Quantum Mechanical Bell Test Prediction - Demonstration of A Bell Inequality Violation

Demonstration of A Bell Inequality Violation

Now choose as the orientation angles of the transmission axes

a = 0, a′ = π/4, b = π/8, b′ = 3 π/8.

(6)

Then

EΦ(a, b) = cos 2(π/8) = 0.707,

(7a)

EΦ(a, b′) = cos 2(3π/8) = −0.707,

(7b)

EΦ(a′, b) = cos 2(−π/8) = 0.707,

(7c)

and

EΦ(a′, b′) = cos 2(π/8) = 0.707.

(7d)

Therefore the quantum mechanical prediction for the CHSH test statistic is

SΦ = EΦ(a, b) − EΦ(a, b′) + EΦ(a′, b) + EΦ(a′, b′) = 2.828,

(8)

exceeding the CHSH Bell test limit of 2 and thus completing the proof of a version of Bell's Theorem. In fact, all entangled quantum states yield predictions in violation of the inequality, as Gisin (1991) and Popescu and Rohrlich (1992) have independently demonstrated. Popescu and Rohrlich (1992) also show that the maximum amount of violation is achieved with a quantum state of maximum degree of entanglement, exemplified by |Φ> of Eq. (1).

Read more about this topic:  Quantum Mechanical Bell Test Prediction

Famous quotes containing the words bell, inequality and/or violation:

    You owe me ten shillings,
    Say the bells of St. Helen’s.
    When will you pay me?
    Say the bells of Old Bailey.
    When I grow rich,
    Say the bells of Shoreditch.
    Pray when will that be?
    Say the bells of Stepney.
    I am sure I don’t know,
    Says the great bell of Bow.
    —Unknown. The Bells of London (l. 13–22)

    A man willing to work, and unable to find work, is perhaps the saddest sight that fortune’s inequality exhibits under this sun.
    Thomas Carlyle (1795–1881)

    There is all the difference in the world between the criminal’s avoiding the public eye and the civil disobedient’s taking the law into his own hands in open defiance. This distinction between an open violation of the law, performed in public, and a clandestine one is so glaringly obvious that it can be neglected only by prejudice or ill will.
    Hannah Arendt (1906–1975)