Which of the following does the Eighth Amendment prohibit?

The Eighth Amendment of the United States Constitution specifically prohibits "cruel and unusual punishments." This amendment is a critical component of the Bill of Rights, aimed at ensuring that punishments for crimes are not only fair but also humane. The underlying principle is that the state should not impose excessive or degrading treatment on individuals, particularly those who are incarcerated. The interpretation of what constitutes "cruel and unusual" has evolved through various Supreme Court rulings, shaping the legal landscape regarding prison conditions, the death penalty, and sentencing practices.

The focus of the Eighth Amendment is distinctly on punishment, hence the other options do not fall under its scope. Unreasonable searches are addressed by the Fourth Amendment, the quartering of soldiers pertains to the Third Amendment, and unlawful detainment is covered by the protections of the Fifth and Fourteenth Amendments regarding due process. Therefore, option A is the only correct choice related directly to the Eighth Amendment.