Questions tagged [quantum-information]

For questions about quantum information theory. In physics and computer science, quantum information is information that is held in the state of a quantum system. Quantum information is the basic entity of study in quantum information theory and can be manipulated using engineering techniques known as quantum information processing. (Wikipedia)

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In the context of Quantum theory of Information, Typical eigenvectors are permutations of basis vectors. Why?

Why is this so? Can someone please give me detailed steps with an explanation?
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If one had a verifiable solution to P versus NP problem, how, and why, would one go about submitting it?

Asking for a friend. The exclusivity/elitism of the field (and the dominance-human hierarchy), as well as the outcomes of "exploitation of "discoveries" throughout history have friend leaning away ...
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Does Controlled-U gate entangle qubits?

I've read C-NOT gate entangles qubits, but is it only for C-NOT or any arbitrary CU gate (apart from the likes if CI) entangles qubits?
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Error parameters from Qiskit backends

In order to build a custom noise model in Qiskit Aer, I requested the error parameters from different backends and got 3 (9) parameters for each single-qubit (two-qubit) gate as output. However, I ...
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It two unitaries are delta apart in trace norm, then what is the trace norm of outputs states when the same input state is applied to two unitaries?

Suppose we are given two unitary matrices $U$ and $V$, with the following guarantee, $$||U - V||_1 \geqslant \delta$$ for some $\delta \geqslant 0$. We apply an input density state $\rho$ ...
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Quantum Neural Network

I am a newbie to quantum machine learning. I am trying to build a quantum neural network (QNN). What I studied so far about QNN is that input would be qubits and hidden layer parameter can be set ...
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Entanglement to the nth butterfly degree? [closed]

Two days ago, I asked if entanglement was natural and nearly unavoidable if two quantum particles touched or flimsy and fragile in this thread: Entanglement - Natural and Unavoidable or Difficult to ...
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More than one Schmidt coefficient implies entanglement?

I'm studying Quantum Information Theory by Mark M. Wilde, and I got stuck in solving the exercise 3.8.2 in page 100. The exercise is to show that a pure bipartite state is entangled if and only if it ...
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Constructing and Measuring in an Arbitrary 3-qubit basis

As part of a Quantum Theory project I have "constructed" an arbitrary 3-qubit basis: $\left|B_0\right> =\left|000\right>$ $\left|B_1\right> = \frac{1}{\sqrt{2}}\cos(x)(\left|100\right> +...
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Questions on the max-relative entropy $D_{\max}(\rho||\sigma)$

The max-relative entropy between two states is defined as $$D_{\max }(\rho \| \sigma):=\log \min \{\lambda: \rho \leq \lambda \sigma\},$$ where $\rho\leq \sigma$ should be read as $\sigma - \rho$ is ...
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Questions about the Hamiltonian of a decay

In paper Simulating quantum systems on a quantum computer the author mention in section 3, simulating a decay to obtain the ground state, and give the Hamiltonian for that: $$H=H_1+H_2 + H_{1I}\otimes ...
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Is there a systematic way to build quantum circuits?

The question is quite straightforward. In classical computation, there exists several ways to build logical circuits based on thruth tables and Karnaugh maps. Is there anything equivalent for quantum ...
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How does the teleportation circuit work after the initial entanglement?

I'm trying to understand why we do what we do when we teleport a state from Alice's first qubit to Bob's qubit. I understand the initial entanglement, but could use help walking through the program. ...
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Half of Standard Basis Measurement

I know that we can measure a state in standard basis (Z) where the post measurement state is either $|0\rangle$ or $|1\rangle$. But can you do a 'half-Z' basis measurement? I mean, you only measure ...
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How does Quantum Teleportation works? [duplicate]

I've started learning Quantum Computing from the Qiskit Textbook and was able to easily understand or work out everything until it came to the working of Quantum Teleportation I can understand the ...
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Deriving Bloch vector $dr$ from master equation

I am trying to derive the Bloch vector $dr$ for a measurement of a observable in any arbitrary direction $\theta$. For context this is the setup and derivation I have for continuous measurement along ...
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Is quantum deletion via a partial randomization procedure possible?

