Measuring coherence of quantum measurements

Abstract

The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on the implementation of its complementary concept, coherence from quantum measurements. By devising an accessible criterion which holds true in any classical statistical theory, we demonstrate that noncommutative quantum measurements violate this constraint, rendering it possible to perform an operational assessment of the measurement-based quantum coherence. In particular, we verify that polarization measurements of a single photonic qubit, an essential carrier of one unit of quantum information, are already incompatible with classical, i.e., incoherent, models of a measurement apparatus. Thus, we realize a method that enables us to quantitatively certify which quantum measurements follow fundamentally different statistical laws than expected from classical theories and, at the same time, quantify their usefulness within the modern framework of resources for quantum information technology.

Experimental Progress on Quantum Coherence: Detection, Quantification, and Manipulation

“…[ 195,196 ] Frameworks suited to the coherence of quantum measurements have also been introduced. [ 197,198 ]…”

“…Ref. [197] first considered a method of detecting the coherence of a quantum measurement based on computing the variance of the measurement statistics and comparing it with classically (incoherently) achievable data. The practicality of this approach was demonstrated using data from a single‐qubit photonic experimental setup.…”

Direct characterization of coherence of quantum detectors by sequential measurements

“…[8][9][10][11][12][13][14][15] The time-reversal approach allows for the investigation of the properties of quantum measurements qualitatively from the perspective of quantum states. [16][17][18] In addition, the quantum resource theories for quantification of quantum properties of quantum measurements have been developed very recently [19][20][21][22] and have been applied to investigate coherence of quantumoptical detectors. 23 Thus developing efficient approaches to characterize the quantum properties of quantum measurements is important for both the fundamental investigations and practical applications.…”

Directly Characterizing the Coherence of Quantum Detectors by Sequential Measurement

“…[8][9][10][11][12][13][14][15] The time-reversal approach allows to investigate the properties of quantum measurements qualitatively from the perspective of quantum states. [16][17][18] In addition, the quantum resource theories to properly quantify the quantum properties of quantum measurements has been developed very recently, [19][20][21][22] and has been applied to investigate an important quantum property, the coherence, of quantum-optical detectors. 23 Thus, developing efficient approaches to characterize the quantum properties of quantum measurements is important for both the fundamental investigations and practical applications.…”