When two particles are entangled the state of either one is a mixed state that can only be described with a density operator. (in the most convenient basis the density matrix for either particle is ##diag(1/2,1/2)##, equal probability of measuring spin-up or spin down).stephen8686 said:when two particles are entangled, we must describe them using the density operator because it is a mixed state.
The singlet state is the state of a single quantum system that will produce measurement results at two spatially separated detectors. It is a pure state with a wave function - but it is not the state of either particle considered in isolation.But I have another source that says that the singlet state of two spins is an entangled state, but that has a wavefunction.
To rephrase what @Nugatory said, the state that simultaneously describes both particles together is pure, while the state that describes any of the particles alone is mixed.stephen8686 said:I have a source that says when two particles are entangled, we must describe them using the density operator because it is a mixed state. But I have another source that says that the singlet state of two spins is an entangled state, but that has a wavefunction. So could someone explain what I am misunderstanding? Are all entangled states mixed states or only some?
Entanglement is a quantum mechanical phenomenon in which two or more particles become connected in such a way that the state of one particle cannot be described without also describing the state of the other particle, even if they are separated by large distances.
A mixed state is a quantum state that cannot be described by a single wave function, but instead requires a statistical mixture of multiple wave functions. This can occur when a system is not in a pure state, but is instead a combination of multiple pure states.
A pure state is a quantum state that can be described by a single wave function. It is a state in which the system has a definite and well-defined set of properties, and its evolution can be described by the Schrödinger equation.
Entanglement can lead to seemingly paradoxical effects, such as particles appearing to communicate with each other instantaneously even when separated by large distances. It also allows for the phenomenon of quantum superposition, where a particle can exist in multiple states simultaneously.
Entanglement has potential applications in quantum computing, cryptography, and teleportation. It is also being studied for use in quantum communication and quantum sensing, where its ability to transmit information instantaneously could have practical benefits.