The paper, Quantum deletion is possible via a partial randomization procedure claims that it is possible to bypass the no-deleting theorem by a procedure called R-deletion. But this seems to go ...
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Information content of qubits

I have two question concerning information content of qubit. Question 1: How many classical bits are needed to represent a qubit: A qubit can be represented by a vector $q = \begin{pmatrix}\alpha \\\...
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Graphs are represented using oracle, where oracle is the adjacency matrix. Is there any simple example of this?

I have been reading papers on graph theory in quantum computing. Mostly, papers explain that they use adjacency matrix to represent the graph. But I could't find the practical simple example to ...
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Measurements of entropy

I am starting on quantum computing and I got to entropy measurements, but that has me stuck, because there seems to be a lack of resources for newcomers on those concepts and their utility. Anyone ...
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Guide for Quantum Information and Computing Internships and Learning Opportunities

I know this perhaps not a suitable topic for this SE - after all, this is about QC knowledge sharing - but I am wondering if this could be a resource for people who are interested in the field, are ...
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Convert a quantum Phase Oracle into a Probability Oracle

Suppose we have an oracle $O_f$ that given an initial state $|x\rangle$ maps it into the following state: $$ O_f : |x\rangle \mapsto e^{if(x)} |x\rangle $$ Now, assuming that $f(x) \in [0,1]$, is it ...
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How to calculate the Von Neuman entropy on qiskit with the module quantum_info?

I am trying to wrap my head around he quantum_info module on qiskit, since most of the functions on qiskit.tools are going to be ...
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Aproximating unitaries with elements from a t-design

(This is basically a reference request) I am wondering if there are any results out there on to what accuracy a given unitary can be approximated with an element drawn from a t-design. To ...
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What do the numbers of the operation object in QuantumCircuit.data outputs?

When you have a quantum circuit and use QuantumCircuit.data you get a list with objects of this type (this is the one for a X gate acting on qubit 0 y a 2 qubits Quantum Circuit): (qiskit.extensions....
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Is there a measure similar to the Helstrom measurement which can distinguish between more than 2 pure quantum states?

My understanding is the Helstrom measurement distinguishes between 2 pure quantum states. Is there a measure similar to the Helstrom measurement which can distinguishes between more than 2 pure ...
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State fidelity in Qiskit

Can someone provide me an example for finding state fidelity of two circuits? For example, if I have a Toffoli gate with two different approaches of decomposition then how do I calculate fidelity ...
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What is the quantum state transmitted to Bob in BB84 protocol?

Sender (Alice) wants to exchange private encryption key with Bob using BB84 protocol. She generate a binary string (1010100010010111),and encode using Hadamard gate and identity gate (HHHIIHIHHIIIHIIH)...
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How is the theory of modular representation involved with error-correction?

Recently, I have heard that the theory of modular representation can be involved with error correction in quantum information theory. However, from a point of view of mathematician, I am still quite ...
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How do I know in which state the qubit is in each step of the circuit for the simulator in qiskit?

I would like to know how to know in which state a qubit is (I am talking about single-qubit errors), because in order to apply a non unitary gate in the simulator I have to renormalize the state or ...
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2answers
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How to read the elements of a circuit in qiskit?

I would like to know if there is a way to read the elements of a circuit. What I mean is if I have a QuantumCircuit object, can I obtain the gates that are applied ...
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1answer
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Is there a lower bound on the average diamond norm of two uniformly random unitaries U1 and U1 of dimension D that are sampled from haar measure?

I could not find any lower bound on the diamond norm for two uniformly random unitaries of dimension D sampled from the haar measure.
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Regarding quantum support vector machine using qiskit [duplicate]

I would like to ask, how can I add my own .csv data file to run a quantum support vector machine using qiskit ? I don't want to use already existing datasets in sklearn, scikit-learn library.
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Is back in time (classical) information transfer possible (based on delayed choice entanglement swapping)?

Delayed choice entanglement swapping. Two pairs of entangled photons are produced, and one photon from each pair is sent to a party called Victor. Of the two remaining photons, one photon is sent to ...
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Further entangling two ebits to obtain $|0000\rangle + |1111\rangle$ state

I have two ebits $e1$ and $e2$ and my 4-qubit system is in the state: $$(|00\rangle + |11\rangle) (|00\rangle + |11\rangle)$$ Ignoring the normalizing constants for now. As mentioned, I need to ...
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Can we combine the square roots inside the definition of the fidelity?

