Questions tagged [quantum-information]

NOTE: We are currently in the middle of removing this tag, so please don't use it! For questions about the quantum analogues of concepts in information theory, please use the information-theory tag.

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RAC for XOR functions

I need the optimal encoding protocol for 3 $\rightarrow$ 1 Classical RAC such that the receiver is able to retrieve any one of the initial bits, as well as the XOR combinations of those bits. ( If a, ...
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38 views

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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65 views

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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99 views

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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270 views

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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1answer
52 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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154 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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82 views

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
101 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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25 views

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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79 views

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
110 views

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
45 views

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
46 views

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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1answer
151 views

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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177 views

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
152 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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2answers
177 views

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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50 views

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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1answer
94 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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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
30 views

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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28 views

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
263 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
68 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
80 views

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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49 views

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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315 views

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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80 views

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
127 views

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
104 views

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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1answer
48 views

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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3answers
122 views

Find probability of a single qubit's measurement results from a 5 qubit state

I have a tensor product of a 5 qubit state $|h\rangle$. From this I want to calculate the probability of the 2nd qubit being in state $|1\rangle$. Can someone show me how I can do this? I know I can ...
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1answer
447 views

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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338 views

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
144 views

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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2answers
70 views

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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1answer
243 views

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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380 views

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 transposed $1$-...
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1answer
69 views

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 H^{\...
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77 views

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
33 views

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 = - \...