Nonlocality and the Correlation of Measurement Bases

Abstract

Nonlocal nature apparently shown in entanglement is one of the most striking features of quantum theory. We examine the locality assumption in Bell-type proofs for entangled qubits, i.e. the outcome of a qubit at one end is independent of the basis choice at the other end. It has recently been claimed that in order to properly incorporate the phenomenon of self-observation, the Heisenberg picture with time going backwards provides a consistent description. We show that, if this claim holds true, the assumption in nonlocality proofs that basis choices at two ends are independent of each other may no longer be true, and may pose a threat to the validity of Bell-type proofs. Key words: Nonlocality, Basis choices, EntanglementThe nonlocal nature exhibited in quantum entanglement is arguably the most distinctive departure from classical physics. After Bell's pioneering work [1] in testing nonlocality in entangled quantum systems, a number of variations of theoretical models [2,3,4] and experimental confirmations have followed [5]. While these truly marvelous results appear to have confirmed the validity of quantum theory and triumphed over locality imposed by relativity, subtle related issues remain. That is, although quantum theory indeed appears to possess nonlocality, this property cannot be used for superluminal signalling. This is rather puzzling because there seems to exist faster-than-light influencing yet superluminal signalling is not allowed. Another puzzling feature related to entanglement is the negativity shown in the conditional entropy of entangled quantum systems [6]. While a number of interpretations have been made with regard to this negativity [7], this issue is still considered to be unsettled [8]. Due to this negativity, Cerf and Adami [6] have proposed to interpret entanglement as a qubit and anti-qubit correlation where anti-qubit is a qubit traveling backwards in time.In Bell-type inequality proofs such as that of Clauser-Horne-Shimony-Holt [2],

Relational Decision-Making Processes

“…In order to examine the properties of entanglement in a new model, it is appropriate to study the physical reality of the observer's choice of reference frame with respect to the observed (i.e., as opposed to the previous consideration of observed [state vectors] with respect to observers [observables]). In (Song, 2009), the correlation of the observer's choices was considered with the following entangled state:…”