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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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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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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1answer
134 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
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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
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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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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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95 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 ...
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How to measure entanglement in an algorithm?

Entanglement in Algorithms Most algorithms in quantum computing find their strength in making use of entanglement. I am interested in evaluating the amount of entanglement generated within an ...
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1answer
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Shor's Code: Understanding how it satisfies Knill Laflamme Theorem

I'm new to Quantum Error Correction, and I have a question on Shor's Code. If we have a protected subspace, $V \subset \mathbf{C}^2\otimes \cdots \otimes \mathbf{C}^2$ $V=\operatorname{span}\{|0_{...
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1answer
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Stabilizer state QFI lower limit query

On page 1 of this paper it states that the QFI (Quantum Fisher Information) for pure states $\psi$ is $$\mathcal{Q}(\psi) = \sum_{i,j=1}^n\text{Tr}(X_iX_j\psi)-\text{Tr}(X_i \psi)\text{Tr}(X_j \psi)~~~...
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1answer
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Quantum Fisher information for pure states query

Assume that a density matrix is given in its eigenbasis as $$\rho = \sum_{k}\lambda_k |k \rangle \langle k|.$$ On page 19 of this paper, it states that the Quantum Fisher Information is given as $$F_{...
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Why can we forget about the ancilla bit in Grover's algorithm?

$\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1|}\def\ket#1{|#1\rangle}$ When using Grover's algorithm to invert a function $f\colon \{0,1\}^m \rightarrow \{0,1\}$, an ancilla bit is used in ...
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Can everything in QM be described with degrees instead of matrices and vectors?

I found this explanation. "The Hadamard gate can also be expressed as a 90º rotation around the Y-axis, followed by a 180º rotation around the X-axis. So $H=XY^{1/2}H = X Y^{1/2}H=XY^{1/2}$." Can ...
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1answer
81 views

Trace of Hermitian Operator and Operator Function

I am having trouble understanding the following step. From: $$\operatorname{trace}\left(\sum_z |z\rangle\langle z| \rho_A |z\rangle\langle z| * \log( \sum_z |z\rangle\langle z| \sum_x |\langle x|z \...
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Entanglement-assisted hashing bound for asymmetric depolarizing channels

I reading the paper EXIT-Chart Aided Quantum Code Design Improves the Normalised Throughput of Realistic Quantum Devices, which proposes the use of QTCs in order to do quantum error correction for ...
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How do I compute the Relative Entropy between pure and mixed states?

Let $$ \rho = \begin{bmatrix} .7738 & -.0556 \\ -.0556 & .0040 \end{bmatrix} , \sigma = \begin{bmatrix} .9454 & -.2273 \\ -.2273 & .0546 \end{bmatrix} \\$$ As you can ...
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General Master Equation with Decoherence Query

The following general master equation (from this paper 'Dynamical quantum correlations of Ising models on arbitrary lattice and their resilience to decoherence') describes the various types of ...
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65 views

Should a Pauli $X$ matrix equal the identity matrix to be unitary?

My understanding is that any unitary matrix must have its inverse be equal to its conjugate transpose. Looking at the pauli x gate as shown here: $$\begin{bmatrix}0&1\\1&0\end{bmatrix}$$ It ...
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1answer
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Intuitive meaning of the eigenvalues and eigenvectors of a reduced density matrix

I am trying to figure out the intuitive meaning behind the eigenvalues and eigenvectors of a reduced density matrix. I understand that of a density matrix- the eigenvalues are the probability the ...
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The importance of length-4 cycles in Quantum LDPC codes

It is a proven and well-known fact that length-4 cycles are detrimental to the performance of classical LDPC codes. This is due to the fact that such short cycles impair the decoding algorithm (Sum ...
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1answer
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Is it possible to have entanglement with different sized parties or with more than 2 parties?

All the entanglement I've see is between 2 parties that have the same number of qubits. Is it possible to have entanglement where each party has a different number of qubits? Is it possible to have ...
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Error message for Classical Probability coding in Python

strong textHi guys I am doing a coding exercise for probabilities in vectors. Exercise 2 (1 point). As you recall, we may also write the probability distribution as a stochastic vector p⃗ =[p0p1]p→=...
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Determining the quantum secret

I earlier posted I question Representing a Bell measurement on non adjacent qubits for which I got an excellent answer. Now I want to build upon that and do further analysis which is where I am stuck. ...
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1answer
112 views

Find the reduced density matrix for a four-qubit system

I have the state vector $|p\rangle$ made up of 4 qubits. Say system A is made up of the first and second qubits while system B is made up of qubits 3 and 4. I want to find the reduced density matrix ...
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1answer
43 views

Find the local unitary that takes the bell state to a state phi that has an extractable bell state

I have a state $|p\rangle$ that has an extractable Bell state and I want to write it as a Bell state, $|b\rangle$, with a local unitary acting on one side. Basically I am trying to find a local ...
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1answer
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What are the Main Classes of Quantum Error-Correcting Codes?

