Final answer:
The 'right to challenge unlawful detention by state' is known as habeas corpus, a fundamental legal procedure that permits individuals to contest the validity of their incarceration in court.
Step-by-step explanation:
The "right to challenge unlawful detention by state" is commonly known as habeas corpus, which is a legal procedure that allows an individual in custody to challenge the legality of their detention. This principle is entrenched in many rule-of-law countries, allowing detained individuals to appear before a court to be informed of the charges against them. The significance of habeas corpus was highlighted in cases like Boumediene v. Bush and Hamdi v. Rumsfeld, where the United States Supreme Court affirmed that even foreign detainees at Guantánamo Bay and U.S. citizens designated as enemy combatants have a right to due process and the ability to challenge their detention.
These principles are rooted in the broader concept of the rights of the accused, which include the right to be informed of charges, to counsel, to a speedy and public trial, and to appeal decisions to a higher court. The practice of habeas corpus is a critical element in protecting these rights and ensuring that the government cannot arbitrarily hold individuals without just cause or due process.