picos.expressions.exp_quantentr¶

Implements QuantumEntropy, NegativeQuantumEntropy.

Classes

class picos.expressions.exp_quantentr.NegativeQuantumEntropy(X, Y=None)[source]¶

Bases: Expression

Negative or quantum relative entropy of an affine expression.

Definition

Let $X$ be an $n \times n$ -dimensional symmetric or hermitian matrix.

If no additional expression $Y$ is given, this is the negative quantum entropy

$\operatorname{Tr}(X \log(X)).$
If an additional affine expression $Y$ of same shape as $X$ is given, this is the quantum relative entropy

$\operatorname{Tr}(X\log(X) - X\log(Y)).$
If an additional scalar valued real affine expression $Y$ is given, this is the homogenized negative quantum entropy

$\operatorname{Tr}(X \log(X/y)).$

Warning

When you pose an upper bound on this expression, then PICOS enforces $X \succeq 0$ through an auxiliary constraint during solution search. When an additional expression $Y$ is given, PICOS enforces $Y \succeq 0$ as well.

__init__(X, Y=None)[source]¶

Construct a NegativeQuantumEntropy.

Parameters

X (AffineExpression) – The affine expression $X$ .
Y (AffineExpression) – An additional affine expression $Y$ . If necessary, PICOS will attempt to reshape or broadcast it to the shape of $X$ .

__le__(other)[source]¶: Return a constraint that the expression is upper-bounded.

__neg__()[source]¶: Denote the negation of the expression.

property X¶: The expression $X$ .

property Y¶: The additional expression $Y$ , or None.

property iscomplex¶: Whether X and Y are complex expressions or not.

property n¶: Length of X.

class picos.expressions.exp_quantentr.QuantumEntropy(X, Y=None)[source]¶

Bases: Expression

Quantum or negative quantum relative entropy of an affine expression.

Definition

Let $X$ be an $n \times n$ -dimensional symmetric or hermitian matrix.

If no additional expression $Y$ is given, this is the quantum entropy

$-\operatorname{Tr}(X \log(X)).$
If an additional affine expression $Y$ of same shape as $X$ is given, this is the negative quantum relative entropy

$\operatorname{Tr}(X \log(Y) - X\log(X))$
If an additional scalar valued real affine expression $Y$ is given, this is the homogenized quantum entropy

$-\operatorname{Tr}(X \log(X/y))$

Warning

When you pose a lower bound on this expression, then PICOS enforces $X \succeq 0$ through an auxiliary constraint during solution search. When an additional expression $Y$ is given, PICOS enforces $Y \succeq 0$ as well.

__ge__(other)[source]¶: Return a constraint that the expression is lower-bounded.

__init__(X, Y=None)[source]¶

Construct an QuantumEntropy.

Parameters

X (AffineExpression) – The affine expression $X$ .
Y (AffineExpression) – An additional affine expression $Y$ . If necessary, PICOS will attempt to reshape or broadcast it to the shape of $X$ .

__neg__()[source]¶: Denote the negation of the expression.

property X¶: The expression $X$ .

property Y¶: The additional expression $Y$ , or None.

property iscomplex¶: Whether X and Y are complex expressions or not.

property n¶: Length of X.

Fork me on GitLab