Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTrade-off relations of l_1-norm coherence for multipartite systems
119
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the trade-off relations given by the l_1-norm coherence of general multipartite states. Explicit trade-off inequalities are derived with lower bounds given by the coherence of either bipartite or multipartite reduced density matrices. In particular, for pure three-qubit states, it is explicitly shown that the trade-off inequality is lower bounded by the three tangle of quantum entanglement.
rate research
Read More
We investigate the nonlocality distributions among multiqubit systems based on the maximal violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality of reduced pairwise qubit systems. We present a trade-off relation satisfied by these maximal violations, which gives rise to restrictions on the distribution of nonlocality among the subqubit systems. For a three-qubit system, it is impossible that all pairs of qubits violate the CHSH inequality, and once a pair of qubits violates the CHSH inequality maximally, the other two pairs of qubits must both obey the CHSH inequality. Detailed examples are given to illustrate the trade-off relations, and the trade-off relations are generalized to arbitrary multiqubit systems.
Quantum coherence is the most fundamental of all quantum quantifiers, underlying other well-known quantities such as entanglement, quantum discord, and Bell correlations. It can be distributed in a multipartite system in various ways -- for example, in a bipartite system it can exist within subsystems (local coherence) or collectively between the subsystems (global coherence) and exhibits a trade-off relation. In quantum systems with more than two subsystems, there are more trade-off relations, due to the various decomposition ways of the coherence. In this paper, we experimentally verify these coherence trade-off relations in adiabatically evolved quantum systems using a spin system by changing the state from a product state to a tripartite entangled state. We study the full set of coherence trade-off relations between the original state, the bipartite product state, the tripartite product state, and the decohered product state. We also experimentally verify the monogamy inequality and show that both the quantum systems are polygamous except for the initial product state. We find that despite the different types of states involved, the properties of the state in terms of coherence and monogamy are equivalent. This illustrates the utility of using coherence as a characterization tool for quantum states.
We investigate whether a trade-off relation between the diagonal elements of the mean square error matrix exists for the two-parameter unitary models with mutually commuting generators. We show that the error trade-off relation which exists in our models of a finite dimension system is a generic phenomenon in the sense that it occurs with a finite volume in the spate space. We analyze a qutrit system to show that there can be an error trade-off relation given by the SLD and RLD Cramer-Rao bounds that intersect each other. First, we analyze an example of the reference state showing the non-trivial trade-off relation numerically, and find that its eigenvalues must be in a certain range to exhibit the trade-off relation. For another example, one-parameter family of reference states, we analytically show that the non-trivial relation always exists and that the range where the trade-off relation exists is up to about a half of the possible range.
Entanglement and coherence are two essential quantum resources for quantum information processing. A natural question arises of whether there are direct link between them. And by thinking about this question, we propose a new measure for quantum state that contains concurrence and is called intrinsic concurrence. Interestingly, we discover that the intrinsic concurrence is always complementary to coherence. Note that the intrinsic concurrence is related to the concurrence of a special pure state ensemble. In order to explain the trade-off relation more intuitively, we apply it in some composite systems composed by a single-qubit state coupling four typical noise channels with the aim at illustrating their mutual transformation relationship between their coherence and intrinsic concurrence. This unified trade-off relation will provide more flexibility in exploiting one resource to perform quantum tasks and also provide credible theoretical basis for the interconversion of the two important quantum resources.
The quantification of the measurement uncertainty aspect of Heisenbergs Uncertainty Principle---that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two incompatible observables---has regained a lot of interest recently. Several approaches have been proposed and debated. In this paper we consider Ozawas definitions for inaccuracies (as root-mean-square errors) in approximate joint measurements, and study how these are constrained in different cases, whether one specifies certain properties of the approximations---namely their standard deviations and/or their bias---or not. Extending our previous work [C. Branciard, Proc. Natl. Acad. Sci. U.S.A. 110, 6742 (2013)], we derive new error-trade-off relations, which we prove to be tight for pure states. We show explicitly how all previously known relations for Ozawas inaccuracies follow from ours. While our relations are in general not tight for mixed states, we show how these can be strengthened and how tight relations can still be obtained in that case.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