Classically, we have the Hamming Code, Turbo Code, Reed-Solomon Code, etc. I am interested in knowing the classes of quantum error-correcting codes. They don't have to be analogous to classical codes, ...
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Non maximally entangled states for QKD

Why aren't non maximally entangled states produced and used in quantum key distribution schemes? What would be the advantage/disadvantage to use such states rather than maximally entangled ones?
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Can the Kraus decomposition always be chosen to be a statistical mixture of unitary evolutions?

If $\mathcal{E}$ is a CPTP map between hermitian operators on two Hilbert spaces, then we can find a set of operators $\{K_j\}_j$ such that $$\mathcal{E}(\rho)=\sum_j K_j\rho K_j^\dagger $$ in the ...
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Why is the resource theory approach used in quantum information processing?

What are the advantages and applications of using the resource theory approach in QIP ? What specific problems can be solved using in particular this approach ?
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Density Evolution to Optimize QLDPC code design

Density Evolution is a simulative tool that models the behaviour of SPA (sum-product) decoders. It is useful because it enables the optimization of code designs so that extensive simulations can be ...
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2answers
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The merit of quantum error correction codes

We know that word error rate (WER) rather than qubit error rate (QER) is used to evaluate the performance of quantum Turbo codes and quantum LDPC codes. In classical coding theory, when we are ...
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1answer
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How to integrate Simulaqron on ProjectQ

I am trying to simulate quantum teleportation on ProjectQ using simulaqron (enabling me to use quantum internet for teleportation) however I am not sure if my approach is right. In the working paper ...
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The most important quantum question , how to force a superposition qubit to collapses to an exact value? [closed]

Note: forcing a superposition qubit to collapses to 1, means cancel the other value 0 to get 1 appear Question details step by step: ...
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What is $\mathbb{Z}_2$ symmetry?

I encountered the notion of $\mathbb{Z}_2$ symmetry in an article. Can someone give a definition?
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Find probability of a single qubit's measurement results from a 5 qubit state

I have a tensor product of a 5 qubit state |h>. From this I want to calculate the probability of the 2nd qubit being in state |1>. Can someone show me how I can do this? I know I can use the Born rule ...
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1answer
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import error :No module named 'qiskit_aqua'

I have an error when I use Quantum SVM kernel algorithm from Qiskit aqua. This is my code section with imports: ...
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Measuring Coherence Length for T1 and T2 values with IBMQ Experience

So I'm currently working on a little program to measure how long the coherence time of a qubit is. Basically the idea is to initialise a qubit with a X or H gate then stick in a varying amount of ...
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1answer
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What is the intuition of using Hadamard gate in quantum fourier transform?

According to this answer by rrtucci, I still cannot catch the spirit of QFT algorithm. So I would like to ask why are we using the Hadamard gate when computing the Fourier Transform? Moreover, what ...
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Does entanglement allow communication of user specified information or not?

At first when I heard about entanglement, I thought "Neat, so we can make a manipulation on our quantum computer here in such a way that can be interpreted as a binary output somewhere else, and have ...
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How to implement NM Algorithm for Variational Quantum Eigensolver?

First of all: thanks for reading again. I appreciate the feedback I have gotten from this community the past weeks as I started to feel ready to ask questions about quantum computing topics. I am ...
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Does the Choi-Jamiolkowski isomorphism really establish a connection between kinematics and dynamics?

I understand the mathematical construction of the Choi-Jamiolkowski isomorphism aka channel-state duality. It all makes sense formally, yet I still struggle to grasp its physical (or quantum-...
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Geometric interpretation of 1-distillability

This is a sequel to Motivation for the definition of k-distillability Geometrical interpretation from the definition of 1-distillability The eigenstate $|\psi\rangle$ of the partially ...
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Motivation for the definition of k-distillability

Definition of k-distillability For a bipartite state $\rho$, $H=H_A\otimes H_B$ and for an integer $k\geq 1$, $\rho$ is $k$-distillable if there exists a (non-normalized) state $|\psi\rangle\in ...
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Bell State 11 not working for parity curve

I am currently writing a script to automate the creation of parity curves for a 2 qubit bell state and then calculate fidelity and proving entanglement from that (inspired by this paper). It was going ...
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1answer
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How to prove the following bosonic entanglement expression?

Based on the article given by J. L. Ball, I. Fuentes-Schuller, and F. P. Schuller, Phys. Lett. A 359, 550 (2006) had used the following expression of von-Neumann entropy \begin{equation} S = - \...