (paraphrasing, see below) "antidegradable channels have zero capacity because of the no-cloning theorem". Is there a formal derivation of the capacity of an antidegradable ...
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How to prove there's no quantum channel that clones all classical states?
Considering a qubit $\scr H =\Bbb C^2$ I have seen a proof of the no-cloning theorem for pure states. I wonder how do you prove it for a classical state? 1)That is, how do I prove that there is no ...
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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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