**Core Concept**
Brain stem death is a clinical diagnosis that involves the irreversible loss of brain stem function. This condition is considered a significant indicator of death, and it is essential to recognize the signs to establish the diagnosis accurately. The brain stem contains vital centers that regulate breathing, heart rate, blood pressure, and eye movements.

**Why the Correct Answer is Right**
The fixed, dilated pupil that does not react to light is a crucial sign of brain stem death. This occurs due to the loss of parasympathetic innervation from the Edinger-Westphal nucleus, which is responsible for pupillary constriction. The absence of light reflex (pupillary constriction in response to light) is a reliable indicator of brain stem dysfunction. Additionally, the loss of sympathetic input results in pupillary dilation. This sign is often considered the most reliable indicator of brain stem death, as it is less susceptible to variability in clinical examination.

**Why Each Wrong Option is Incorrect**
**Option A:** Absent Doll's eye reflex is a sign of brain stem dysfunction but is not as specific or reliable as fixed, dilated pupils for diagnosing brain stem death.
**Option C:** Cheyne-Stokes breathing is a pattern of breathing that may be observed in patients with brain stem dysfunction, but it is not a specific indicator of brain stem death.
**Option D:** Decerebrate posture is a sign of upper brain stem dysfunction, which is not sufficient to diagnose brain stem death.

**Clinical Pearl / High-Yield Fact**
When assessing brain stem function, it is essential to evaluate the pupillary reflexes, particularly the light reflex. A fixed, dilated pupil that does not react to light is a critical sign of brain stem death that should not be overlooked.

**✓ Correct Answer: B. Fixed dilated pupil not reacting to light**