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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28 views

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

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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2answers
188 views

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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1answer
58 views

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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1answer
390 views

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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1answer
32 views

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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Conditional min and max entropy intution

Let's start with the classical min- and max-entropies. These correspond to the most conservative way of estimating unpredictability and the total number of outcomes with nonzero probability ...
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1answer
45 views

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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56 views

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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Quantum Circuit teleportation

Sender and receiver use teleportation protocol,where sender teleport a quantum state $\left| \varphi \right>=\alpha\left| 0 \right> + \beta \left|1\right>$ to receiver . I want to implement ...
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57 views

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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3answers
185 views

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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1answer
84 views

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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0answers
38 views

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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1answer
25 views

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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1answer
69 views

Qubit measurement of the state $\frac{1}{\sqrt2}|00\rangle+\frac{i}{2}|01\rangle-\frac{1}{2}|11\rangle$

If we measure the first qubit and obtain $|0\rangle$, what does the second qubit collapses to? $$ \left| \varphi \right>=\frac{1}{\sqrt{2}} \left| 00 \right> + {\frac{i}{2}} \left| 01\right> ...
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what are the angles 𝜃, and ϕ values of the following quantum state? [duplicate]

I need to find the coordinate 𝜃 and ϕ values of the quantum state on the bloch sphere $$ \left| \varphi \right>=\frac{1+i}{\sqrt{3}} \left| 0 \right> + {\sqrt{\frac{1}{3}}} \left| 1\right> $$...
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1answer
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What is the practical interest of superdense coding?

When you enter the field of quantum communications, you run at some point into the concept of superdense coding. Basically it is a way to encode classical bits on the qubits of a quantum channel, ...
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1answer
57 views

Does the Lieb-Robinson bound constrain the speed of entanglement information transmission?

I just learned from the existence of the theoretical Lieb-Robinson bound, which indicates that the speed at which information can be propagated in non-relativistic quantum systems cannot exceed this ...
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1answer
75 views

Syndrome extraction operator as matrix?

I am trying to understand how to achieve the syndrome extraction operator matrix in quantum repetition code (if it even exists). It is given that the syndrome is defined here (page 4) as: [perform]...
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1answer
104 views

Finding the optimal projective measurement to distinguish between two pure states

I would like some help on what should be a simple computation that I'm failing to see through to the end. Suppose I have a qubit which can be in the state $|v\rangle$ with probability $p$, or $|w\...
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Does higher channel fidelity imply higher entanglement fidelity?

Consider two noisy quantum channels (CPTP maps), $\Phi_1^A$ and $\Phi_2^A$, acting on a system $A$. Suppose that for any pure state $\left|\psi\right>\in \mathcal H_A$, $$ F\big(\psi, \Phi_1^A(\psi)...
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1answer
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Quantum adder mod 4 [closed]

Does anyone has (or is aware of) a solution to Nielsen's QCQI 4.36 exercise: construct a circuit to add two-qubit numbers x and y modulo 4 vs $|x,y\rangle \rightarrow |x, x+y \mod 4\rangle$
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Find the qutrit analogue of certain qubit and ququart formulas of Li and Qiao for testing separability

In eqs. (33), (43)-(46), (56) of their paper, "Separable Decompositions of Bipartite Mixed States" https://arxiv.org/abs/1708.05336, Li and Qiao present a number of formulas pertinent to testing the ...
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1answer
46 views

Will there be quantum to digital converters in the same way we need digital to analog converters to communicate between the 2 mediums?

I know this forum is for more technical questions... As my interest is in music, I was thinking about the nature of analog and digital mediums. And I just thought, for some reason, we have 'Quantum ...
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Number of columns mismatch

So I have the following code qgan = QGAN(real_data, bounds, num_qubits, batch_size, num_epochs, snapshot_dir=None) with num qubits being defined as ...
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1answer
50 views

Entanglement entropy's role in quantum information

I am just new to the concepts of entanglement entropy and how it is used to measure the entanglement in systems. I want to know the role of entanglement entropy in quantum information, in general.
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2answers
67 views

How do qubits use the “superposition” to make many trials instead of just some?

Ok, I understand the difference between quantum bits and classical bits. But, unfortunately, all explanations on the Internet stop at this point. This is what I understand that happens: A particle ...
2
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1answer
62 views

What are some examples of applications of quantum information to other sciences?

