# Classical randomness in quantum measurements

@article{DAriano2005ClassicalRI, title={Classical randomness in quantum measurements}, author={Giacomo Mauro D’Ariano and Paoloplacido Lo Presti and Paolo Perinotti}, journal={Journal of Physics A}, year={2005}, volume={38}, pages={5979-5991} }

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 classical nature. It is then natural to ask which apparatuses are indecomposable, i.e. do not correspond to any random choice of apparatuses. This problem is interesting not only for foundations, but also for applications, since most optimization strategies…

## 132 Citations

### Clean positive operator valued measures

- Mathematics
- 2005

In quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure (POVM). A quantum channel transforms POVMs into POVMs, generally…

### Bounding sets of sequential quantum correlations and device-independent randomness certification

- Computer Science, MathematicsQuantum
- 2020

This work shows how one can robustly certify over 2.3 bits of device-independent local randomness from a two-quibt state using a sequence of measurements, going beyond the theoretical maximum of two bits that can be achieved with non-sequential measurements.

### Implementation of quantum measurements using classical resources and only a single ancillary qubit

- Computer Sciencenpj Quantum Information
- 2022

It is argued that the scheme proposed can be favorable for experimental realization of POVMs, as noise compounding in circuits required by the scheme is typically substantially lower than in the standard scheme that directly uses Naimark’s dilation theorem.

### Maximal randomness from partially entangled states

- PhysicsPhysical Review Research
- 2020

Entangled quantum systems can be used to violate Bell inequalities. According to Bell's theorem, whenever we see a Bell violation we can be sure that the measurement outcomes are not the result of an…

### The unavoidable information flow to environment in quantum measurements

- PhysicsJournal of Mathematical Physics
- 2018

This work characterize the size of the post-measurement system by determining the class of measurements for the observable in question that allow the subsequent realization of any measurement process compatible with the said observable, and shows that these two classes coincide when the first observable is extreme.

### Studies on the Role of Entanglement in Mixed-state Quantum Computation

- Physics
- 2008

In this thesis, I look at the role of quantum entanglement in mixed-state quantum computation. The model we consider is the DQC1 or `power of one qubit' model. I show that there is minimal bipartite…

### Measures and applications of quantum correlations

- Physics, Computer Science
- 2016

This work gives an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations (QCs) in composite states, and focuses on various approaches to define and quantify general QCs, based on different yet interlinked physical perspectives.

### The information-theoretic costs of simulating quantum measurements

- Computer ScienceArXiv
- 2012

An extension of the Devetak–Winter theorem on classical data compression with quantum side information to the case in which the sender is not required to receive the outcomes of the simulated measurement, and a single-letter converse theorem demonstrating optimality is proved.

### Quantum steering: a review with focus on semidefinite programming

- Computer ScienceReports on progress in physics. Physical Society
- 2017

This review gives an overview of how to characterise quantum steering through semidefinite programming, which provides efficient numerical methods to address a number of problems, including steering detection, quantification, and applications.

### Simulating Positive-Operator-Valued Measures with Projective Measurements.

- MathematicsPhysical review letters
- 2017

This work proves that every measurement on a given quantum system can be realized by classical randomization of projective measurements on the system plus an ancilla of the same dimension, and shows that deciding whether it is PM simulable can be solved by means of semidefinite programming.

## References

SHOWING 1-10 OF 22 REFERENCES

### Quantum measuring processes of continuous observables

- Mathematics
- 1984

The purpose of this paper is to provide a basis of theory of measurements of continuous observables. We generalize von Neumann’s description of measuring processes of discrete quantum observables in…

### A single quantum cannot be cloned

- PhysicsNature
- 1982

If a photon of definite polarization encounters an excited atom, there is typically some nonvanishing probability that the atom will emit a second photon by stimulated emission. Such a photon is…

### Impossibility of measuring the wave function of a single quantum system.

- PhysicsPhysical review letters
- 1996

The general impossibility of determining the state of a single quantum system is proved for arbitrary measuring schemes, including a succession of measurements. Some recently proposed methods are…

### Informationally complete measurements and group representation

- Mathematics
- 2004

Informationally complete measurements on a quantum system allow one to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that…

### The quantum theory of measurement

- Physics
- 1991

The amazing accuracy in verifying quantum effects experimentally has recently renewed interest in quantum mechanical measurement theory. In this book the authors give within the Hilbert space…

### Quantum detection and estimation theory

- Physics
- 1969

A review. Quantum detection theory is a reformulation, in quantum-mechanical terms, of statistical decision theory as applied to the detection of signals in random noise. Density operators take the…

### Foundations of quantum mechanics and ordered linear spaces : Advanced Study Institute, Marburg 1973

- Mathematics
- 1974

Orderings of vector spaces.- Duality of cones in locally convex spaces.- Order unit and base norm spaces.- Minimal decompositions in base normed spaces.- Simplex spaces.- Representation of Banach…

### EXTREMAL DECISION RULES IN QUANTUM HYPOTHESIS TESTING

- Mathematics
- 1999

We present a complete description of the extreme points of the convex set of all decision rules in testing multiple hypotheses concerning a quantum system whose states are described by density…

### Probabilistic and Statistical Aspects of Quantum Theory

- Physics
- 1982

Foreword to 2nd English edition.- Foreword to 2nd Russian edition.- Preface.- Chapters: I. Statistical Models.- II. Mathematics of Quantum Theory.- III. Symmetry Groups in Quantum Mechanics.- IV.…