Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [semidefinite-programming]

Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron. (Wikipedia)

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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}}(\mathcal{E}) = \max_{\rho_{A'}}…
user1936752
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How to calculate the conditional min-entropy via a semidefinite program?

I am trying to formulate the calculation of conditional min-entropy as a semidefinite program. However, so far I have not been able to do so. Different sources formulate it differently. For example, in this highly influential paper, it has been…
QuestionEverything
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Semi-definite program for smooth min-entropy

The conditional min-entropy is defined as (wiki): $$ H_{\min}(A|B)_{\rho} \equiv -\inf_{\sigma_B}\inf_{\lambda}\{\lambda \in \mathbb{R}:\rho_{AB} \leq 2^{\lambda} \mathbb{I} \otimes \sigma_B\} $$ And the smooth min-entropy is defined…
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How can I implement partial transpose on a variable in Picos (Python, trying to solve an SDP)?

I try to optimise a quantity via an SDP. I optimise over all PPT measurement operators and hence have the constraints $\Pi_k^{T_B} \succeq 0$ (PPT) for my measurement operators. The part of the code where I define the SDP and constraints…
root
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Quantum Optimization algorithms

The Harrow-Hassidim-Lloyd (HHL) algorithm for quantum matrix inversion (linear algebra) bridges classical math to quantum math and has been adopted for quantumizing many classical applications, such as linear regression and deep neural…
develarist
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Are all extremal points of the feasible set of an arbitrary affine equation pure states?

Suppose I have one constraint on quantum states, i.e., $\Lambda(\rho)=Y$ where $Y$ is a Hermitian matrix and $\Lambda$ is a linear and Hermitian preserving map. Note that $\rho$ and $Y$ can in general have different dimensions. Let's denote all…
narip
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$3 \rightarrow 1$ QRAC encoding for XOR functions

I'm currently working on QRAC and was wondering if there's an encoding protocol in $3 \rightarrow 1$ such that the receiver is able to retrieve any one of the XOR combinations of the bits, along with the original bits itself ( a grand total of 7…
Vaisakh M
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Semi-definite program for conditional smooth max-entropy

I am aware of a SDP formulation for smooth min-entropy: question link. That program for smooth min-entropy was found in this book by Tomachiel: page 91. However, I am yet to come across a semi-definite formulation for smooth max-entropy. There is…
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Super-dense coding by adding quantum correlations between classical bits

Consider the following non-local game between Alice, Bob (who are spatially separated but share a maximally entangled state) and a referee: Referee samples two question bits "$x,y$" and sends them to Alice. Alice sends 1 answer bit "$a$" to…
Soham Ghosh
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Finding the violating bound of CHSH using the first level of NPA hierarchy on MATLAB

I've been trying to implement the NPA hierarchy in MATLAB using CVX library. To start off with, I thought of finding the bound of CHSH using the first level of NPA hierarchy. I represented my gram matrix as an addition of 2 matrices, One consisting…
Karthik Nambiar
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Semi-Definite Program to maximise $P(X)$ with a fixed CHSH value

This question should be theoretically simple, yet I'm struggling as something may be incorrect about my code. I am trying to plot a graph of the maximum probability ($P(x)$) of a given system against CHSH violation values. We can do this using the…
Largecooler21
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Linear and logarithmic constraint in semidefinite programming

I am trying to minimize the largest component of a vector ${\bf x} = (x_1, x_2, x_3, x_4)$, where $x_1 \ge x_2 \ge x_3 \ge x_4$, such that it satisfies a set of linear inequalities given by ${\bf A} {\bf x} \le {\bf b}$. Furthermore, I want that,…
QuestionEverything
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