picos.expressions.exp_quantcondentr

Implements QuantumConditionalEntropy.

Classes

class picos.expressions.exp_quantcondentr.QuantumConditionalEntropy(X, subsystems, dimensions=2)[source]

Bases: Expression

Quantum conditional entropy of an affine expression.

Definition

Let X be an N \times N-dimensional symmetric or hermitian matrix. Then this is defined as

-S(X) + S(\operatorname{Tr}_i(X)),

where S(X)=-\operatorname{Tr}(X\log(X)) is the quantum entropy, and \operatorname{Tr}_i denotes the partial trace with respect to the i-th subsystem.

Warning

When you pose a lower bound on this expression, then PICOS enforces X \succeq 0 through an auxiliary constraint during solution search.

__ge__(other)[source]

Return a constraint that the expression is lower-bounded.

__init__(X, subsystems, dimensions=2)[source]

Construct an QuantumConditionalEntropy.

Parameters

  • X (AffineExpression) – The affine expression X.

  • subsystems (int or tuple or list) – A collection of or a single subystem number, indexed from zero, corresponding to subsystems that shall be traced over. The value -1 refers to the last subsystem.

  • dimensions (int or tuple or list) – Either an integer d so that the subsystems are assumed to be all of shape d \times d, or a sequence of subsystem shapes where an integer d within the sequence is read as d \times d. In any case, the elementwise product over all subsystem shapes must equal the expression’s shape.

property X

The expression X.

property dimensions

The dimensions of the subsystems of X.

property iscomplex

Whether X is a complex expression or not.

property n

Length of X.

property subsystems

The subsystems being traced out of X.