Entropy Squeezing of Superposition States of Vacuum State and Coherent State x Shu-Fen Li, Hong-Cai Li (College of Physics and Optoelectronics Information Science and Technology, Fujian Normal University, Fuzhou 350007, China) Entropy Squeezing and Variance of Superposition State when the amplitudes R of weights b and coherent states take different values The compression satisfies the entropy uncertainty relation and the Heisenberg uncertainty relation respectively, and the entropy compression measures the compression property of the light field more sensitively than the variance compression.
Information entropy is a basic physical quantity in information science. This concept was first introduced by Shannon and Weaver. Information entropy as a measure of quantum state or classical state information was established by Wehrl. Recently, the Shannon entropy and WehrS of odd-even coherent state and superposition coherent state have been studied. The author discusses and obtains the relationship between entropy, field noise and compression, and shows that the study of entropy has both quantum information optics and the quantum statistical properties of the optical field. Significance.
The study of the optical field compression effect has always been an attractive research topic in quantum optics. In the past a large number of studies on the theory of optical field compression, generally starting from the Heisenberg uncertainty relationship, using a certain positive light field The variance of the cross component is used to measure the quantum fluctuation of the light field, and whether or not the quadrature component of the light field has a compression effect is judged based on whether it is smaller than the vacuum limit. However, according to the theory of statistical physics, in many cases, differential compression involves only the second-order statistical moments of the optical field density matrix and does not include high-order statistical moment information. Therefore, it is not possible to accurately measure sub-fluctuations. A more appropriate The physical quantity used to measure the fluctuations is the information entropy of the system. More than 40 years ago, Everett and Hirschman proposed the universal significance of the entropy uncertainty relationship, which was later proved by Beckner, Bialyniki-Birula and Mycielski. According to the entropy uncertainty relation, the method of variance compression can be used to measure the quantum fluctuation of the orthogonal component of the optical field with entropy, and the concept of entropy compression of the optical field is established. Fang Yufa et al. applied this method to study the entropy compressibility of various quantum states of different light fields.* Fund Project: Natural Science Foundation of Fujian Province (A0210014); Funding Project of Fujian Provincial Department of Education (JA02168). In this paper, we study the entropy compression properties of superposition state light fields in vacuum state and coherent state. By comparing entropy compression with variance compression, the relationship between entropy compression and variance compression is illustrated.
1 The entropy-squeezed vacuum state of the superposition state of the vacuum and coherent states I and the superposition state of the coherent state la are the quantum states (pure states or mixed states) described by the density matrix P, defining the position entropy and the momentum entropy respectively. For the corresponding entropy uncertainty relation =exp(Sp) is the entropy index, the expression of the wave function of the coherent state in the coordinate representation and the momentum representation is where the expression of the vacuum state in the coordinate representation and the momentum representation is: First, calculate the position entropy Sx0 and the momentum entropy Sp0 of the vacuum state. From (2) and (6), we can get the corresponding entropy index as W=ne(A=x,p). Weigh the A component of the light field and show the entropy compression. . It is easy to prove that positional entropy and momentum entropy of coherent states are obtained by equations (7) and (8). Both the positional entropy and the momentum entropy of the coherent state and the vacuum state are vacuum limits, satisfying the minimum entropy uncertainty relation and not appearing. Entropy compression.
- (6) The density matrix of the superposition state I> can be found in the coordinate representation and momentum representation as <xIPI x> = C* exp(-x). Substituting the above equation into (2) can solve for the superposition state The positional entropy and momentum entropy are difficult to find because of its analytical formula. The compressive properties of the superposition entropy are analyzed by numerical calculation. From (2) (9) (10), position entropy and momentum entropy are functions of R, b. To facilitate the analysis, let C = 0, b take different values, and plot the entropy index Wc, Wp as a function of the parameter R (particle size is -=IT2=R2) (see).
The curve of WX,WP with the parameter R is shown in (c) 1(d). When O=0, b takes a different value greater than zero. When R takes a small value, the entropy index wx of the superposition state W Ih has no compressibility, while the wp component has a change in the entropy index wxwp of the compressed superposition state Ih with the parameter R. Curvilinearity, which satisfies the uncertainty relation of entropy.
2 Variance Compression of the Superposition of Vacuum and Coherent States The two orthogonal amplitude operators of a single-mode optical field are defined as they satisfy the commutation relationship: = i The quantum of x, p is based on the Heisenberg uncertainty relation. The product of fluctuations should satisfy (Ax)2(A)2>(AA)2 If the light field is in the coherent state IT, the quantum fluctuation of its quadrature component operator xp is visible, and the coherent state is the amplitude of the light field. The minimum uncertainty of the operator x, and the mean square fluctuation of xp is the same. It is shown that the coherent state of the light field does not have a compression effect, and the vacuum state T=0 is a special case of the coherent state, and it also has no compression effect.
(12) can be obtained when the light field is in the superposition state of the vacuum state and the coherent state. The mean square fluctuation of the xp component is the mean square fluctuation (x) of the xp component when b takes a different value (Ax)2 (Ap 2) The curve with the parameter R changes from (c), 2(d): When = 0 and b> 0, the x-component of the superposed state Ih does not have compressibility, while the mean square fluctuation of the p-component is compared. (a) and (a): When b takes a different value less than zero and R=0~1, the mean square fluctuations of the entropy index wx and the x component of the superposition state Ih are both compressible and the wx ratio is x. The component mean square fluctuations more sensitively reflect the superposition state compression effect. When R takes a large value, the mean square fluctuations of the wx and x components are not compressed; comparing (b) and (b) results in: when R takes a large value, the mean square fluctuation of the p component is not compressed at all While the entropy index wp is compressible, the visible entropy index WP is more sensitive than the mean square fluctuation of the p component to measure the compression properties of the light field.
Comparing (c) 1(d) with (c), 2(d) can be obtained: when b is greater than zero, the entropy exponent wx mean square fluctuation (Ax)2(Ap)2 with the parameter R and The mean square fluctuations of the x component are not compressible, and the mean square fluctuations of the entropy exponent ang and the p component are compressible, and the mean square fluctuation of the angbi p component can more sensitively measure the compression properties of the superposition state.
3 Conclusion For the superposition Ih of the vacuum state and the coherent state, when the weight b and the amplitude r of the coherent state take different values, the entropy compression and the variance compression satisfy the entropy uncertainty relation and the Heisenberg uncertainty relation, respectively. Entropy compression is more achievable for highly sensitive measurement of compression than variance compression.
I-pulse feeder units are distinctively fabricated for I-pulse SMT pick and place machine models. I-pulse feeder designs are fitted to provide accuracy during component feeding process. I-pulse feeders are also capable of minimizing component loss. Our company provide good quality I-pulse feeder and we assure you that all our SMT feeders are well maintained and undergo strict quality assurance process before releasing it to our customers. Feel free to contact us for any inquiries regarding I-pulse feeder products and our customer support personnel are always on-line to provide answer.
Ipulse Feeder,IPulse Tape Feeder,IPulse Component Feeder,IPulse M1 Tape Feeder.Yamaha i-pulse Feeder
ShenZhen KDW Electronics Co.,Ltd , https://www.smtsplicetape.com