Nice reference; didn't know it before. After ridiculing the textbook form of Born's rule, Peres says among others:
Just as in the thermal interpretation. In the introduction, he echoes another point of the thermal interpretation:Asher Peres said:If you visit a real laboratory, you will never find there Hermitian operators. All you can see are emitters (lasers, ion guns, synchrotrons and the like) and detectors. The experimenter controls the emission process and observes detection events. The theorist’s problem is to predict the probability of response of this or that detector, for a given emission procedure. Quantum mechanics tells us that whatever comes from the emitter is represented by a state ρ (a positive operator, usually normalized to 1). Detectors are represented by positive operators ##E_µ##, where µ is an arbitrary label whose sole role is to identify the detector. The probability that detector µ be excited is tr(ρ##E_µ##). A complete set of ##E_µ##, including the possibility of no detection, sums up to the unit matrix and is called a positive operator valued measure (POVM) .
The various ##E_µ## do not in general commute, and therefore a detection event does not correspond to what is commonly called the “measurement of an observable.” Still, the activation of a particular detector is a macroscopic, objective phenomenon. There is no uncertainty as to which detector actually clicked. [...]
Traditional concepts such as “measuring Hermitian operators,” that were borrowed or adapted from classical physics, are not appropriate in the quantum world. In the latter, as explained above, we have
emitters and detectors, and calculations are performed by means of POVMs.
Asher Peres said:The situation is much simpler: the pair of photons is a single, nonlocal, indivisible entity . . . It is only because we force upon the photon pair the description of two separate particles that we get the paradox [...]