scholarly journals Locally undetermined states, generalized Schmidt decomposition, and application in distributed computing

2009 ◽  
Vol 9 (11&12) ◽  
pp. 997-1012
Author(s):  
Y. Feng ◽  
R. Duan ◽  
M. Ying
Keyword(s):  
Distributed Computing ◽  
Quantum State ◽  
Fault Tolerant ◽  
A Priori ◽  
Sufficient Conditions ◽  
Quantum States ◽  
Consensus Problem ◽  
Schmidt Decomposition ◽  
Pure States ◽  
Necessary And Sufficient

Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient conditions for a pure multipartite state to be locally undetermined, and moreover, characterizing precisely all the pure states sharing the same set of reduced states with it. Interestingly, local determinability of pure states is closely related to a generalized notion of Schmidt decomposition. Furthermore, we find that locally undetermined states have some applications to the well-known consensus problem in distributed computing. To be specific, given some physically separated agents, when communication between them, either classical or quantum, is unreliable, then there exists a totally correct and completely fault-tolerant protocol for them to reach a consensus if and only if they share a priori a locally undetermined quantum state.

scholarly journals ON THE EXISTENCE OF PHYSICAL TRANSFORMATIONS BETWEEN SETS OF QUANTUM STATES

2004 ◽  
Vol 02 (01) ◽  
pp. 11-21 ◽  
Author(s):  
ANTHONY CHEFLES ◽  
RICHARD JOZSA ◽  
ANDREAS WINTER
Keyword(s):  
Simple Proof ◽  
Sufficient Conditions ◽  
Quantum States ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Physical Transformation ◽  
Pure States ◽  
Necessary And Sufficient

Let A={ρ1,…,ρn} be a given set of quantum states. We consider the problem of finding necessary and sufficient conditions on another set B={σ1,…,σn} that guarantee the existence of a physical transformation taking ρi to σi for all i. Uhlmann has given an elegant such condition when both sets comprise pure states. We give a simple proof of this condition and develop some consequences. Then we consider multi-probabilistic transformations between sets of pure states which leads to conditions for the problem of transformability between A and B when one set is pure and the other is arbitrary.

Minimum guesswork discrimination between quantum states

2015 ◽  
Vol 15 (9&10) ◽  
pp. 737-758
Author(s):  
Weien Chen ◽  
Yongzhi Cao ◽  
Hanpin Wang ◽  
Yuan Feng
Keyword(s):  
Error Probability ◽  
Sufficient Conditions ◽  
Optimization Criterion ◽  
Quantum States ◽  
Actual State ◽  
Information Theoretic ◽  
Minimum Error ◽  
State Discrimination ◽  
Semidefinite Programming Problem ◽  
Necessary And Sufficient

Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able to use a brute-force strategy to query the state, discrimination measurement with minimum error probability does not necessarily minimize the number of queries to get the actual state. In light of this, we take Massey's guesswork as the underlying optimization criterion and study the problem of minimum guesswork discrimination. We show that this problem can be reduced to a semidefinite programming problem. Necessary and sufficient conditions when a measurement achieves minimum guesswork are presented. We also reveal the relation between minimum guesswork and minimum error probability. We show that the two criteria generally disagree with each other, except for the special case with two states. Both upper and lower information-theoretic bounds on minimum guesswork are given. For geometrically uniform quantum states, we provide sufficient conditions when a measurement achieves minimum guesswork. Moreover, we give the necessary and sufficient condition under which making no measurement at all would be the optimal strategy.

