Abstract
Minimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their d 2 -outcomes are enough to reconstruct any d -dimensional quantum state. For this reason, MIC-POVMs are referred to as standard measurements for quantum information. Here, we report an experiment with entangled photon pairs that certifies, for what we believe is the first time, a MIC-POVM for qubits following a device-independent protocol (i.e., modeling the state preparation and the measurement devices as black boxes, and using only the statistics of the inputs and outputs). Our certification is achieved under the assumption of freedom of choice, no communication, and fair sampling.
Highlights
A minimal informationally complete positive operatorvalued measure (MIC-POVM) [1, 2] is a measurement on a d-dimensional quantum system that: (i) is informationally complete (IC), i.e., its statistics determine completely any quantum state and allow for a simple statereconstruction and (ii) is minimal, since it has the minimum number of outcomes a measurement must have to be IC, namely, d2 [3]
To identify the values of γxy and γbxy that provide the largest gap between the experimental value of (5) and the maximum possible value of (6), we performed a series of numerical optimizations using the Nelder-Mead method [22], with target function defined as the difference between experimental value of (5) and a bound of (6), with variable coefficients γxy and γbxy and fixed values of k
Quantum information identifies MIC-POVMs as the standard quantum measurements for information processing tasks as they are informationally complete and optimal for tomographic and cryptographic purposes
Summary
A minimal informationally complete positive operatorvalued measure (MIC-POVM) [1, 2] is a measurement on a d-dimensional quantum system that: (i) is informationally complete (IC), i.e., its statistics determine completely any quantum state and allow for a simple statereconstruction and (ii) is minimal, since it has the minimum number of outcomes a measurement must have to be IC, namely, d2 [3]. MIC-POVMs are the “standard” measurements in quantum information [10] and have a privileged role in informationtheoretic reconstructions of quantum theory [10]. MIC-POVMs have been aimed at in photonic experiments of qubit [11], qutrit [12, 13], and two-qubit [14] tomography, quantum key distribution [11], and generalized measurements using quantum walks [14, 15]. All these experiments made assumptions about the state preparation and the functioning of the measurement devices and have limited applicability to cryptographic scenarios
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