Related papers: Quantum Tomography under Prior Information
Quantum mechanics describes seemingly paradoxical relations between the outcomes of measurements that cannot be performed jointly. In Hilbert space, the outcomes of such incompatible measurements are represented by non-orthogonal states. In…
Quantum theory imposes fundamental limitations to the amount of information that can be carried by any quantum system. On the one hand, Holevo bound rules out the possibility to encode more information in a quantum system than in its…
Quantum tomography is a critically important tool to evaluate quantum hardware, making it essential to develop optimized measurement strategies that are both accurate and efficient. We compare a variety of strategies using nearly pure test…
Quantum labeling tasks ask one to recover the missing associations between classical outcome labels and the effects forming the POVM. We study labeling in the multiple-shot regime, allowing a finite number of uses of the device and the most…
Self-testing is a promising approach to certifying quantum states or measurements. Originally, it relied solely on the outcome statistics of the measurements involved in a device-independent (DI) setup. Extra physical assumptions about the…
In this paper we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can…
We present a two-step protocol for quantum measurement tomography that is light on classical co-processing cost and still achieves optimal sample complexity in the system dimension. Given measurement data from a known probe state ensemble,…
Efficiently extracting information from pure quantum states using minimal observables on the main system is a longstanding and fundamental issue in quantum information theory. Despite the inability of probability distributions of position…
Measurement incompatibility is a cornerstone of quantum mechanics. In the context of estimating multiple parameters of a quantum system, this manifests as a fundamental trade-off between the precisions with which different parameters can be…
We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some…
In the general theory of quantum measurement, one associates a positive semidefinite operator on a $d$-dimensional Hilbert space to each of the $n$ possible outcomes of an arbitrary measurement. In the special case of a projective…
Characterizing complex quantum systems is a vital task in quantum information science. Quantum tomography, the standard tool used for this purpose, uses a well-designed measurement record to reconstruct quantum states and processes. It is,…
We prove necessary and sufficient conditions for the informational completeness of an arbitrary set of Gaussian observables on continuous variable systems with finite number of degrees of freedom. In particular, we show that an…
We show that measuring any two quantum states by a random POVM, under a suitable definition of randomness, gives probability distributions having total variation distance at least a universal constant times the Frobenius distance between…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
Starting from a simple estimation problem, here we propose a general approach for decoding quantum measurements from the perspective of information extraction. By virtue of the estimation fidelity only, we provide surprisingly simple…
Many prominent quantum computing algorithms with applications in fields such as chemistry and materials science require a large number of measurements, which represents an important roadblock for future real-world use cases. We introduce a…
Here, we leverage recent advances in information theory to develop a novel method to characterise the dominant character of the high-order dependencies of quantum systems. To this end, we introduce the Q-information: an…
Characterization of quantum processes is a preliminary step necessary in the development of quantum technology. The conventional method uses standard quantum process tomography, which requires $d^2$ input states and $d^4$ quantum…
We investigate the problem of bounding the quantum process fidelity given bounds on the fidelities between target states and the action of a process on a set of pure input states. We formulate the problem as a semidefinite program and prove…