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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42 views

Give an explicit derivation of the formula for the two-qubit absolute separability Hilbert-Schmidt probability $\approx 0.00365826$

The two-qubit eigenvalue ($\lambda_i$ >= 0, $i=1,\ldots,4$, $\lambda_4=1-\lambda_1-\lambda_2-\lambda_3$) condition of Verstraete, Audenaert, de Bie and de Moor AbsoluteSeparability (p. 6) for ...
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60 views

A question about quantum noise model

Now, I try to understand some concept of Quantum Noise Model and Quantum Channel. The Quantum Noise can be represented as a quantum operator with their own probability. As far as I concerned,(I dont ...
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70 views

Meaning behind obtaining a hermitian operator for measurement in another basis?

If $$P_{+} = |+\rangle\langle+|=\frac{1}{2}(|0\rangle\langle0|+|0\rangle\langle1|+|1\rangle\langle0| +|1\rangle\langle1|)$$ and $$P_{-} = |-\rangle\langle-|=\frac{1}{2}(|0\rangle\langle0|-|0\rangle\...
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Finding a class $C$ of bipartite PPT states such that entanglement of $\rho \in C$ implies entanglement of $\rho + \rho^{\Gamma}$

Consider an entangled bipartite quantum state $\rho \in \mathcal{M}_d(\mathbb{C}) \otimes \mathcal{M}_{d'}(\mathbb{C})$ which is positive under partial transposition, i.e., $\rho^\Gamma \geq 0$. As ...
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60 views

What is the deep physical reason behind the existence of bound entanglement? [closed]

In Quantum Information processing, we can extract entanglement from $n$-copies of a weakly entangled state to produce a fully or highly entangled states in $d$-dimensions, using the known distillation ...
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104 views

Why should we use density matrices to simulate quantum systems with noise?

Why we should use density matrices to simulate quantum systems with noise? I found that the any QEC circuit is included by some quantum gates just like normal cases, which means the state vector can ...
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57 views

Where to publish quantum algorithm related paper

I am an undergraduate student and I wrote a paper for my research program on quantum information. To be more specific, it is about using a novel quantum algorithm to do signal/image processing. It won ...
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1answer
64 views

Definition of quantum min-relative entropy

In John Watrous' lectures, he defines the quantum min-relative entropy as $$D_{\min}(\rho\|\sigma) = -\log(F(\rho, \sigma)^2),$$ where $F(\rho,\sigma) = tr(\sqrt{\rho\sigma})$. Here, I use this ...
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92 views

Can a Kraus representation act as the identity on 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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91 views

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, and how to calculate it using the stabilizer formalism simulation ...
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1answer
45 views

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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1answer
45 views

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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55 views

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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1answer
32 views

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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99 views

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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1answer
125 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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55 views

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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1answer
104 views

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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38 views

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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65 views

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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68 views

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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58 views

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
109 views

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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44 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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1answer
55 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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29 views

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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1answer
27 views

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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1answer
30 views

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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48 views

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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69 views

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
46 views

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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1answer
55 views

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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1answer
56 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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1answer
57 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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48 views

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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1answer
107 views

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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410 views

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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50 views

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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2answers
55 views

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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1answer
44 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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44 views

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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277 views

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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1answer
26 views

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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43 views

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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46 views

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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35 views

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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