I find looking at physical processes through the lens of quantum information science rather interesting. I know of a few applications of it: quantum computation; solid state (tensor network approach)...
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1answer
716 views

No-cloning theorem and fan-out gate

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-...
4
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1answer
182 views

Why are $d^2$ dimensions required to describe a density matrix?

A density matrix is defined as: $$\sum p_i |\psi_i \rangle \langle \psi_i|$$ If the dimensionality of each $|\psi_i \rangle$ is $d$, why does it take $d^2$ dimensions to represent a density matrix? (...
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1answer
36 views

Minimum number of ancilla qubits to unitarily simulate a measurement?

Let's say I have a ket which is a momentum eigenket $| p \rangle$ and then I measure the position and obtain $|x' \rangle$. $$ | p \rangle = \int | x \rangle \langle x | p \rangle dx \to | x' \...
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2answers
74 views

Minimum number of ancilla qubits required to make a transformation unitary?

Background The counterpart of a NOT gate is the CNOT gate. They make use of ancilla qubits to achieve this. Question Given an arbitrary non-unitary transformation what are the minimum number of ...
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1answer
81 views

Understanding the monogamy of entanglement with respect to GHZ States

Given the GHZ state wrt n = 3: $\frac{|000⟩ + |111⟩}{\sqrt{2}}$, I'm trying to understand how the principle of monogamy of entanglement manifests here. I came across this explanation. Let’s say ...
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2answers
87 views

Does this setup violate relativity?

Suppose Alice needs to transmit a bit of information about something which happened just before $t = 0$ to Bob who is light years away from Alice. Entangled pairs of qubits, $\left|00\right> + \...
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Clarification on the information content of a qubit [duplicate]

I saw a video in which a guy from IBM was explaining (very generally) quantum computing, it's difference with classical computing etc. The talk was not technical at all, it was intended for a broad ...
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1answer
30 views

Entropy of a shared state as measured by the individual parties

Suppose I prepare a Bell state $|\beta_{00}\rangle$, and distribute the product state $|\beta_{00}\rangle_{12}|\beta_{00}\rangle_{34}|\beta_{00}\rangle_{56}$ without telling them which state I ...
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Using quantum computers to calculate definite integrals?

Question How would a quantum computer calculate a definite integral (without resorting to approximations) of a function? Motivation According to a post of mine (in the context of classical field ...
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1answer
113 views

How good is basic_device_noise_model() simulating the noise in the quantum computer?

Is there any paper or article about the performance of the noise model using basic_device_noise_model()? For example, like the noise model in the code below. ...
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2answers
71 views

Does partial tracing a system with three shared Bell states give the identity?

Suppose I share three Bell states among two participants Alice and Bob and Charlie in the following manner: $$ |\psi\rangle=\left(\dfrac{|0\rangle_1|0\rangle_2+ |1\rangle_1|1\rangle_2}{\sqrt{2}}\...
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2answers
138 views

How is partial trace related to operator sum representation?

In Quantum Computation and Quantum Information by Nielsen and Chuang, the authors introduce operator sum representation in Section 8.2.3. They denote the evolution of a density matrix, when given an ...
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Give an explicit example of a $d = 4$ SIC-POVM

For $q=e^{2 \pi i/3}$, the set of $d^2$ vectors ($d=3$) \begin{equation} \left( \begin{array}{ccc} 0 & 1 & -1 \\ 0 & 1 & -q \\ 0 & 1 & -q^2 \\ -1 & 0 & 1 \\ -q &...
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32 views

Out-of-time-order correlation function in the interaction picture?

Recently there has been interest in understanding the out of time order correlation function (OTOC) $F$, which essentially compares the overlap of two operators $W$ and $V$ acting on a state in two ...
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0answers
67 views

How close are we in achieving computation over reals using quantum qubits? [duplicate]

I recently attended a seminar where a professor of quantum cryptography told the audience that one quantum qubit can theoretically store "infinite information". I was very intrigued by this statement, ...
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2answers
102 views

How to define a quantum channel for the partial trace?

I understand that the partial trace is a linear map, a completely positive map and a trace-preserving map. However, I have no idea how to define a quantum channel with the partial trace because ...

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