No, a classical computer cannot fully simulate quantum measurement without using some form of randomness. Quantum measurement is inherently probabilistic, and it involves the collapse of the quantum state into one of the possible measurement outcomes according to the probabilities dictated by the wave function.
Classical computers, on the other hand, operate deterministically, meaning that their computations follow predetermined rules and produce the same output for the same input. They do not naturally possess the inherent randomness required for simulating quantum measurement outcomes.
To simulate quantum measurement, classical computers often employ pseudorandom number generators (PRNGs) to introduce randomness into their calculations. PRNGs use deterministic algorithms to generate sequences of numbers that approximate randomness. However, these sequences are not truly random and are based on initial seed values.
While PRNGs can provide an effective means to introduce randomness into classical simulations of quantum systems, they are not equivalent to the inherent randomness found in quantum measurements. In practice, the use of PRNGs in simulations allows for statistical analysis and approximations of quantum behavior rather than exact replication.
It's important to note that quantum computers, with their inherently probabilistic nature, can naturally simulate quantum measurements without the need for external randomness. Quantum algorithms can leverage quantum randomness to sample from the probability distribution defined by the quantum state. This property is one of the key advantages of quantum computers over classical computers for certain computations.