Multiconsensus of first-order multiagent systems with directed topologies

2020 ◽  
Vol 34 (23) ◽  
pp. 2050240
Author(s):  
Xiao-Wen Zhao ◽  
Guangsong Han ◽  
Qiang Lai ◽  
Dandan Yue
Keyword(s):  
Multiagent Systems ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Consensus Problem ◽  
Multiple Agents ◽  
First Order ◽  
The Matrix ◽  
Directed Topologies ◽  
Necessary And Sufficient ◽  
Theoretical Results

The multiconsensus problem of first-order multiagent systems with directed topologies is studied. A novel consensus problem is introduced in multiagent systems — multiconsensus. The states of multiple agents in each subnetwork asymptotically converge to an individual consistent value in the presence of information exchanges among subnetworks. Linear multiconsensus protocols are proposed to solve the multiconsensus problem, and the matrix corresponding to the protocol is designed. Necessary and sufficient conditions are derived based on matrix theory, under which the stationary multiconsensus and dynamic multiconsensus can be reached. Simulations are provided to demonstrate the effectiveness of the theoretical results.

scholarly journals The Problem of Invariance in Nonlinear Discrete-Time Dynamic Systems

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1241
Author(s):  
Alexey Zhirabok
Keyword(s):  
Discrete Time ◽  
Dynamic Systems ◽  
Fault Tolerant ◽  
Sufficient Conditions ◽  
Fault Detection And Isolation ◽  
Time Dynamic ◽  
Differentiable Functions ◽  
Algebra Of Functions ◽  
Necessary And Sufficient ◽  
Algebraic Approaches

The paper considers the problem of invariance with respect to the unknown input for discrete-time nonlinear dynamic systems. To solve the problem, the algebraic approaches, called algebra of functions and logic–dynamic approach, are used. Such approaches assume that description of the system may contain non-differentiable functions. Necessary and sufficient conditions of solvability the problem are obtained. Moreover, procedures which find the appropriate functions and matrices are developed. Some applications of such invariance in fault detection and isolation, disturbance decoupling problem, and fault-tolerant control are considered.

TWO-MODE GAUSSIAN DENSITY MATRICES AND SQUEEZING OF PHOTONS

1992 ◽  
Vol 06 (10) ◽  
pp. 1657-1709 ◽  
Author(s):  
ROBERT R. TUCCI
Keyword(s):  
Fundamental Equation ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Second Law ◽  
Gaussian State ◽  
Density Matrices ◽  
Duhem Equation ◽  
Gaussian Density ◽  
Pure States ◽  
Necessary And Sufficient

In this paper, we generalize to 2-mode states the 1-mode state results obtained in a previous paper. We study 2-mode Gaussian density matrices (i.e., density matrices of the form: exponential of a quadratic polynomial in the creation and annihilation operators for the two modes). We find a linear transformation which maps the two annihilation operators, one for each mode, into two new annihilation operators that are uncorrelated and unsqueezed. This allows us to express the density matrix as a product of two 1mode density matrices. We find general conditions under which 2-mode Gaussian density matrices become pure states. Possible pure states include the 2-mode squeezed pure states commonly mentioned in the literature, plus other pure states never mentioned before. We discuss the entropy and thermodynamic laws (Second Law, Fundamental Equation, and Gibbs-Duhem Equation) for the 2-mode states being considered. We study the change in entropy that is produced when a 2-mode Gaussian state is subjected to a measurement of the complex amplitude of one of its two modes. We derive upper and lower bounds for the final (i.e., after the measurement) entropy of the unmeasured mode, and we give necessary and sufficient conditions for the achievement of these bounds. The existence of the bounds is shown to be a consequence of the concavity property of the entropy function.

Quantum readout of Physical Unclonable Functions

2012 ◽  
Vol 10 (01) ◽  
pp. 1250001 ◽  
Author(s):  
BORIS ŠKORIĆ
Keyword(s):  
Quantum State ◽  
Degrees Of Freedom ◽  
Quantum Computer ◽  
Single Photon ◽  
Trusted Computing ◽  
A Priori ◽  
Special Property ◽  
Quantum States ◽  
Unique Challenge ◽  
Physical Unclonable Functions

