Final answer:
While the exact Supreme Court case that stipulates correctional officers employed by a private firm are not entitled to qualified immunity is not mentioned, the principle of qualified immunity generally does not extend to private individuals or employees of private corporations.
Step-by-step explanation:
The specific Supreme Court case that held that correctional officers employed by a private firm are not entitled to qualified immunity from suits by prisoners does not seem to be explicitly provided in the excerpts you have posted. However, the concept of qualified immunity generally applies to government officials performing discretionary functions, providing protection from suits so long as their conduct does not violate clearly established statutory or constitutional rights which a reasonable person would have known.
Yet, based on the general understanding of law, private individuals, including those working for private firms, such as private prison employees, are typically not afforded qualified immunity in the same way as government employees. It is important to differentiate between public and private actors in terms of legal protections and liabilities. While I cannot give a specific case based on the information provided, the explanation of qualified immunity and its application to public versus private actors might be helpful for understanding the context of your question.