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Abstract
Any interaction between finite quantum systems in a separable joint state can be viewed as encoding classical information on an induced holographic screen. Here we show that when such an interaction is represented as a measurement, the quantum reference frames (QRFs) deployed to identify systems and pick out their pointer states induce decoherence, breaking the symmetry of the holographic encoding in an observer-relative way. Observable entanglement, contextuality, and classical memory are, in this representation, logical and temporal relations between QRFs. Sharing entanglement as a resource requires a priori shared QRFs.
Highlights
The holographic principle (HP) states, in its covariant formulation, that for any finite spacelike boundary B, open or closed, the classical, thermodynamic entropy S(L(B)) of any light-sheet L(B) of B satisfies: Received: 9 February 2021 Accepted: 27 February 2021 Published: 3 March 2021Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.S(L(B)) ≤ A(B)/4, (1)where A(B) is the area of B in Planck units [1]
The HP was motivated by the Bekenstein bound on the thermodynamic entropy of a black hole (BH), and has traditionally been interpreted as a bound on the thermodynamic entropy of, and the classical information encodable on, an independently-defined surface B, e.g., the stretched horizon of a BH [2,3]; see [1,4] for reviews
We show that sequential pointer measurements break the SN symmetry of the screen B, inducing decoherence (Section 3.3)
Summary
The holographic principle (HP) states, in its covariant formulation, that for any finite spacelike boundary B, open or closed, the classical, thermodynamic entropy S(L(B)) of any light-sheet L(B) of B satisfies: Received: 9 February 2021 Accepted: 27 February 2021 Published: 3 March 2021. A obtains exactly N bits of information about B from this channel and vice versa, entirely independently of the internal dynamics HA and HB With this construction, we can state the following generalized holographic principle (cf [5] Thm. 1): GHP: If but only if a pair of finite quantum systems A and B have a separable joint state |AB = |A |B , there is a finite spacelike surface B, with area A(B) ≥ A(B)min = 4ln2NlP2 , N the dimension of HAB and lP the Planck length, that implements HAB as a classical channel. These results together suggest that, far from being “an apparent law of physics that stands by itself” [1], the HP in its generalized GHP form is central to quantum information theory
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