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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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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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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170 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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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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65 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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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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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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74 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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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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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
45 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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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
61 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
693 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-...
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175 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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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
73 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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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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110 views

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
78 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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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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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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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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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
84 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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1answer
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About a necessary condition for quantum error correcting codes

I'm John and I have a question which I have been thinking about. I'm studying quantum information, especially, quantum error-correcting codes. When I learned some types of quantum codes (e.g. 5 qubits ...
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1answer
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Expectation Value of Stabilizer

Given that operator $S_M$, which consists entirely of $Y$ and $Z$ Pauli operators, is a stabilizer of some graph state $G$ i.e. the eigenvalue equation is given as $S_MG = G$. In the paper 'Graph ...
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1answer
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What is the problem in demonstrating quantum supremacy?

I am new to the quantum world and it's computing. But it accidentally hit in my mind that DWave built a quantum computer with 2000 qubits which can be use to simulate the whole observable universe or ...
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2answers
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Does anyone has some code for Mathematica or Python to convert a diagonal matrix into Dirac (bra-ket) notation?

I have the following matrix which I have to translate into Dirac's notations. \begin{array}{cccccccc} \frac{1}{2} \left(q_0+q_3\right){}^2 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{...
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How to construct Schur-Weyl decomposition of independent and identically distributed mixed qudit states?

Given a $d$-dimensional Hilbert space $\mathcal{H} \approx \mathbb{C}^{d}$ (i.e. a qudit system) if I have $N$ identical copies of a mixed state I can use Schur-Weyl duality to decompose the state as $...
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Marriott-Watrous style amplification with a quantum input

$\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1|}\def\ket#1{|#1\rangle}$ In MW05 the authors demonstrate so-called "in-place" amplitude amplification for QMA, exhibiting a method for Arthur ...
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Implementing B92 protocol on IBM Qx

I wanted to implement the B92 protocol on IBM Qx. Implementing the protocol would require that a particular qubit should not be measured when using a particular base i.e. there should be no output at ...
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133 views

Quantify the probability in guessing the Hamiltonian?

Background Let's say I know my experimentalist friend has been measuring the eigenvalues of a physical system. I can see the $M$ measurements are noted in a sheet of paper and I assume the ...
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1answer
41 views

Dephasing in graph states

In a recent paper Graph States as a Resource for Quantum Metrology. In the Appendix it states: We model an $n$ qubit graph state $G$ undergoing iid dephasing via $$G \to G^{\text{dephasing}} = \...
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1answer
106 views

What can we know about the eigenvalues of a reduced density matrix knowing the eigenvalues of the original matrix?

What information can we get out about the eigenvalues of a reduced density matrix knowing the eigenvalues of the original matrix? For example, it can be proved that if all the eigenvalues of a ...
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How can infinite information be theoretically encoded or stored in a single qubit?

I've just gotten started with Nielsen and Chuang's text, and I'm a little stuck. They mention that theoretically, it would be possible to store an infinite amount of information in the state of a ...
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1answer
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About production and disagreements between density matrices

So let's say there are $2$ experimentalists who have density matrix systems $A$ and $B$. They both agree that for the experiment they need identical density matrices $\rho_A = \rho_B$ which is a mixed ...
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1answer
92 views

Could second quantisation and QFT become a problem when scaling up quantum computers?

So I was wondering about the following: I can encode an algorithm in position $\hat x$ in quantum mechanics. However, in QFT position is not an operator it becomes a parameter $x$. Has anyone ...
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Conditional probability between parameter and operator in quantum mechanics?

Background So I came across a question on conditional probability in quantum mechanics: There's an interesting comment which tells why this does not work for "the non-commutative case". I was ...