Can quantum states be controlled or randomized for communication using quantum entanglement?

I see

"FTL" Communication with Quantum Entanglement? (which has some really awesome potential answers)

Quantum entanglement as practical method of superluminal communication

and,

Quantum communication

The typical answer for why communication using quantum entanglement cannot be done appear to come down to a few issues: 1) the measuring of a quantum state is a terminal process, 2) there is no reference frame for the two actors Alice and Bob, and 3) there is no control of the quantum state of the feature being measured.

By a “terminal process”, it is meant that after the quantum feature is measured a first time, then that same feature cannot be measured again at a later time. For example, at time t0, Bob measures the spin of one electron as up (which means that Bob knows Alice’s entangled electron must be down). Bob is then unable to measure that same electron at a later time, t1, i.e., after Alice has manipulated the spin of her electron to be something other than down.

By “no reference frame”, it is meant that Bob does not know what direction “up” is for Alice, and vice versa. As an example, if “up” is away from the center of the Earth, Alice is at the equator, and Bob is at the North Pole, then “up” for Alice is at a right angle to “up” for Bob. Alice and Bob are unable to agree on “up” until after comparing their measurement results.

By “no control”, it is meant that the quantum feature being measured cannot be controlled by either Alice or Bob. For example, if Alice has a first set of electrons that have been entangled with a second set of electrons that Bob has, then the spins of the first set of electrons, as a whole, are random. Alice is unable to force all of the electrons of her set of electrons to all spin the same direction.

The “terminal process” issue can be overcome by using multiple sets of quantum particles. E.g., Alice has the first, third, fifth, … sets of electrons that are respectively entangled with the second, fourth, sixth, … sets of electrons that Bob has. Alice and Bob then agree beforehand: that at time t0, Alice will manipulate the first set and Bob will measure the second set; that at time t1, Alice will manipulate the third set and Bob will measure the fourth set; that at time t2, Alice will manipulate the fifth set and Bob will measure the sixth set; etc.

The “no reference frame” issue is usually addressed by Alice and Bob comparing their results classically (i.e., at light speed or slower and not instantaneously).

Alternatively, what if Alice and Bob agree that at t0, Alice will make the first set of electrons spin “down” (so that the second set of electrons that Bob has should spin “up”); then at t1, in order to send a binary 0, Alice does not manipulate the third set of electrons so that both Alice’s third set of electrons and Bob’s fourth set of electrons each have random directions; then at t2, in order send a binary 1, Alice manipulates all the electrons of the fifth set of electrons to spin “down” (causing Bob’s sixth set of electrons to all spin “up”). Even if Bob does not know what “up” or “down” is, Bob can still tell if all of the electrons of a set of electrons are spinning randomly, or are all spinning the same direction.

This requires that Alice has the ability to make all of the electrons of a set of electrons spin in the same direction, which runs into the “no control” issue.

The “no control” issue seems to come from that Alice must measure her set of electrons instead of manipulate her set of electrons. But what if instead of measuring her sets of electrons, Alice manipulates or does not manipulate her set of electrons?

Getting to a more specific question, does Alice have the ability to control all the spins of a set of electrons and, if so, can Bob identify if a set of electrons are all spinning the same direction or are spinning randomly? Or more generally: can quantum states be controlled or randomized for communication using quantum entanglement?

• Entanglement is the result of a correlation. Entanglement can be maintained if the Hamiltonian of the system has an eigenbasis of correlated states. If the components of the system are separated and are governed by their own Hamiltonian, the components evolve separately. If two sets of electrons were under this interaction Hamiltonian and then Alice and Bob took each set and the electrons have random spin orientations, Alice cannot manipulate her electrons in anyway to align Bob's electrons. All the entanglement guarantees is that their results will be correlated under the same manipulations. – Daniel Kerr Jul 10 '16 at 16:41
• So if Alice manipulates her electrons, then the entanglement is lost and Bob only sees random spin orientations, even though Alice's spins have all been aligned? – B. King Jul 12 '16 at 3:27
• If Alice manipulates her electrons then yes, from Bob's perspective the entanglement is lost unless she communicates to Bob what her manipulations were and what the result of those measurement were. This is assuming Bob didn't already have a complete description of the quantum state a priori and only has a description of the state of the particle he measures. Put in another way Bob only has access to the reduced density matrix traced over Alice's particle. From his perspective his particle is in a mixed state. – Daniel Kerr Jul 12 '16 at 3:40

The set of possible distributions from a density matrix $\rho$ is parametrized by some hidden variable $\lambda$ so that such correlations are statistically some summation $$C(a,~b)~=~\int d\lambda \rho(\lambda)A(a,~\lambda)B(b,~\lambda).$$ the settings for a detector $a,~a'$ and $b,~b'$ and their values $A$ and $B$ respectively determine differences $$C(a,~b)~-~C(a,~b')~=~\int d\lambda \rho(\lambda)A(a,~\lambda)\big(B(b,~\lambda)~-~B(b',~\lambda)\big)$$ by triangle inequality can be found to satisfy $$|C(a,~b)~-~C(a,~b')|~\le~2~\pm~|C(a',~b)~+~C(a',~b')|,$$ that gives the CHSH (Clauser, Horne, Shimony, Holt) inequality. This is a variant of the Bell inequality. This means there is no underlying classical system one can appeal to using this hidden variable $\lambda$. This also leads to the Tsirelson bound that I comment in greater detail here. This is backed by the Aspect experiments, which found violations these classical-like inequalities and support the existence of this quantum (Tsirelson) bound.
Now suppose that you did try anyway to communicate nonlocally. Say with the above spin particles in a magnetic field. The energy splitting is $\Delta E~=~\mu B_z$ and so the frequency is $\omega~=~\mu B_0/\hbar$. You then say, I will frequency modulate this so my partner with the other EPR pair can measure this precession modulate and receive a signal faster than light. That will not work, for with each qubit you partner has, half the Bell state, you have to furnish information about the setting of their apparatus to make the measurement. That gives them the full information necessary. That will require a classical signal.