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## Main Question or Discussion Point

I’m a layman who has reviewed some popular literature on QM. Apologies in advance for my naivety.

I’m of the impression that the quantum spin (±½) of an electron can be determined as it travels through a Stern-Gerlach apparatus (SGA) for the single direction in which the SGA is aligned (say, along the X-axis). Spin along other axes is a superposition of those states, with amplitudes corresponding to the angle departing from X. Spin is also said to be complementary. Spin measurement along different axes is mutually exclusive. For example, “

It seems possible, at least in theory, to obtain values for both X and Z spin at the same time by the following method. Please let me know where it goes wrong.

1). Two electrons are prepared in an entangled, total-spin-zero state (each has spin opposite the other).

2). Two SGAs are oriented perpendicularly, one X-axis aligned and the other Z-axis aligned.

3). Each entangled electron is sent simultaneously through one of the perpendicular SGAs.

4). Spin X is determined for one electron while spin Z is determined for the other, at the same time.

5). Each electron had spin opposite the other, so spin X

I’m of the impression that the quantum spin (±½) of an electron can be determined as it travels through a Stern-Gerlach apparatus (SGA) for the single direction in which the SGA is aligned (say, along the X-axis). Spin along other axes is a superposition of those states, with amplitudes corresponding to the angle departing from X. Spin is also said to be complementary. Spin measurement along different axes is mutually exclusive. For example, “

*A particle cannot have definite values for both X and Z at the same time.*” [ref]It seems possible, at least in theory, to obtain values for both X and Z spin at the same time by the following method. Please let me know where it goes wrong.

1). Two electrons are prepared in an entangled, total-spin-zero state (each has spin opposite the other).

2). Two SGAs are oriented perpendicularly, one X-axis aligned and the other Z-axis aligned.

3). Each entangled electron is sent simultaneously through one of the perpendicular SGAs.

4). Spin X is determined for one electron while spin Z is determined for the other, at the same time.

5). Each electron had spin opposite the other, so spin X

*and*spin Z of both electrons were simultaneously determined.
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