Bell tests and Bell's theorem used to interpret the test results opened the door to quantum information processing, such as quantum computation and quantum communication. Based on the erroneous interpretation of the test results, quantum information processing contradicts a well-established mathematical fact in point-set topology. In this study, the feasibility of quantum computation and quantum communication is investigated. The findings are as follows. (a) Experimentally confirmed statistical predictions of quantum mechanics are not evidence of experimentally realized quantum information processing systems. (b) Physical carriers of quantum information coded by quantum bits (qubits) do not exist in the real world. (c) Einstein's ensemble interpretation of wave-function not only will eliminate inexplicable weirdness in quantum physics but also can help us see clearly none of quantum objects in the real world carries quantum information. The findings lead to an inevitable conclusion: Without carriers representing quantum information, physical implementations of quantum information processing systems are merely an unrealizable myth. This conclusion contradicts relevant results in the literature. While all relevant results published nowadays support quantum information processing, the present work shows that quantum information processing systems rely on the assumption that qubits exist physically, but the assumption does not hold. Examples are given for illustrating the results reported here. For readers who are unfamiliar with point-set topology, the examples may alleviate difficulty in understanding the results.