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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Can a Kraus representation be always an identity to any operator?

In the textbook “Quantum Computation and Quantum Information” by Nielsen and Chuang, it is stated that there exists a set of unitaries $U_i$ and a probability distribution $p_i$ for any matrix A, $\...
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What is the pseudo threshold of a QECC using stabilizer formalism

Can someone explain what is the threshold and the pseudo threshold of a Quantum Error Correction Code , for instance the 9-qubit code. I'm familiar with quantum information and quantum circuit and ...
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Confused regarding explanation of Schumachers compression in N&C

On page 547 of N&C, for $|\psi_{0}\rangle=|0\rangle$ and $|\psi_{1}\rangle=(|0\rangle+|1\rangle)/\sqrt{2}$ and for $|\tilde{0}\rangle=\cos(\pi/8)|0\rangle+\sin(\pi/8)|1\rangle$ and $|\tilde{1}\...
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What can be inferred about the closeness of reduced qubit states from the closeness of the bipartite quantum state?

Given a qubit state $|\psi\rangle \in \mathcal{H}$, and two bipartite general mixed states $\rho$ and $\sigma$, such that, $$\langle \psi|\otimes \langle \psi|\rho - \sigma |\psi\rangle \otimes |\psi \...
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Is the Hilbert-Schmidt probability simply zero that a generic rank-2 two-qubit (“pseudo-pure”) density matrix is separable?

The multifacted evidence is very compelling--although not yet presented in a formal proof--that the Hilbert-Schmidt probability that a generic (full rank/rank-4) two-qubit density matrix is separable ...
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Recording Quantum Queries

Question is about techniques from this paper. Essentially the paper provides a way to record what queries were asked to a quantum-accessible oracle. We have the oracles: \begin{aligned} &\text { ...
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Question regarding part of the proof for the typical subspace theorem

Part three (going by N&C page 544) states that $$tr(S(n)\rho^{\otimes n})=tr(S(n)\rho^{\otimes n}P(n,\epsilon))+tr(S(n)\rho^{\otimes n}(I-P(n,\epsilon))).$$ Now I understand how the term on the ...
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How to measure the sign of quantum amplitudes

I have a quantum state on $ n $ qubits ($ 2^n $ amplitudes) for which I know the amplitudes are real numbers. I want to take the state out as a vector. I can estimate the magnitude of the amplitudes ...
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117 views

Are the skills learned for a degree in Computer Engineering helpful in learning Quantum Computing? [closed]

Next year, I will be a senior Computer Engineering student. Saying that, I have studied computer organization, electrical circuits, electronics and data structures. Our university provides an ...
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Coherent Information and Entanglement Breaking channels

The book by John Watrous, "The Theory of Quantum Information" is an exciting read for anyone wanting to research quantum information theory. The following question presumes some background ...
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Semi-definite program for smooth min-entropy

The conditional min-entropy is defined as (wiki): $$ H_{\min}(A|B)_{\rho} \equiv -\inf_{\sigma_B}\inf_{\lambda}\{\lambda \in \mathbb{R}:\rho_{AB} \leq 2^{\lambda}\sigma_B\} $$ And the smooth min-...
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Joint system of RAB after purification of A into R

Given a pure state $|\psi\rangle_{AB}$ on a joint system $AB$, we can consider the reduced density operator $\sigma_A = Tr_B(|\psi \rangle \langle \psi|)$ on $A$ and subsequently purify this state ...
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Other than distance, what other metrics can be used to compare quantum error correcting codes?

Using classical error correction (or channel coding) as a reference, I'd like to be able to compare QECC's from different constructions. Distance is a reasonable measure and you can argue that an $[[...
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Bra-Ket Notation and Proof of a Ket Equation in Two-Party Shared-Entanglement Setting

Disclaimer: I had posted this question previously on the physics StackExchange, but received no response there. My question is two-part. First, imagine a bipartite quantum state $|\Phi \rangle_{AB}$, ...
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How do you transmit known information using quantum teleportation/communication?

This is one of those things I think I knew well and now I've forgotten. Alice has a 1 she wants to transmit to Bob using quantum information sciences. How is Alice able to send a 1 to Bob? When things ...
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Are quantum operations reversible?

If We perform some unitary operations on a Quantum State $|A\rangle$ after which it becomes$|A'\rangle$. Then if we perform the inverse of all those unitary operations on the state $|A'\rangle$ in ...
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1answer
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I want to create a depolarizing channel on IBM qiskit

I want to replicate the depolarizing noise channel for a 4 qubit circuit system, where p is the probability for an error. I tried doing this: But I get the error ...
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30 views

How can I print out a state vector of a specific wire?

