Mathematical nature of and a family of lower bounds for the success probability of unambiguous discrimination

2002 ◽  
Vol 65 (4) ◽  
Author(s):  
Xiaoming Sun ◽  
Shengyu Zhang ◽  
Yuan Feng ◽  
Mingsheng Ying
Keyword(s):  
Lower Bounds ◽  
Success Probability ◽  
Unambiguous Discrimination

scholarly journals Lower bounds of success probabilities for high-fidelity approach in KLM scheme

2018 ◽  
Vol 16 (04) ◽  
pp. 1850033
Author(s):  
Kazuto Oshima
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Quantum Teleportation ◽  
Success Probability ◽  
High Fidelity

In the Knill–Laflamme–Milburn (KLM) scheme, the success probability of quantum teleportation is given by [Formula: see text], where [Formula: see text] is the number of the ancilla qubits. For the high-fidelity approach in the KLM scheme, the success probability averaged for all input states is approximately given by [Formula: see text] for large [Formula: see text]. We give an exact lower bound of the success probability and show how the corresponding ancilla state is settled for the high-fidelity approach for arbitrary [Formula: see text].

Runtime Analysis of the (μ + 1) EA on Simple Pseudo-Boolean Functions

2006 ◽  
Vol 14 (1) ◽  
pp. 65-86 ◽  
Author(s):  
Carsten Witt
Keyword(s):  
Lower Bounds ◽  
Boolean Functions ◽  
Success Probability ◽  
Population Based ◽  
Upper And Lower Bounds ◽  
Rigorous Analysis ◽  
Search Spaces ◽  
Discrete Search ◽  
Family Trees ◽  
Theoretical Developments

Although Evolutionary Algorithms (EAs) have been successfully applied to optimization in discrete search spaces, theoretical developments remain weak, in particular for population-based EAs. This paper presents a first rigorous analysis of the (μ + 1) EA on pseudo-Boolean functions. Using three well-known example functions fromthe analysis of the (1 + 1) EA, we derive bounds on the expected runtime and success probability. For two of these functions, upper and lower bounds on the expected runtime are tight, and on all three functions, the (μ + 1) EA is never more efficient than the (1 + 1) EA. Moreover, all lower bounds growwith μ. On a more complicated function, however, a small increase of μ provably decreases the expected runtime drastically. This paper develops a newproof technique that bounds the runtime of the (μ + 1) EA. It investigates the stochastic process for creating family trees of individuals; the depth of these trees is bounded. Thereby, the progress of the population towards the optimum is captured. This new technique is general enough to be applied to other population-based EAs.

scholarly journals Multiple-shot and unambiguous discrimination of von Neumann measurements

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 425
Author(s):  
Zbigniew Puchała ◽  
Łukasz Pawela ◽  
Aleksandra Krawiec ◽  
Ryszard Kukulski ◽  
Michał Oszmaniec
Keyword(s):  
Success Probability ◽  
Adaptive Methods ◽  
Alternative Proof ◽  
Von Neumann ◽  
Minimum Error ◽  
Unambiguous Discrimination ◽  
Depth Study ◽  
Multiple Shot ◽  
Perfect Discrimination ◽  
Von Neumann Measurements

We present an in-depth study of the problem of multiple-shot discrimination of von Neumann measurements in finite-dimensional Hilbert spaces. Specifically, we consider two scenarios: minimum error and unambiguous discrimination. In the case of minimum error discrimination, we focus on discrimination of measurements with the assistance of entanglement. We provide an alternative proof of the fact that all pairs of distinct von Neumann measurements can be distinguished perfectly (i.e. with the unit success probability) using only a finite number of queries. Moreover, we analytically find the minimal number of queries needed for perfect discrimination. We also show that in this scenario querying the measurements in parallel gives the optimal strategy, and hence any possible adaptive methods do not offer any advantage over the parallel scheme. In the unambiguous discrimination scenario, we give the general expressions for the optimal discrimination probabilities with and without the assistance of entanglement. Finally, we show that typical pairs of Haar-random von Neumann measurements can be perfectly distinguished with only two queries.

PROGRAMMABLE AND CONTROLLED REMOTE UNAMBIGUOUS QUANTUM-STATE DISCRIMINATION BASED ON NONLOCAL SYSTEM–ANCILLA CONDITIONAL ROTATION

2011 ◽  
Vol 25 (22) ◽  
pp. 2991-2999
Author(s):  
LIBING CHEN ◽  
YUHUA LIU ◽  
HONG LU
Keyword(s):  
Quantum State ◽  
Quantum Channel ◽  
Success Probability ◽  
The State ◽  
Initial State ◽  
Final State ◽  
Unitary Evolution ◽  
Unambiguous Discrimination ◽  
State Discrimination ◽  
System Data

We propose and prove a theoretical scheme of realizing programmable and controlled remote quantum-state unambiguous discrimination (UD) based on nonlocal system–ancilla unitary evolution. By decomposing the evolution process from the initial state to the final state, we first construct the required nonlocal unitary evolution, which is a nonlocal conditional rotation. Utilizing the entanglement property of Greenberger–Horne–Zeilinger (GHZ) class state, we then design a quantum network for implementing the controlled nonlocal conditional rotation gate, and thus provide a feasible physical means to realize the remote UD. The features of the scheme is that the particular pair of states of system (data register) that can be remotely and unambiguously discriminated is specified by the state of the ancilla (program register). Furthermore, a third side is included, who may participate the process of quantum remote implementation as a supervisor. When the quantum channel is partially entangled, the third one can rectify the state distorted by the imperfect quantum channel. The success probability of implementing this remote UD is also investigated.

Sign in / Sign up

Export Citation Format

Share Document