, and relative to two subsystems A and B, Bell introduces his famous theorem associated with 4 states, i.e., 2-qubit vectors into a combined space of Hilbert This consequence had not previously been noticed and seemed unreasonable at the time the phenomenon involved is now known as quantum entanglement. The essence of the paradox is that particles can interact in such a way that it is possible to measure both their position and their momentum more accurately than Heisenberg’s uncertainty principle allows, unless measuring one particle instantaneously affects the other to prevent this accuracy, which would involve information being transmitted faster than light as forbidden by the theory of relativity (“spooky action at a distance”). On the other hand, in 1935 Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) propose a thought experiment by which they try to demonstrate that the wave-function does not provide a complete description of physical reality (and which gives rise to the famous EPR paradox), and hence that the Copenhagen interpretation is unsatisfactory resolutions of the paradox have important implications for the interpretation of quantum mechanics. If a state is inseparable, it is called an entangled state. Therefore, this state will be separable if there exist vectors In H A ⊗ H B, the most general state is of the form Then, since not all states are separable states (and thus product states) we will carry out the following analysis. In fact, states of the composite system that can be represented in this form are called separable states. Those states of composite systems that can be represented as tensor products of subsystem states constitute the complement in the set of pure states, the product states. ” indicates the tensor product (also known as Kronecker’s product) whileĪre vectors providing the states of both subsystems, such as elementary particles. In fact, Schrödinger defined the entangled of pure states as the pure quantum stateĪssociated to composite systems like A and B that cannot be represented in the form of simple tensor products of subsystem state-vectors, that is , First, we should mention the key pieces in Quantum Information Processing (in general), and Quantum Computing, and Communications (in particular), i.e., the Principle of Superposition and the quantum entanglement, both closely related to the work of Erwin Schrödinger.
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