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… 

Figures from this paper

Quantum Nonlocality and Quantum Correlations in the Stern-Gerlach Experiment
TLDR
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
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
A Survey of the Concept of Disturbance in Quantum Mechanics
TLDR
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
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
TLDR
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
TLDR
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
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
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
TLDR
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
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
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
TLDR
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
TLDR
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
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.
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
...
1
2
...