Transition Probability (fidelity) for pairs of density operators can be defined as "functor" in the hierarchy of "all" quantum systems and also within any quantum system. The introduction of "amplitudes" for density operators allows for a more intuitive treatment of these quantities, also pointing to a natural parallel transport. The latter is governed by a remarkable gauge theory with strong relations to the Riemann-Bures metric.
Protocols for discriminating between a pair of channels or for estimating a channel parameter can often be aided by adaptivity or by entanglement between the probe states. This can make it difficult to bound the best possible performance for such protocols. In this paper, we introduce a quantity that we call the relative fidelity of a given pair of channels and a pair of input states to those channels. Constraining the allowed input states to all pairs of states whose fidelity is greater than some minimum "input fidelity" and minimising this quantity over the valid pairs of states, we get the …
We compare and contrast the error probability and fidelity as measures of the quality of the receiver's measurement strategy for a quantum communications system. The error probability is a measure of the ability to retrieve {\it classical} information and the fidelity measures the retrieval of {\it quantum} information. We present the optimal measurement strategies for maximising the fidelity given a source that encodes information on the symmetric qubit-states.
Practical Fidelity Estimation for Noisy Quantum Devices Using Direct and Survival-Probability-Based Protocols
Indian Institute of Science Education and Research Mohali（印度科学教育研究学院莫哈利分校）；Technical University of Denmark（丹麦技术大学）；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；VTT Technical Research Centre of Finland（芬兰国家技术研究中心）
We present an algorithm of quantum engineering of large-amplitude>5 high-fidelity>0.99 even/odd Schrodinger cat states (SCSs) using a single mode squeezed vacuum (SMSV) state as resource. Set of k beam splitters (BSs) with arbitrary transmittance and reflectance coefficients sequentially following each other acts as a hub that redirects a multiphoton state into the measuring modes simultaneously measured by photon number resolving (PNR) detectors. We show that the multiphoton state splitting guarantees significant increase of the success probability of the cat state generator compared to its i…
Silicon offers an attractive material platform for hardware realization of quantum computing. In this study, a microscopic stochastic simulation method is developed to model the effect of random interface charge traps in silicon metal-oxide-semiconductor (MOS) quantum gates. The statistical results show that by using a fast two-qubit gate in isotopically purified silicon, the two-qubit silicon-based quantum gates have the fidelity >98% with a probability of 75% for the state-of-the-art MOS interface quality. By using a composite gate pulse, the fidelity can be further improved to >99.5% with t…
Trace inequalities are general techniques with many applications in quantum information theory, often replacing classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivate entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki $L_p$ spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki-Lieb-Thirring and Golden-Thompson inequalities from (Sutter, Berta \& Tomamichel 2017). Then, using the Haag…
In this paper we study the protection of N-qubit Greenberger-Horne- Zeilinger (GHZ) state and generalized N-qubit GHZ states in amplitude damping channel by means of quantum weak measurement and flip operations. We derive the explicit formulas of the performances of the protection scheme: average fidelity, average probability and the average quantum fisher information (QFI). Moreover, the analytical results for maximizing the average fidelity and probability are obtained. We show that our scheme can effectively protect the average QFI of phase for GHZ states and generalized GHZ states. The pro…
High fidelity quantum state transfer is an essential part of quantum information processing. In this regard, we address the problem of maximizing the fidelity in a quantum state transformation process satisfying the Liouville-von Neumann equation. By introducing fidelity as the performance index, we aim at maximizing the similarity of the final state density operator with the one of the desired target state. Optimality conditions in the form of a Maximum Principle of Pontryagin are given for the matrix-valued dynamic control systems propagating the probability density function. These provide a…
Efficient and high-fidelity entanglement in cavity QED without high cooperativity
Institute of Atomic and Molecular Sciences, Academia Sinica（中央研究院原子与分子科学研究所）；John A. Paulson School of Engineering and Applied Science, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Division of Physics, Mathematics and Astronomy, and Alliance for Quantum Technologies (AQT), California Institute of Technology（加州理工学院物理、数学和天文学系及量子技术联盟）；Department of Physics, Harvard University（哈佛大学物理系）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
In this paper, a generalized input state dependent deletion machine called probabilistic quantum deletion machine is proposed. Considering the Pati-Braunstein deletion machine as a benchmark, the machine is characterized by its deletion probability and the probability of error in deletion. It is observed that there are parameters for which increase in error in deletion can increase the fidelity of deletion. It is also shown that the Pati-Braunstein deletion machine is easily derivable for a certain value of deletion probability. Further the deletion machine can offer better fidelity of deletio…
Purity and coherence of a quantum state are recognized as useful resources for various information processing tasks. In this article, we propose a fidelity based valid measure of purity and coherence monotone and establish a relationship between them. This formulation of coherence is extended to quantum correlation relative to measurement. We have also studied the role of weak measurement on purity.
Universality cost of non-Gaussian enhancement in continuous-variable quantum teleportation: A fidelity--deviation trade-off
Institute for Convergence Research and Education in Advanced Technology, Yonsei University（延世大学先进技术与教育融合研究所）；Department of Statistics and Data Science, Yonsei University（延世大学统计与数据科学系）；Department of Physics, Jeju National University（济州国立大学物理系）；Department of Quantum Information, Yonsei University（延世大学量子信息系）
