International Journal of Quantum Information

SENSITIVITY OF HILBERT AND BURES DISTANCES TO QUBIT PERTURBATIONS

SIMONA SALVINI, Stefano Olivares, Matteo G. A. Paris

Published Feb 1, 2007• 1 citation

Abstract

We compare the sensitivity of Hilbert and Bures distances between two qubits in revealing small perturbations occurring to one of the qubits. We also analyze sensitivity in revealing perturbations to noise parameter of a depolarizing channel.

DOI: 10.1142/s0219749907002578

Related papers

Distances between qubits and sensitivity to perturbations

SIMONA SALVINI, Stefano Olivares, Matteo G. A. Paris

We address the sensitivity of Bures and Hilbert distances between two qubits in revealing (i) small perturbations occurring to one of the qubits and (ii) small changes of the noise parameter in a noisy channel. A general relation is derived, as well as specific bounds for perturbations induced by relevant noisy quantum channels.

Laser PhysicsApr 1, 20072 citations

Decoherence models and their effects on quantum maps and algorithms

Mario Leandro Aolita, Marcos Saraceno

In this work we study several models of decoherence and how different quantum maps and algorithms react when perturbed by them. Following closely Ref. [1], generalizations of the three paradigmatic one single qubit quantum channels (these are the depolarizing channel, the phase damping channel and the amplitude damping channel) for the case of an arbitrarily-sized finite-dimensional Hilbert space are presented, as well as other types of noise in phase space. More specifically, Grover's search algorithm's response to decoherence is analyzed; together with those of a family of quantum versions of chaotic and regular classical maps (the baker's map and the cat maps). A relationship between how sensitive to decoherence a quantum map is and the degree of complexity in the dynamics of its associated classical counterpart is observed; resulting in a clear tendency to react the more decoherently the more complex the associated classical dynamics is.

arXiv:quant-ph/0504211Apr 27, 20050 citations

Compare Quantum Operation Sensitivity for Different Distance Measures

Zhihao Ma, Wang Miao-Yin

In this paper, we compare the quantum operation sensitivity for different distance measures. We find that, among all usual distance measures, Bures fidelity is more sensitive to quantum operation than others. This may explain in some sense why fidelity is so useful in quantum information theory.

Communications in Theoretical PhysicsApr 1, 20102 citations

Weighted Bures length uncovers quantum state sensitivity

Paweł Kurzyński

The unitarity of quantum evolutions implies that an overlap between two initial states does not change in time. This property is commonly believed to explain the apparent lack of state sensitivity in quantum theory, a feature that is prevailing in classical chaotic systems. However, classical state sensitivity is based on a distance between two trajectories in phase space which is a completely different mathematical concept than an overlap between two vectors in Hilbert space. It is possible that state sensitivity in quantum theory can be detected with the help of some special metric. Here we show that the recently introduced Weighted Bures length achieves this task. We numerically investigate a unitary cellular automaton of N interacting qubits and analyze how a single-qubit perturbation affects the evolution of WBL between the unperturbed and perturbed states. We observe a linear growth of WBL if the qubits are arranged into a cyclic graph and an exponential growth if they are arranged into a random bipartite graph.

arXiv:2106.14081Physical review. ENov 18, 20213 citations

Geometric observation for Bures fidelity between two states of a qubit

Jing‐Ling Chen, Libin Fu, Abraham Albert Ungar +1 more

In this Brief Report, we present a geometric observation for the Bures fidelity between two states of a qubit.

arXiv:quant-ph/0112169Physical Review AJan 11, 200226 citations

Quantum differential privacy under noise channels

Ya-Ru Bai, Yuan-Hong Tao, Shuhui Wu +2 more

Abstract Quantum differential privacy is a way to protect privacy in quantum computing. It perturbs the final state of quantum computing by a specific quantum noise channel and makes the output useless to the attackers, so as to achieve privacy protection. In this paper, we study the quantum differential privacy under three channels: bit flip channel, phase flip channel and depolarizing channel. We calculate the privacy parameters for these three channels based on the proportional distance. We show the privacy protection capability by calculating the decay rates of the trace distances of two arbitrary quantum states before and after passing through the channels. Under the same privacy budget, we compare the fidelities, the trace distances between the real outputs and the outputs after entering the channels, and analyze the privacy protection performance of different quantum channels in detail.

Physica ScriptaFeb 12, 20242 citations