Compressively Characterizing High-Dimensional Entangled States with Complementary, Random Filtering

Abstract

The resources needed to conventionally characterize a quantum system are overwhelmingly large for high-dimensional systems. This obstacle may be overcome by abandoning traditional cornerstones of quantum measurement, such as general quantum states, strong projective measurement, and assumptionfree characterization. Following this reasoning, we demonstrate an efficient technique for characterizing high-dimensional, spatial entanglement with one set of measurements. We recover sharp distributions with local, random filtering of the same ensemble in momentum followed by position-something the uncertainty principle forbids for projective measurements. Exploiting the expectation that entangled signals are highly correlated, we use fewer than 5000 measurements to characterize a 65,536-dimensional state. Finally, we use entropic inequalities to witness entanglement without a density matrix. Our method represents the sea change unfolding in quantum measurement, where methods influenced by the information theory and signal-processing communities replace unscalable, brute-force techniques-a progression previously followed by classical sensing.

Quantifying Photonic High-Dimensional Entanglement

“…Several works have reported efficient methods for the full characterization of the quantum state [21][22][23][24], based on the extra assumption that the state is of high purity. Others discussed the certification of high-dimensional entanglement using mutually unbiased basis [25,26], two-dimensional subspaces [27], or assuming that certain quantities (e.g., total angular momentum) are conserved [15].…”

Characterizing Genuine Multilevel Entanglement

“…which shows decomposability into |GHZ (2) and |GHZ (3) The generalization to an arbitrary number of systems N and arbitrary dimension D follows straightforward. In summary, the state is is decomposable with respect to all possible bipartitions.…”

“…2 in the main text. We then apply V A1A2 , V D1D2 to |G (2) . Those are for the further analysis in this example defined as…”

Quantum process identification: a method for characterizing non-markovian quantum dynamics

“…Other areas of study closely related to QPI include the theory of non-Markovian quantum dynamics [16,17], the theory of quantum system identifiability [34], limitations of the quantum channel formalism [35][36][37], and the construction of effective bath models to simulate open quantum dynamics [38,39]. More broadly, QPI falls under the general topic of learning quantum states and dynamics [32,[40][41][42][43][44][45][46][47][48][49][50][51][52], including dimension estimation [53][54][55][56][57] and determination of causal structure [58].…”