Suppose we start from 2 wires (q0 and q1) and through some quantum gates, suppose we measure q1 wire only. As we measure the q1 wire, the state vector of this quantum state would be determined ...
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42 views

Hamming Weight algorithm

Is there any quantum algorithm that can improve a calculation time for determining the Hamming weight of an arbitrary bit string? The Deutsch-Jozsa algorithm seems like it would be useful for this ...
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Convert a two-ququart (16 x 16) density matrix into normal form--so that the components of the Bloch vectors of the two reduced systems are all zero

The two-ququart ($16 \times 16$) "Hiesmayr-Loffler" density matrix https://iopscience.iop.org/article/10.1088/1367-2630/15/8/083036/meta, (https://arxiv.org/abs/2004.06745 eq. (13)), What ...
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What is the shortest sequence of decomposition a given single-qubit unitary gate

Given a single-qubit unitary matrix, can we find the shortest sequence of Clifford + T gates that correspond to that unitary? According to Fast and efficient exact synthesis of single qubit unitaries ...
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Confusion over HSW theorem depicted in Nielsen and Chuang

On page 560, it states that $$C^{(1)} \geq S(\frac{\varepsilon(|{\psi}\rangle\langle{\psi}|) +\varepsilon(|{\varphi}\rangle\langle{\varphi}|)}{2} - \frac{1}{2}\varepsilon(|{\psi}\rangle\langle{\psi}|)-...
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Are Bell states distinguishable through LOCC?

Define $|\psi^{00}\rangle = \frac{1}{\sqrt2}(|00\rangle + |11\rangle)$ and $|\psi^{01}\rangle = \frac{1}{\sqrt2}(|00\rangle - |11\rangle)$, and consider the state $$ |0\rangle\langle 0|^C\otimes |\psi^...
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Mutual information of Choi state=0, what would that imply about the quantum channel?

Classically, if the mutual information between the input and output of some channel or circuit $= 0$, it means the output is independent of the input, and the circuit is in a way 'useless'. For the ...
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2answers
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What can be said about the closeness of two states if the difference of their fidelity measured with respect to a fixed state is close to 0?

Suppose I have two states $\rho$ and $\sigma$. We are given that, $$Tr((\rho - \sigma)|\psi\rangle\langle\psi|) \geq \epsilon$$ where $|\psi\rangle$ is a fixed state and $\epsilon \rightarrow 0$, ...
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Question about the practical use of super dense coding in information transmission [duplicate]

Question about the practical use of super dense coding in information transmission: We know that by using super dense coding it is possible to transmit 2n classical bits transmitting n qubits, ...
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Under what situation is $\sum_{i} p_{i}S(\rho_i)$ > 0

Concerning the Von Neumann Entropy $S(\rho) = H(pi) + \sum_{i}p_{i}S(\rho_{i})$, under what circumstances does $\sum_{i}piS(\rho_{i})$ become greater than 0? I am aware it occurs when $\rho_{i}$ is ...
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49 views

a question about quantum gate decomposition on simulator or emulator

I have read a paper about "approximated decomposition" of a unitary single gate (Solovay-Kitaev algorithm) which told us a any unitary single gate can be decomposed into {Hadamard, Phase} with any ...
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52 views

How to decompose unitary quantum gate in current simulator or emulator?

I have a question about how to decompose a unitary quantum gate in a currently existing simulator or emulator. I have read some papers about SK algorithm and other algorithms which aim to decompose ...
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Find the number of elements in the Schmidt decomposition of a pure state

Consider a pure state $\boldsymbol{\eta} \in \mathcal{H}_{AB}$. There exist orthonormal sets $\{\alpha_1, \alpha_2 \dots \alpha_i\} \subset \mathcal{H}_A$ and $\{\beta_1, \beta_2 \dots \beta_i\} \...
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Does quantum computers give any advantage over classical computers in Sudoku?

To my basic knowledge I know that solving a generalized Sudoku problems is an NP-complete problem so, is there any possible way quantum computers give an advantage over classical computers in this ...
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Is there a gate that puts a qubit into superposition with a not so purely probabalistic (50 50) outcome?

I know that a Hadamard states is a purely probabalistic one; e.g. $$H\vert 0\rangle=a\vert 0\rangle+b\vert 1\rangle$$ where $a^2=0.5$ and $b^2=0.5$. Are there any states in which the ...
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For what kinds of problems is quantum interference used in quantum computers?

I know that the wave like nature of the electrons allows the qubits to interfere with each other amplifying correct answers and canceling out wrong answers. But what kind of problems that use this ...
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How to simulate master equation with a term of “cascaded formalism” with QuTiP?

