Related papers: Random measurement bases, quantum state distinctio…
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…
The spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space…
We study a generalization of entanglement testing which we call the "hidden cut problem." Taking as input copies of an $n$-qubit pure state which is product across an unknown bipartition, the goal is to learn precisely where the state is…
Similarly to quantum states, also quantum measurements can be "mixed", corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely…
We describe a technique for self consistently characterizing both the quantum state of a single qubit system, and the positive-operator-valued measure (POVM) that describes measurements on the system. The method works with only ten…
Quantum noise constitutes a fundamental obstacle to realizing practical quantum technologies. To address the pivotal challenge of identifying quantum systems least affected by noise, we introduce the purest quantum state identification,…
Suppose we want to benchmark a quantum device held by a remote party, e.g. by testing its ability to carry out challenging quantum measurements outside of a free set of measurements $\mathcal{M}$. A very simple way to do so is to set up a…
It is known that the quantum fidelity, as a measure of the closeness of two quantum states, is operationally equivalent to the minimal overlap of the probability distributions of the two states over all possible POVMs; the POVM realizing…
We investigate the relationship between projective measurements and positive operator-valued measures (POVMs) in the task of quantum steering. A longstanding open problem in the field has been whether POVMs are more powerful than projective…
The reconstruction of quantum states from experimental measurements, often achieved using quantum state tomography (QST), is crucial for the verification and benchmarking of quantum devices. However, performing QST for a generic…
We discuss a possibility to build a programmable quantum measurement device (a "quantum multimeter"). That is, a device that would be able to perform various desired generalized, positive operator value measure (POVM) measurements depending…
The standard approach to quantum measurement discrimination is to perform the given unknown measurement on a probe state, possibly entangled with an auxiliary system, and make a decision based on the measurement outcome obtained. In this…
The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup…
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,…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
It is a fundamental property of quantum mechanics that information is lost as a result of performing measurements. Indeed, with every quantum measurement one can associate a number -- its POVM norm constant -- that quantifies how much the…
The discrimination of non-orthogonal quantum states with reduced or without errors is a fundamental task in quantum measurement theory. In this work, we investigate a quantum measurement strategy capable of discriminating two coherent…
Using the convex optimization method and Helstrom family of ensembles introduced in Ref. [1], we have discussed optimal ambiguous discrimination in qubit systems. We have analyzed the problem of the optimal discrimination of N known quantum…
In this report, we present a framework for implementing an arbitrary $n$-outcome generalized quantum measurement (POVM) on an $m$-qubit register as a sequence of two-outcome measurements requiring only single ancillary qubit. Our procedure…
We analyze quantum state tomography in scenarios where measurements and states are both constrained. States are assumed to live in a semi-algebraic subset of state space and measurements are supposed to be rank-one POVMs, possibly with…