Quantum Instruments

Post date: May 14, 2013 3:28:20 PM

The first paper in the series is written with Justin Dressel. He has been developing a stateless formulation of quantum mechanics. The essential idea is both preparations and detections of a particle can be viewed as operations of some more general object, the quantum instrument. The later idea is quite old, being first described by Davies and Lewis in 1970 - but given in a rather impenetrable mathematical way so the idea has not really made its way out of the 70's. We take this approach, and show how any measurement outcome or correlation function can be reformulated as actions of the quantum instrument - with no mention of quantum states (or observables) at all! Even stranger, when we go to reintroduce states to the picture, we can get the usual picture of a density operator predicting the outcomes of future measurements - but we can also get a "retrodictive" density operator, that produces retrodictions of events that happened in the past, but have no direct access to. We even get things like "bidirectional states" and "interdictive states", objects that describe the statistics of events when there are past and future boundary conditions on the state, or that describe both past and future events at the same time, respectively.

We give examples of these states with a detector that can resolve photon number - up until a saturation number.

We also make connection with the "two-time" reformulation of Aharonov et al. The things Yakir Aharonov and his collaborators interpret as retro-causal, we interpret as retro-dictive. In other words, it is about the process of mental inference from future to past, rather than the future affecting the past in a physical or mechanistic way.

This also puts our oar into the ongoing debate about the reality status of the quantum wavefunction. As card-carrying Quantum Bayesians, we don't subscribe to any physical reality of the wavefunction. Indeed, if all statistics about events in the laboratory can be reproduced with no mention of the state at all, we are back to just the outcomes of events - and the quantum instrument - as the bedrock reality.