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Hong Kong researchers have demonstrated that indefinite causal order can yield unbounded energy savings in quantum metrology, overturning previous assumptions that such advantages were limited to constant factors. This breakthrough applies specifically to finite-dimensional systems in the pre-asymptotic regime, offering significant efficiency gains for estimating geometric phases without requiring infinite dimensions. The findings suggest practical pathways for optimizing resource-constrained quantum measurement protocols and autonomous devices.

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Hong Kong Team Finds Limitless Quantum Metrology Advantage

Quantum ZeitgeistOctober 3, 20265 min read

Can quantum sensors achieve unbounded gains in efficiency using only a finite number of dimensions? An indefinite ordering strategy now demonstrates an initial probe requiring *R* times less energy than any definite approach achieving equivalent precision when dimensionality scales as Ω(*N*²) and measurement shots are O(exp[π*d*/16]/poly(*d*)). This overturns suggestions that such benefits remain limited to constant factors within practical systems.

Investigations reveal advantageous behaviors typically observed within the context of a harmonic oscillator. This advantage is, however, specific to infinite-dimensional settings, and its finite-dimensional analogue remains elusive, with recent findings suggesting limitations to bounded constant factors in finite dimensions. Arbitrarily large advantages can arise for finite-dimensional systems operating in the finite sample regime. An unbounded separation exists between definite and indefinite causal order when estimating a geometric phase linked to two sets of N displacements generated by discrete position and momentum operators acting upon a d-dimensional quantum system; this holds true for any specified constant R. An…

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