Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNote on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures
51
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The monogamy relations satisfied by quantum correlation measures play important roles in quantum information processing. Generally they are given in summation form. In this note, we study monogamy relations in product form. We present product-form monogamy relations for Bell nonlocality for three-qubit and multi-qubit quantum systems. We then extend our studies to other quantum correlations such as concurrence.
rate research
Read More
We study the uncertainty relation in the product form of variances and obtain some new uncertainty relations with weight, which are shown to be tighter than those derived from the Cauchy Schwarz inequality.
The monogamy of quantum entanglement captures the property of limitation in the distribution of entanglement. Various monogamy relations exist for different entanglement measures that are important in quantum information processing. Our goal in this work is to propose a general monogamy inequality for all entanglement measures on entangled qubit systems. The present result provide a unified model for various entanglement measures including the concurrence, the negativity, the entanglement of formation, Tsallis-q entropy, Renyi-q entropy, and Unified-(q,s) entropy. We then proposed tightened monogamy inequalities for multipartite systems. We finally prove a generic result for the tangle of high-dimensional entangled states to show the distinct feature going beyond qubit systems. These results are useful for exploring the entanglement theory, quantum information processing and secure quantum communication.
We investigate the monogamy relations related to the concurrence and the entanglement of formation. General monogamy inequalities given by the {alpha}th power of concurrence and entanglement of formation are presented for N-qubit states. The monogamy relation for entanglement of assistance is also established. Based on these general monogamy relations, the residual entanglement of concurrence and entanglement of formation are studied. Some relations among the residual entanglement, entanglement of assistance, and three tangle are also presented.
Sensitivity conjecture is a longstanding and fundamental open problem in the area of complexity measures of Boolean functions and decision tree complexity. The conjecture postulates that the maximum sensitivity of a Boolean function is polynomially related to other major complexity measures. Despite much attention to the problem and major advances in analysis of Boolean functions in the past decade, the problem remains wide open with no positive result toward the conjecture since the work of Kenyon and Kutin from 2004. In this work, we present new upper bounds for various complexity measures in terms of sensitivity improving the bounds provided by Kenyon and Kutin. Specifically, we show that deg(f)^{1-o(1)}=O(2^{s(f)}) and C(f) < 2^{s(f)-1} s(f); these in turn imply various corollaries regarding the relation between sensitivity and other complexity measures, such as block sensitivity, via known results. The gap between sensitivity and other complexity measures remains exponential but these results are the first improvement for this difficult problem that has been achieved in a decade.
We present a new kind of monogamous relations based on concurrence and concurrence of assistance. For $N$-qubit systems $ABC_1...C_{N-2}$, the monogamy relations satisfied by the concurrence of $N$-qubit pure states under the partition $AB$ and $C_1...C_{N-2}$, as well as under the partition $ABC_1$ and $C_2...C_{N-2}$ are established, which give rise to a kind of restrictions on the entanglement distribution and trade off among the subsystems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
