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Questions tagged [quantum-operation]

For questions about quantum channels or more generally quantum maps and the related formalism. For questions about unitary operations, please use quantum-gate instead.

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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 ...
Josu Etxezarreta Martinez's user avatar
7 votes
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Rotation resolutions in operations for qubits in commercial implementations

I have found information about Honeywell provider supporting operations with high-resolution rotations (i.e. around $\pi/500$) here. What are typical maximal rotation resolution values supported by ...
Mariusz's user avatar
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How does the extremality of a POVM reflect on its Naimark dilation isometry?

Let $\mu:\Sigma\to\mathrm{Pos}(\mathcal X)$ be some POVM, with $\Sigma$ the finite set of possible outcomes, and $\mathrm{Pos}(\mathcal X)$ the set of positive semidefinite operators on a finite-...
glS's user avatar
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Is it possible to obtain a closed-form expression of the diamond distance between two single-qubit channels?

I would like to compute the diamond norm of the difference of two single-qubit channels $\Phi_1$ and $\Phi_2$. This difference is equal to, for any $2\times2$ complex matrix $\rho$: $$\...
Tristan Nemoz's user avatar
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Why is combined amplitude and phase damping considered sufficient for noise modeling?

In QECC literature, I often come across the "combined amplitude and phase damping channel" as being representative of a realistic noise model which makes sense (as amplitude damping and de-...
Sam's user avatar
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Verification of local unitary equivalence between two pure states

This might be a non-trivial and hard problem. I've been thinking about this for days but couldn't find a good answer, so I hope any of you could give me a good answer/intuition for me to move forward. ...
userflux9674's user avatar
6 votes
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225 views

What are examples of zero capacity quantum channels with Choi rank less than $d$?

All the currently known examples of quantum channels with zero quantum capacity are either PPT or anti-degradable. These notions can be conveniently defined in terms of the Choi matrix of the given ...
mathwizard's user avatar
6 votes
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Quantum channel Holevo information additivity: proof approach

I have an interesting idea for a proof approach that someone might find useful. Here it is. Suppose we are given a quantum qubit channel $N$ (for example the amplitude damping channel) whose Holevo ...
user120404's user avatar
5 votes
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What is the best quantum process tomography method?

This question is somewhat related to this question. What is currently the best method for quantum process tomography? By best I mean, the one that can achieve the best accuracy of estimation per qubit ...
Quantum Guy 123's user avatar
5 votes
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77 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 ...
Yack's user avatar
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Why is the quantum Fisher information $J_f=[f(\frac43-f)]^{-1}$ for maximally entangled qubit pairs?

I am reading paper Channel Identification and its Impact on Quantum LDPC Code Performance where the authors discuss the scenario where the decoder of a Quantum LDPC code uses an estimation of the ...
Josu Etxezarreta Martinez's user avatar
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Real-life examples of classical-quantum channels

In quantum information theory, classical-quantum channels are considered to be channels whose input is the realizations $x\in\mathcal{X}$ of a classical random variable to a quantum state $\rho_x^B$, ...
Josu Etxezarreta Martinez's user avatar
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A measure of entanglement created by a unitary operation

Let $U$ be a unitary matrix acting on a 3-qubit system. If there is no correlation among any pairs of the three qubits, the unitary operation can be represented as $U = U_1 \otimes U_2 \otimes U_3$, ...
user185671631's user avatar
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Is there a known deterministic counterexample for non-additivity of minimal output entropy?

Hastings has proved that the minimal output entropy is not additive: it may happen that $S_{\mathrm{min}}(\Phi_1 \otimes \Phi_2) < S_{\mathrm{min}}(\Phi_1)+S_{\mathrm{min}}(\Phi_2) $ for quantum ...
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How to find the Choi state of a bipartite quantum channel?

The Choi state of a quantum channel $\mathcal{N}_A$ acting on a system $\rho_A \in \mathcal{H}^A$ is given by: $Choi(\mathcal{N}_A) =( \mathcal{I}_{A'} \otimes \mathcal{N}_A)|\Phi^+\rangle \langle\...
junfan02's user avatar
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What's a "natural" way to show that, for unital channels, $\Phi(X)=X$ iff $[X,A_a]=0$ for all Kraus operators $A_a$?

This is a statement proved in Watrous, Theorem 4.25, page 229 of the online version. Let $\Phi\in\mathrm C(\mathcal X)$ be a unital channel with Kraus representation $\Phi(X)=\sum_a A_a X A_a^\dagger$....
glS's user avatar
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What is the quantum capacity of the combined amplitude and phase damping channel?

Quantum capacity for the amplitude damping channel and the pure dephasing channel have closed-form formulas as it can be seen in section 24.7.2 of From Classical to Quantum Shannon Theory. However, I ...
Josu Etxezarreta Martinez's user avatar
4 votes
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106 views

What is the algorithm for the optimal decoder in a quantum erasure channel?

