# Probing qubit by qubit: Properties of the POVM and the information/disturbance tradeoff

@article{Sparaciari2014ProbingQB, title={Probing qubit by qubit: Properties of the POVM and the information/disturbance tradeoff}, author={Carlo Sparaciari and Matteo G. A. Paris}, journal={International Journal of Quantum Information}, year={2014}, volume={12}, pages={1461012} }

We address the class of positive operator-valued measures (POVMs) for qubit systems that are obtained by coupling the signal qubit with a probe qubit and then performing a projective measurement on the sole probe system. These POVMs, which represent the simplest class of qubit POVMs, depends on 3 + 3 + 2 = 8 free parameters describing the initial preparation of the probe qubit, the Cartan representative of the unitary coupling, and the projective measurement at the output, respectively. We…

## 6 Citations

Quantum Nonlocality and Quantum Correlations in the Stern-Gerlach Experiment

- PhysicsEntropy
- 2018

This paper demonstrates that the Stern–Gerlach experiment possesses a quantum nonlocal character that has not previously been visualized or presented before, and shows that this feature of the SGE violates the Clauser–Horne–Shimony–Holt Bell inequality.

Disturbance-Disturbance uncertainty relation: The statistical distinguishability of quantum states determines disturbance

- PhysicsScientific Reports
- 2018

The Heisenberg uncertainty principle, which underlies many quantum key features, is under close scrutiny regarding its applicability to new scenarios. Using both the Bell-Kochen-Specker theorem…

Quantifying the hybrid entanglement of the Stern-Gerlach experiment using discrete reductions

- Computer Science, Physics
- 2021

A Survey of the Concept of Disturbance in Quantum Mechanics

- PhysicsEntropy
- 2019

This concise paper gathers the different concepts and definitions of disturbance that have emerged through time through time in Quantum Mechanics for the better understanding of this topic.

An effective iterative method to build the Naimark extension of rank-n POVMs

- Mathematics
- 2017

We revisit the problem of finding the Naimark extension of a probability operator-valued measure (POVM), i.e. its implementation as a projective measurement in a larger Hilbert space. In particular,…

Disturbance-Disturbance uncertainty relation: The statistical distinguishability of quantum states determines disturbance

- PhysicsScientific reports
- 2018

The Heisenberg uncertainty principle, which underlies many quantum key features, is under close scrutiny regarding its applicability to new scenarios, and it is proposed to quantify disturbance in terms of the square root of the Jensen-Shannon entropy distance between the probability distributions before and after the measurement process.

## References

SHOWING 1-10 OF 18 REFERENCES

Information Gain versus State Disturbance for a Single Qubit

- PhysicsOpen Syst. Inf. Dyn.
- 2006

It is pointed out that the optimality of efficient quantum operations among those inducing a given operator-valued measure is related to Davies' characterization of convex invariant functions on hermitian operators.

Canonical Naimark extension for generalized measurements involving sets of Pauli quantum observables chosen at random

- Mathematics, Physics
- 2013

We address measurement schemes where certain observables are chosen at random within a set of non-degenerate isospectral observables and then measured on repeated preparations of a physical system.…

Geometric theory of nonlocal two-qubit operations

- Physics, Mathematics
- 2003

We study nonlocal two-qubit operations from a geometric perspective. By applying a Cartan decomposition to su(4), we find that the geometric structure of nonlocal gates is a 3-torus. We derive the…

Discrimination of quantum states

- Computer Science
- 2004

In this tutorial review the power of the POVM concept is illustrated on examples relevant to applications in quantum cryptography, including generalized measurements (POVMs) in the Appendices.

The modern tools of quantum mechanics

- Physics
- 2012

We address the basic postulates of quantum mechanics and point out that they are formulated for a closed isolated system. Since we are mostly dealing with systems that interact or have interacted…

Optimal quantum repeaters for qubits and qudits

- Physics
- 2005

A class of optimal quantum repeaters for qubits is suggested. The schemes are minimal, i.e., they involve a single additional probe qubit, and optimal, i.e., they provide the maximum information…

Optimal probabilistic cloning and purification of quantum states

- Computer Science
- 2004

The examples reveal that the probabilistic cloner may yield higher fidelity than the best deterministic cloner even when the states that should be cloned are linearly dependent and are drawn from a continuous set.

Information-disturbance tradeoff in continuous-variable Gaussian systems

- Computer Science
- 2006

The tradeoff between information gain and state disturbance is quantified by fidelities and, after optimization with respect to the measurement, analyzed in terms of the energy carried by the signal and the probe.

Quantum nondemolition measurement saturates fidelity trade-off

- Physics
- 2005

Quantum mechanics sets a bound between the quality of estimation from measurement of a single copy of a d-level system and the degree of disturbance of this system. We show that ideal quantum…

Fidelity balance in quantum operations.

- PhysicsPhysical review letters
- 2001

I derive a tight bound between the quality of estimating the state of a single copy of a d-level system, and the degree the initial state has to be altered in the course of this procedure. This…