I would like to simulate this master equation with QuTiP. The term in the second line is the so called "cascaded formalism" used for eliminates any feedback from system to the input nodes. But the ...
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Smallest Distance-5 Quantum Error Correction Code?

Is it known/proven what the smallest quantum error correction code is that can correct arbitrary two-qubit Pauli errors? I can think of the nested/concatenated 5-qubit code or a 25-qubit version of ...
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Is there any published research on quantum fault tolerant circuits that are designed for a specific task or algorithm?

I have searched for works that focus on designing a fault-tolerant quantum circuit for a specialized application and only found 'Error-corrected quantum annealing with hundreds of qubits' by Pudenz, ...
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How to decide which quantum device to use if a quantum algorithm is given?

I'm planning to write my master thesis in quantum computing. The subject of the thesis is to find out which attributes (properties, features) of quantum algorithms respectively their implementations (...
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1answer
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Exponential Growth of Noise in Quantum Computers

I recently listened to a presentation for Introductory Quantum Computing. It was very general and meant to give the listeners an idea about the potential for Quantum Computing. The speaker ended the ...
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Physical Interpretation of Non-Trace Preserving Quantum Operations

In Chapter 8 of Nielsen and Chuang's Quantum Computation and Quantum Information, a mathematical framework is developed to describe the dynamics of open quantum systems. Suppose the initial state of ...
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How does quantum teleportation relate to quantum encryption?

I am in grade 11 and am trying to work on a project, but I find this question a little confusing. I am trying to talk about the implications of quantum teleportation, specifically quantum encryption ...
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How to compute the tensor product of the depolarizing channel with the identity?

Consider two quantum systems A and B, B goes through a depolarizing noise channel, while A is not changed, i.e., they go through the channel $\mathbb{I}_A \otimes \mathcal{E_{\text{depol}}} $. If the ...
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1answer
42 views

Why does the entangled pair need to be entangled to perform teleportation?

Why does the entangled pair (the mechanism of teleportation) need to entangle to start with in order for the teleportation to proceed? After you perform the Bell measurement, doesn't it just break the ...
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Cannot interpret transformations on the bloch sphere as matrix multiplications

I understand that X,Y and Z gates are rotations around the axes with the respective letters, but I cannot understand how can Y gate multiply the amplitude of 0 with unreal number and have it landing ...
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Trying to get a provider from IBMQ but get 'No provider matches the criteria.'

I have created a circuit and then run the following: provider = IBMQ.get_provider('ibm-q') And this is what I get: ...
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Why don't quantum computing scientists build two 50-qubit processors and connect them in parallel instead of building one 100-qubit processor?

Isn't it more scalable to build multiple processors of a lower qubit and connect them in parallel instead of building one processor of a higher qubit?
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Is it right to think of superposition as just angle?

Based on my current understanding, a qubit is represented as a vector $(a, b)$ which satisfy $a^2 + b^2 = 1$. Classical bit one can be represented as $(0, 1)$ and bit zero can be represented as $(1, ...
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Writing Grover's Iterator in different computational phase [duplicate]

This question is from Nielson and Chuang's Quantum Computation and Quantum Information: Here $|\alpha\rangle$ is given by: $$\frac{1}{\sqrt{N-M}}\sum_{x} "|x\rangle $$ where $\sum_{x}" |x\rangle$ is ...
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What kind of operators should I perform on 4-qubit state $|\psi\rangle_A|GHZ\rangle$ to get expression like $|\Psi\rangle_4$?

Alice wants to send Bob qubit in state $|\psi_A\rangle = \alpha|0\rangle_A + \beta|1\rangle_A$ , also she has one qubit from GHZ state $\frac{1}{\sqrt 2}(|0\rangle_a|00\rangle +|1\rangle_a|11\rangle)$....
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Prove that for one-qubit unitaries $\text{Tr}|U-V|=2\max_\psi\|(U-V)|\psi\rangle\|$

Given two 1-qubit rotations $U=R_n (\theta)$ and $V=R_m(\phi)$ with $n$ and $m$ vectors defining a rotation and $\theta, \phi$ angles, define $D(U,V)=Tr(|U-V|)$ where $|U-V|=\sqrt{(U-V)^\dagger (U-V)}$...
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When can a non-completely-positive evolution of a state be physical?

Definitions: a map $\Phi$ is called positive if $\Phi(\rho)$ is positive semidefinite for any positive semidefinite $\rho$, and completely positive (CP) if $\Phi \otimes \mathrm{Id}$ is a positive map ...

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