I'm reading this paper : Holographic Quantum Error Correcting Codes and on page 3 they describe an optimal decoder for erasure channel. The description is for CSS codes but they claim that "it is ...
unknown's user avatar
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Uhlmann's theorem analogue for channels

Let the stabilized channel fidelity between two channels $M_{A\rightarrow B}$ and $N_{A\rightarrow B}$ be defined as $$F(M,N) = \min\limits_{\vert\psi\rangle_{AR}} F\left((M\otimes I_R)\vert\psi\...
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Analyzing the composition of a channel with its adjoint in relation with an identical composition obtained for the channel's complement

Let us consider two quantum channels $\Phi:M_d\rightarrow M_{d_1}$ and $\Phi_c:M_d\rightarrow M_{d_2}$ that are complementary to each other, i.e., there exists an isometry $V:\mathbb{C}^d\rightarrow \...
mathwizard's user avatar
4 votes
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56 views

Is there some notion of work associated with performing a measurement?

Let a measurement be described by POVM elements $M_i$ such that probability $p(i) = Tr[\rho M_i]$ for some state $\rho$. I want to know whether there is some notion of work associated with such ...
Mike's user avatar
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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 ...
K Gautam Shenoy's user avatar
4 votes
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95 views

How to compute the capacity of a quantum channel from its Kraus operators?

Is there a working rule to compute the capacity of a quantum channel described by a set of Kraus operators $\{K_i\}$?
Rob's user avatar
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Forbidden/allowed outputs of a quantum channel

The coherent information of a channel $\mathcal{E}_{A'\rightarrow B}$ is defined as the maximum value obtained by the following function where the maximization is over all input states $$I_{\rm{coh}}(...
user1936752's user avatar
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180 views

What is the difference between intercept-resend attack and measure-resend attack?

I am going through different types of attacks that eve can perform on the quantum channel. I came across the intercept-resend attack and measure-resend attack. What is the difference between the two? ...
Adam Levine's user avatar
4 votes
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457 views

Implementing a depolarizing channel for 2 qubits on IBM Q

I am trying to use IBM Q to perform the following depolarizing channel on a state of 2 qubits $\rho=|\psi \rangle \langle \psi |$: $$\rho \to (1-\lambda)\rho + \frac{\lambda}{4}I$$ This is within ...
The Bosco's user avatar
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3 votes
0 answers
37 views

Fisher information of parametric channel

Suppose $\Phi_\theta$ is a quantum channel whose action can be written for any state $\rho\in \mathcal S(\mathcal H_S)$ in the Stinespring representation as $\Phi_\theta(\rho)= \text{Tr}_E(U_\theta (\...
Quantastic's user avatar
3 votes
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40 views

Infidelity as distance measure

Let $\mathcal{X} \in {\rm CP}(\mathcal{H}, \mathcal{K})$ and unital (compositive positive and unital maps). Let $\mathcal{Y} \in {\rm CPT}(\mathcal{H}, \mathcal{K})$(complete positive and trace ...
Michael.Andy's user avatar
3 votes
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Coherent information is a lower bound of channel capacity. What about coherent information based on Renyi entropies?

It is known that coherent information defined in terms of von Neumann entropies is a lower bound of quantum channel capacity. If we define coherent information in terms of $\alpha$-Renyi entropies, ...
MonteNero's user avatar
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3 votes
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How to write the joint action of a CP map that acts on a single qubit of a bipartite state?

The question Say I have a completely-positive (CP) map $\mathcal{A}_{ij}$ defined in terms of two projectors $\Pi_i = |i\rangle \langle i |$ and $\Pi_j = |j\rangle \langle j |$ that acts on a density ...
RobMuNu's user avatar
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Proof that quantum entanglement does not increase the asymptotic capacity of classical channel

Consider a classical channel $N_{X\rightarrow Y}$ which takes every input alphabet $x\in X$ to output alphabet $y\in Y$ with probability $P(y|x)_{Y|X}$. It is stated in many papers that even if the ...
user1936752's user avatar
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What do you specify when you physically apply a unitary?

In the Environment and Quantum Operations in Nielsen and Chuang, section 8.2.2, they say that when you apply a unitary on a state, you expect the output as the just the state transformed by the ...
Mahathi Vempati's user avatar
3 votes
0 answers
86 views

Three sender quantum simultaneous decoder conjecture

Recently I have started to read about network quantum information theory, where network problems are studied under the classical-quantum channel. For example, capacities of the cq-MAC, cq-broadcast or ...
Josu Etxezarreta Martinez's user avatar
2 votes
0 answers
24 views

Specifying the image of a set of states under the action of a channel

I have a generic channel $\mathcal{N}$ acting on a subspace of states defined on a $d$-dimensional Hilbert space $\mathcal{H}$. I am trying to make a statement about the dimension of the image of that ...
forky40's user avatar
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2 votes
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179 views

How to build the quantum circuit ansatz to implement a diagonal unitary operator with just 1 and -1 elements?

