Dear all,
Next week, Alessandro Palumbo will talk about “Frame-Dependent Traces and the Paradox of the Third Particle”. See below for the abstract.
The talk will take place on Tuesday at 11:00 in HIT E41.1.
Best, Ladina
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Title:
Frame-Dependent Traces and the Paradox of the Third Particle
Abstract:
Physical quantities are inherently frame-relative; accordingly, in the quantum regime, reference frames must be modelled as quantum systems. Within Quantum Reference Frames (QRFs), two main approaches have been developed: the Perspective-Neutral (PN) framework and the Quantum-Information–theoretic (QI) framework. In the PN framework, inconsistencies emerge when tracing subsystems in internal and external descriptions, giving rise to the Paradox of the Third Particle. In this work, we provide a novel, operational resolution of the Paradox. We formalise a statistical consistency requirement equating the external expectation values for gauge-invariant observables, obtained after discarding a subsystem, with the expectation values computed by an internal observer after tracing out in his perspective. We focus on how the notion of tracing out subsystems varies across QRF perspectives. Importantly, we compare the Partial Trace defined with respect to an external observer with the Partial Trace accessible to an internal perspective, carrying out this comparison in both the PN and QI settings. We show that the differing constraints imposed—namely, enforcing gauge invariance either by projection onto the zero–charge sector or by twirling over all charge sectors—lead to distinct outcomes across the two frameworks. In the PN framework, our statistical condition can be satisfied by a unique CP trace–non-increasing channel. We characterise the domain of validity of this map: it succeeds on a well-characterised class of states, whereas the Paradox in its original formulation cannot be resolved outside this class. Conversely, adopting an information-theoretic approach, we define a unique CPTP map performing the analogous task. Crucially, in the QI setting, once restricted to gauge-invariant observables, external and internal Partial Traces can always be consistently compared, thereby satisfying our statistical condition for every state.