Physical unclonable functions (PUFs) are physical structures that are hard to clone and have a unique challenge-response behavior. The term PUF was coined by Pappu et al. in 2001. That work triggered a lot of interest, and since then a substantial number of papers has been written about the use of a wide variety of physical structures for different security purposes such as identification, authentication, read-proof key storage, key distribution, tamper evidence, anti-counterfeiting, software-to-hardware binding and trusted computing. In this paper we propose a new security primitive: the quantum-readout PUF (QR-PUF). This is a classical PUF, without internal quantum degrees of freedom, which is challenged using a quantum state, e.g. a single-photon state, and whose response is also a quantum state. By the no-cloning property of unknown quantum states, attackers cannot intercept challenges or responses without noticeably disturbing the readout process. Thus, a verifier who sends quantum states as challenges and receives the correct quantum states back can be certain that he is probing a specific QR-PUF without disturbances, even if the QR-PUF is far away "in the field" and under hostile control. For PUFs whose information content is not exceedingly large, all currently known PUF-based authentication and anti-counterfeiting schemes require trusted readout devices in the field. Our quantum readout scheme has no such requirement. Furthermore, we show how the QR-PUF authentication scheme can be interwoven with quantum key exchange (QKE), leading to an authenticated QKE protocol between two parties. This protocol has the special property that it requires no a priori secret shared by the two parties, and that the quantum channel is the authenticated channel, allowing for an unauthenticated classical channel. We provide security proofs for a limited class of attacks. The proofs depend on the physical unclonability of PUFs and on the practical infeasibility of building a quantum computer.

scholarly journals An inverse spectral problem for Sturm-Liouville-type integro-differential operators with robin boundary conditions

2019 ◽  
Vol 50 (3) ◽  
pp. 207-221 ◽  
Author(s):  
Sergey Buterin
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Boundary Conditions ◽  
Differential Operators ◽  
A Priori ◽  
Sufficient Conditions ◽  
Robin Boundary Conditions ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
Robin Boundary

The perturbation of the Sturm--Liouville differential operator on a finite interval with Robin boundary conditions by a convolution operator is considered. The inverse problem of recovering the convolution term along with one boundary condition from the spectrum is studied, provided that the Sturm--Liouville potential as well as the other boundary condition are known a priori. The uniqueness of solution for this inverse problem is established along with necessary and sufficient conditions for its solvability. The proof is constructive and gives an algorithm for solving the inverse problem.

scholarly journals Consensus Analysis for High-Order Multi-Agent Systems without or with Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Zhengxin Wang ◽  
Yang Cao
Keyword(s):  
Partial Information ◽  
Sufficient Conditions ◽  
High Order ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Consensus Analysis ◽  
Agent Systems ◽  
Multi Agent ◽  
Necessary And Sufficient

This paper studies the consensus problem for a high-order multi-agent systems without or with delays. Consensus protocols, which only depend on the own partial information of agents and partial relative information with its neighbors, are proposed for consensus and quasi-consensus, respectively. Firstly, some lemmas are presented, and then a necessary and sufficient condition for guaranteeing the consensus is established under the consensus protocol without delays. Furthermore, communication delays are considered. Some necessary and sufficient conditions for solving quasi-consensus problem with delays are obtained. Finally, some simulations are given to verify the theoretical results.

scholarly journals INFORMATION AND OPTIMAL INVESTMENT IN DEFAULTABLE ASSETS

2014 ◽  
Vol 17 (08) ◽  
pp. 1450050 ◽  
Author(s):  
GIULIA DI NUNNO ◽  
STEFFEN SJURSEN
Keyword(s):  
Counting Process ◽  
Partial Information ◽  
A Priori ◽  
Sufficient Conditions ◽  
Random Measure ◽  
Optimal Investment ◽  
Terminal Time ◽  
Necessary And Sufficient ◽  
Forward Integration ◽  
Different Levels

We study optimal investment in an asset subject to risk of default for investors that rely on different levels of information. The price dynamics can include noises both from a Wiener process and a Poisson random measure with infinite activity. The default events are modeled via a counting process in line with large part of the literature in credit risk. In order to deal with both cases of inside and partial information we consider the framework of the anticipating calculus of forward integration. This does not require a priori assumptions typical of the framework of enlargement of filtrations. We find necessary and sufficient conditions for the existence of a locally maximizing portfolio of the expected utility at terminal time. We consider a large class of utility functions. In addition we show that the existence of the solution implies the semi-martingale property of the noises driving the stock. Some discussion on unicity of the maxima is included.

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