Let's consider a set of $N = 2^n$ binary values $S_i \in \left\{-1, 1\right\}$ and define the diagonal matrix $W$ as a quantum unitary operator acting on a system of $n$ qubits: $$ W = \begin{pmatrix} ...
SimoneGasperini's user avatar
2 votes
0 answers
36 views

Is there a Qutip equivalent of "expand_operator" for superoperators?

I want to calculate a superoperator for a small noisy subsystem consisting of $k$ qubits, and expand it to $n > k$ qubits, where the remaining $n-k$ qubits are not subject to any noise. ...
JoJo P's user avatar
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Error in repeated applications of a quantum channel?

Suppose I have two quantum channels. Assume they they consist of $r\in \mathbb{Z}$ applications of unitaries, $U$ and $V$ respectively. Let the error between the channels acting on some state $\rho$ ...
Hans Schmuber's user avatar
2 votes
0 answers
41 views

Why is the quantum capacity quantified by the coherent information?

Most types channel capacities associated to a given quantum channel are quantified using mutual informations (sometimes classical, sometimes quantum, sometimes regularised), which is not surprising ...
glS's user avatar
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2 votes
0 answers
62 views

Can channels be generalized to linear maps from $\mathbb{C}^{n^k}$ to $\mathbb{C}^{n^k}$?

First let's set some terminology. Recall that a quantum channel is in particular a linear map $\Phi : \text{L} ( \mathcal{X}) \rightarrow \text{L} ( \mathcal{Y})$ where $\mathcal{X}$ and $\mathcal{Y}$ ...
user22511's user avatar
2 votes
0 answers
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What is the complementary map of a serial concatenation of quantum channels?

I have been studying serial concatenations of quantum channels, i.e. $\mathcal{N}_{A\rightarrow B}=\mathcal{N}_1\circ\mathcal{N}_2=\mathcal{N}_{B'\rightarrow B}\circ\mathcal{N}_{A\rightarrow B'}$. ...
Josu Etxezarreta Martinez's user avatar
2 votes
0 answers
94 views

Local Hermitian operators can be written as sums over local error operators?

In this paper, near the bottom of the left half of page 3, the authors claim that any local Hermitian operator (one which acts only on a single subsystem of a larger composite system) can be expressed ...
Eulerian's user avatar
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2 votes
0 answers
69 views

What are examples of "LOCC linked" quantum instruments?

Define a quantum instrument $\mathfrak J$ as a collection of completely positive (CP) maps $(\mathcal E_j:j\in\Theta)\subset\mathrm{CP}(\mathcal H)$, such that $\sum_j \mathcal E_j$ is also trace-...
glS's user avatar
  • 25k
2 votes
0 answers
53 views

How to detect and correct swap errors in a quantum circuit?

Let's assume that I have a density matrix $\rho$ that consists of $N$ qubits. If this density matrix undergoes an error-channel that swaps any two qubits with an equal probability, i.e. $$ \mathcal{E}(...
Turbotanten's user avatar
2 votes
0 answers
95 views

A way to check if entanglement is increased or decreased

I was wondering if there is a way to check if the amount of entanglement is increased or decreased after a quantum operation without calculating the actual value. That is, it does not concern with the ...
KEN's user avatar
  • 21
2 votes
0 answers
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What is the best method for estimating average channel fidelity?

This thesis shows an efficient way to estimate average channel fidelity (in chapter 4). However, it is somewhat old (from 2005). Are there any better methods out there? By better I mean: are there ...
Quantum Guy 123's user avatar
2 votes
0 answers
133 views

How to define POVM measurement operators for a composite quantum state

I have an evolved quantum composite state $\hat{\rho}^{\otimes{N}}$ that I retrieved from a quantum channel $\mathcal{E}$, Now I do know how to define a POVM for the evolved states $\hat{\rho}$ that ...
Najeeb Ullah's user avatar
2 votes
0 answers
131 views

Getting Choi-matrix of a subsystem

In Qiskit, for a given QuantumCircuit object, you can compute its Choi-matrix via the corresponding Choi object, for example: <...
Daniele Cuomo's user avatar
2 votes
0 answers
36 views

What applications does single-shot state conversion have?

Many quantum processes are formulated in a resource theoretic approach like entanglement, athermality, asymmetry, coherence, etc. Some of its topics have obvious applications, like distillation where ...
2ub's user avatar
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2 votes
0 answers
35 views

Is quantum deletion via a partial randomization procedure possible?

The paper, Quantum deletion is possible via a partial randomization procedure claims that it is possible to bypass the no-deleting theorem by a procedure called R-deletion. But this seems to go ...
Sujan Vijayaraj's user avatar
1 vote
0 answers
29 views

What is the rank of a superoperator of the form $\Xi (\cdot) = \sum_i^n U_i^\dagger {\cdot}\, U_i$?

Given a superoperator $\Xi$ as $\Xi (\cdot) = \sum_i^n U_i^\dagger \cdot U_i $ where $U_i$ are unitary. What can I say about the image of this map or about the rank of $\Xi$? Also, do you have some ...
relativeentropy's user avatar