scholarly journals Approximating incompatible von Neumann measurements simultaneously

2010 ◽  
Vol 82 (3) ◽  
Author(s):  
Teiko Heinosaari ◽  
Maria Anastasia Jivulescu ◽  
Daniel Reitzner ◽  
Mario Ziman
Keyword(s):  
Von Neumann ◽  
Von Neumann Measurements

Bell inequality for quNits with binary measurements

2003 ◽  
Vol 3 (2) ◽  
pp. 157-164
Author(s):  
H. Bechmann-Pasquinucci ◽  
N. Gisin
Keyword(s):  
Quantum Cryptography ◽  
Bell Inequality ◽  
The Other ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Von Neumann ◽  
Chsh Inequality ◽  
Intermediate States ◽  
Von Neumann Measurements

We present a generalized Bell inequality for two entangled quNits. On one quNit the choice is between two standard von Neumann measurements, whereas for the other quNit there are N^2 different binary measurements. These binary measurements are related to the intermediate states known from eavesdropping in quantum cryptography. The maximum violation by \sqrt{N} is reached for the maximally entangled state. Moreover, for N=2 it coincides with the familiar CHSH-inequality.

scholarly journals Environment-induced dephasing versus von Neumann measurements in proton tunneling

2014 ◽  
Vol 90 (1) ◽  
Author(s):  
A. D. Godbeer ◽  
J. S. Al-Khalili ◽  
P. D. Stevenson
Keyword(s):  
Proton Tunneling ◽  
Von Neumann ◽  
Von Neumann Measurements

scholarly journals ON THE EQUIVALENCE OF THE CH AND CHSH INEQUALITIES FOR TWO THREE-LEVEL SYSTEMS

2003 ◽  
Vol 01 (01) ◽  
pp. 115-133 ◽  
Author(s):  
JOSÉ L. CERECEDA
Keyword(s):  
Quantum Efficiency ◽  
Quantum Systems ◽  
Optimal Choice ◽  
Entangled State ◽  
Von Neumann ◽  
Chsh Inequality ◽  
Realistic Description ◽  
Von Neumann Measurements ◽  
Chsh Inequalities

In this paper we show a Clauser-Horne (CH) inequality for two three-level quantum systems or qutrits, alternative to the CH inequality given by Kaszlikowski et al. [Phys. Rev. A65, 032118 (2002)]. In contrast to this latter CH inequality, the new one is shown to be equivalent to the Clauser-Horne-Shimony-Holt (CHSH) inequality for two qutrits given by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)]. Both the CH and CHSH inequalities exhibit the strongest resistance to noise for a nonmaximally entangled state for the case of two von Neumann measurements per site, as first shown by Acin et al. [Phys. Rev. A65, 052325 (2002)]. This equivalence, however, breaks down when one takes into account the less-than-perfect quantum efficiency of detectors. Indeed, for the noiseless case, the threshold quantum efficiency above which there is no local and realistic description of the experiment for the optimal choice of measurements is found to be [Formula: see text] for the CH inequality, whereas it is equal to [Formula: see text] for the CHSH inequality.

On the general quantum theory of measurement

1969 ◽  
Vol 65 (1) ◽  
pp. 111-122 ◽  
Author(s):  
Arthur I. Fine
Keyword(s):  
Quantum Theory ◽  
Theory Of Measurement ◽  
Quantum Measurements ◽  
Initial State ◽  
Von Neumann ◽  
General Quantum ◽  
Von Neumann Measurements ◽  
Quantum Theory Of Measurement

We use the term ‘measurement’ to refer to the interaction between an object and an apparatus on the basis of which information concerning the initial state of the object may be obtained from information on the resulting state of the apparatus. The quantum theory of measurement is a quantum theoretic investigation of such interactions in order to analyse the correlations between object and apparatus that measurement must establish. Although there is a sizeable literature on quantum measurements there appear to be just two sorts of interactions that have been employed. There are the ‘disturbing’ interactions consistent with the analysis of Landau and Peierls (8) as developed by Pauli (11) and by Landau and Lifshitz (7), and there are the ‘non-disturbing’ interactions explicitly set out by von Neumann ((10), chs. 5, 6), and that dominate the literature. In this paper we shall investigate the most general types of interactions that could possibly constitute measurements and provide a precise mathematical characterization (section 2). We shall then examine an interesting subclass, corresponding to Landau's ideas, that contains both of the above sorts of measurements (section 3). Finally, we shall discuss von Neumann measurements explicitly and explore the purported limitations suggested by Wigner(12) and Araki and Yanase (2). We hope, in this way, to provide a comprehensive basis for discussions of quantum measurements.

scholarly journals Local deterministic simulation of equatorial Von Neumann measurements on tripartite GHZ state

2014 ◽  
Vol 14 (1) ◽  
pp. 217-228
Author(s):  
Arup Roy ◽  
Amit Mukherjee ◽  
Some Sankar Bhattacharya ◽  
Manik Banik ◽  
Subhadipa Das
Keyword(s):  
Ghz State ◽  
Deterministic Simulation ◽  
Von Neumann ◽  
Von Neumann Measurements

scholarly journals On the optimal certification of von Neumann measurements

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Paulina Lewandowska ◽  
Aleksandra Krawiec ◽  
Ryszard Kukulski ◽  
Łukasz Pawela ◽  
Zbigniew Puchała
Keyword(s):  
Numerical Range ◽  
Statistical Significance ◽  
Measurement Procedure ◽  
Input State ◽  
Single Element ◽  
Single Shot ◽  
Quantum Channels ◽  
Von Neumann ◽  
Alternative Hypotheses ◽  
Von Neumann Measurements

AbstractIn this report we study certification of quantum measurements, which can be viewed as the extension of quantum hypotheses testing. This extension involves also the study of the input state and the measurement procedure. Here, we will be interested in two-point (binary) certification scheme in which the null and alternative hypotheses are single element sets. Our goal is to minimize the probability of the type II error given some fixed statistical significance. In this report, we begin with studying the two-point certification of pure quantum states and unitary channels to later use them to prove our main result, which is the certification of von Neumann measurements in single-shot and parallel scenarios. From our main result follow the conditions when two pure states, unitary operations and von Neumann measurements cannot be distinguished perfectly but still can be certified with a given statistical significance. Moreover, we show the connection between the certification of quantum channels or von Neumann measurements and the notion of q-numerical range.

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