Quantum probabilities from quantum entanglement: experimentally unpacking the Born rule

Abstract

The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the quantum and classical realms, as it confers physical significance to reduced density matrices, the essential tools of decoherence theory. Following Bohr's Copenhagen interpretation, textbooks postulate the Born rule outright. However, recent attempts to derive it from other quantum principles have been successful, holding promise for simplifying and clarifying the quantum foundational bedrock. A major family of derivations is based on envariance, a recently discovered symmetry of entangled quantum states. Here, we identify and experimentally test three premises central to these envariance-based derivations, thus demonstrating, in the microworld, the symmetries from which the Born rule is derived. Further, we demonstrate envariance in a purely local quantum system, showing its independence from relativistic causality. rule as an axiom, following the Copenhagen interpretation and most textbooks, a physically transparent derivation would contribute greatly to clarifying the foundations of quantum mechanics. Given its importance to quantum mechanics, and to decoherence theory in particular, a satisfactory explanation of the quantum-toclassical transition depends upon one's ability to derive the Born probability rule (BPR) from simpler quantum mechanical principles.Attempts to reason up to the Born rule in this way have historically frustrated physicists and philosophers in equal measure 7 ; indeed, the absence of universally satisfactory derivations of the BPR has led more pragmatic workers to resign themselves to outright postulation of the Born rule 8 . Such a position is tantamount to abandoning any attempt to explain, on fundamental grounds, how quantum theory might possibly correspond to physical reality, and, as such, is an unpalatable option to many.Relatively recently, the BPR was shown to arise as a consequence of certain properties, which are known to arise from the entanglement of quantum states [8]. The central property, a symmetry known as envariance, has been subjected to tests in its nonlocal form [9], but until now, there has been no experimental substantiation of the other premises underlying this theoretical argument for the BPR. In other words, we know that entangled quantum states have symmetries that imply the Born rule, but we do not know whether physical systems indeed respect these (often counterintuitive) symmetries. The situation is similar to the 'EPR paradox' and Bell's theorem: its violation was predicted by quantum theory, but experimental tests were needed to ascertain that microsystems in our Universe really behave like this! Here, we demonstrate experimentally the validity of three key premises required by this envariance-based BPR derivation, and thereby show that the most controversial logical 'ingredients' of the proof are, in fact, physically soun...

Demonstration of entanglement assisted invariance on IBM's quantum experience

“…As a general observation we note that in both optical experiments [20] , [21] higher fidelities were achieved. However, demonstrating envariance for two qubits on Quantum Experience poses hardly any technical challenge, and more complicated situations including higher dimensional systems can be studied as well.…”

“…Originally discovered in a derivation of Born's rule [13] , [14] , [15] , [16] , it quickly became clear that the emergence of classical reality from quantum physics is deeply rooted in envariantly shared quantum information [17] , [18] , [19] . Nevertheless, the experimental demonstration of envariance poses formidable technological challenges that were only recently overcome in two (quantum) optical experiments [20] , [21] .…”

Eliminating ensembles from equilibrium statistical physics: Maxwell’s demon, Szilard’s engine, and thermodynamics via entanglement

“…1 and Fig. 2, and there are now several experiments [28][29][30][31] that test some of the tenets of the derivation we are about to present.…”

Foundations of statistical mechanics from symmetries of entanglement

“…Finally, we briefly analyze the situation of non-vanishing coupling Hamiltonians, S B h , . For the sake of simplicity we still assume that we can neglect its contribution to the internal energies, but we relax the assumption of ñ s k | being a product state (10). Generally, we have As before we are interested in the fraction of states available to  under the condition that the total internal energy,  E , is given and constant (12).…”