The (Uhlmann-Josza) fidelity of quantum states $\rho$ and $\sigma$ is defined to be $$F(\rho, \sigma) := \left(\mathrm{tr} \left[\sqrt{\sqrt{\rho} \sigma \sqrt{\rho}} \right]\right)^2.$$ However, as ...
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Which of the Jozsa axioms does the Hilbert-Schmidt inner product violate?

The paper Quantum fidelity measures for mixed states considers various differently-normalized variants of the Hilbert-Schmidt inner product $\mathrm{Tr}(A^\dagger B)$ on linear operators as candidate ...
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1answer
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What is “quantum internet” and what is its relation with quantum entanglement?

In a recent news "Scientists Make Major Breakthrough In ‘quantum Entanglement’ That Could Change How The Internet Works" Scientists have managed to entangle two "quantum memories" at a distant ...
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What is a “shot” in quantum computation?

What is a "shot" in relation to quantum computing? I heard it is repeating time, but I don't understand it. Additionally, why is the default number of shots 1,024 in the IBM Q Experience? One more ...
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Show that if $b'$ and $b$ are uncorrelated, then $a'$ and $a$ are uncorrelated

Let $a'_k$ be Bob's measurement result of qubit $ {\Psi_{a_kb_k}}$, assuming a noiseless channel with no eavesdropping. Show that when $b'_k\neq b_k$, $a'_k$ is random and completely uncorrelated ...
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1answer
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Conditional version of the triangle inequality for Von Neumann entropy

I'm trying to solve problem 11.3 in Nielsen Chuang: (3) Prove the conditional version of the triangle inequality: $$ S(A,B|C)\geq S(A|C)-S(B|C) $$ But the inequality seems incorrect. For example,...
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Does quantum computing already possess the level of abstraction to be explicable even without knowledge of physics?

Currently, quantum computer science (in contrast to classical computer science) can mostly only be understood if one has a good inside knowledge of physics, or more precisely quantum physics. Only ...
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Quantum state discrimination and lower bound for conditional von Neumann entropy

Consider two quantum states $\rho_A$ and $\sigma_A$, and define the classical-quantum state over a classical binary system $B$ and $A$, $$\omega_{AB}^\epsilon :=\epsilon \vert 0 \rangle \langle 0 \...
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Convexity of coherent information - erroneous argument!

Consider a state $\rho_{AB}$. Let it have purification $\psi_{A'AB}$. I am interested in the coherent information of this state which is given by $$I(A\rangle B)_\rho = S(B)_\rho - S(AB)_\rho$$ I ...
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1answer
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Compute the output of the quantum teleportation circuit

Sender and receiver use the teleportation protocol, where the sender teleports a quantum state $\left| \varphi \right>=\alpha\left| 0 \right> + \beta \left|1\right>$ to the receiver. I want ...
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Can we apply Grover to meet-in-the-middle attack?

$\newcommand{\Ket}[1]{\left|#1\right>}$ If we have the superposition $$\displaystyle \sum \dfrac{1}{2^n} \Ket x \Ket{ f(x)} \Ket 0 \Ket y \Ket{g(y)} \Ket 0 \Ket {\delta_{x,y}} ,$$ here $\delta_{x,...
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Are there Bell-like violations that can be observed without collecting statistics?

Observing the violation of Bell inequalities, be it in their original formulation, or in the nowadays more commonly used CHSH formulation, involves computing averages of specific experimentally ...
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How many $n$-qubit states are entangled?

My question is a bit broad, but my concern is mainly on understand the ratio between the number of possible linear combinations that can be decomposed in a direct product of states and the number of ...
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How to read a Qubit rotation lookup table?

In many Quantum Inspired Evolutionary Algorithms a lookup table is used to decide the Qubit rotation. But how the lookup table is used is not briefed. Does anyone know how it is done ? An example ...
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What value of K parameter of the following two vectors? [closed]

I have two vectors: $$ a=\begin{pmatrix} {1} & {1} & {1} \ \end{pmatrix} \\ b=\begin{pmatrix} {1} & {2} & {k} \ \end{pmatrix} $$ These vectors should be orthogonal. What is value of $k$...

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