Entanglement transformations of pure Gaussian states

2003 ◽  
Vol 3 (3) ◽  
pp. 211-233
Author(s):  
G. Giedke ◽  
J. Eisert ◽  
J.I. Cirac ◽  
M.B. Plenio
Keyword(s):  
Phase Shifts ◽  
Gaussian State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Optical Elements ◽  
Classical Communication ◽  
Gaussian States ◽  
Beam Splitters ◽  
Pure States ◽  
Necessary And Sufficient

We present a theory of entanglement transformations of Gaussian pure states with local Gaussian operations and classical communication. This is the experimentally accessible set of operations that can be realized with optical elements such as beam splitters, phase shifts and squeezers, together with homodyne measurements. We provide a simple necessary and sufficient condition for the possibility to transform a pure bipartite Gaussian state into another one. We contrast our criterion with what is possible if general local operations are available.

scholarly journals Purification of two-qubit mixed states

2002 ◽  
Vol 2 (5) ◽  
pp. 348-354
Author(s):  
E. Jan\'e
Keyword(s):  
Qubit State ◽  
Entangled State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Mixed States ◽  
Classical Communication ◽  
Maximally Entangled State ◽  
Optimal Protocol ◽  
Necessary And Sufficient

We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of $n$ copies of a two-qubit state.

Local distinguishability of quantum states and the distillation of entanglement

2003 ◽  
Vol 3 (3) ◽  
pp. 203-210
Author(s):  
P.-X. Chen ◽  
C.-Z. Li
Keyword(s):  
Information Entropy ◽  
Quantum States ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Maximal Yield ◽  
Pure States ◽  
New Interpretation ◽  
Necessary And Sufficient ◽  
Special Protocol

This paper tries to probe the relation between the local distinguishability of orthogonal quantum states and the distillation of entanglement. An new interpretation for the distillation of entanglement and the distinguishability of orthogonal quantum states in terms of information is given, respectively. By constraining our discussion on a special protocol we give a necessary and sufficient condition for the local distinguishability of the orthogonal pure states, and gain the maximal yield of the distillable entanglement. It is shown that the information entropy, the locally distinguishability of quantum states and the distillation of entanglement are closely related.

scholarly journals Optimal probes and error-correction schemes in multi-parameter quantum metrology

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 288
Author(s):  
Wojciech Górecki ◽  
Sisi Zhou ◽  
Liang Jiang ◽  
Rafał Demkowicz-Dobrzański
Keyword(s):  
Parameter Estimation ◽  
Error Correction ◽  
Semidefinite Program ◽  
Sufficient Condition ◽  
Quantum Metrology ◽  
Necessary And Sufficient Condition ◽  
Estimation Precision ◽  
Pure States ◽  
Necessary And Sufficient ◽  
Quantum Error

We derive a necessary and sufficient condition for the possibility of achieving the Heisenberg scaling in general adaptive multi-parameter estimation schemes in presence of Markovian noise. In situations where the Heisenberg scaling is achievable, we provide a semidefinite program to identify the optimal quantum error correcting (QEC) protocol that yields the best estimation precision. We overcome the technical challenges associated with potential incompatibility of the measurement optimally extracting information on different parameters by utilizing the Holevo Cramér-Rao (HCR) bound for pure states. We provide examples of significant advantages offered by our joint-QEC protocols, that sense all the parameters utilizing a single error-corrected subspace, over separate-QEC protocols where each parameter is effectively sensed in a separate subspace.

Complete Sets of Observables and Pure States

1968 ◽  
Vol 20 ◽  
pp. 1276-1280 ◽  
Author(s):  
Stanley P. Gudder
Keyword(s):  
Weak Topology ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complete Set ◽  
Pure States ◽  
Complete Sets ◽  
Necessary And Sufficient

It was shown in (1) that a complete set of bounded observables is metrically complete. However, an extra axiom was needed to prove this result (1, footnote, p. 436). In this note we prove the above-mentioned result without the extra axiom. We also show that there is an abundance of pure states if M is closed in the weak topology and give a necessary and sufficient condition for the latter to be the case.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

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