On Uncertainty Relations and Entanglement Detection with Mutually Unbiased Measurements (original) (raw)

Estimating entanglement of unknown states

Applied Physics Letters, 2006

The experimental determination of entanglement is a major goal in the quantum information field. In general the knowledge of the state is required in order to quantify its entanglement. Here we express a lower bound to the robustness of entanglement of a state based only on the measurement of the energy observable and on the calculation of a separability energy. This allows the estimation of entanglement dismissing the knowledge of the state in question.

Entanglement certainty from the uncertainty principle for sequential measurements

We present a new paradigm for capturing the complementarity of two observables. It is based on the entanglement created by the interaction between the system observed and the two measurement devices used to measure the observables sequentially. Our main result is a lower bound on this entanglement and resembles well-known entropic uncertainty relations. Besides its fundamental interest, this result directly bounds the effectiveness of sequential bipartite operations---corresponding to the measurement interactions---for entanglement generation. We further discuss the intimate connection of our result with two primitives of information processing, namely, decoupling and coherent teleportation.

Entanglement in mutually unbiased bases

New Journal of Physics, 2011

One of the essential features of quantum mechanics is that most pairs of observables cannot be measured simultaneously. This phenomenon is most strongly manifested when observables are related to mutually unbiased bases. In this paper, we shed some light on the connection between mutually unbiased bases and another essential feature of quantum mechanics, quantum entanglement. It is shown that a complete set of mutually unbiased bases of a bipartite system contains a fixed amount of entanglement, independently of the choice of the set. This has implications for entanglement distribution among the states of a complete set. In prime-squared dimensions we present an explicit experiment-friendly construction of a complete set with a particularly simple entanglement distribution. Finally, we describe basic properties of mutually unbiased bases composed only of product states. The constructions are illustrated with explicit examples in low dimensions. We believe that properties of entanglement in mutually unbiased bases might be one of the ingredients to be taken into account to settle the question of the existence of complete sets. We also expect that they will be relevant to applications of bases in the experimental realization of quantum protocols in higher-dimensional Hilbert spaces.

Detection of entanglement with few local measurements

Physical Review A, 2002

We introduce a general method for the experimental detection of entanglement by performing only few local measurements, assuming some prior knowledge of the density matrix. The idea is based on the minimal decomposition of witness operators into a pseudo-mixture of local operators. We discuss an experimentally relevant case of two qubits, and show an example how bound entanglement can be detected with few local measurements. 03.67.Dd, 03.67.Hk, A central aim in the physics of quantum information is to create and detect entanglement -the resource that allows to realize various quantum protocols. Recently, much progress has been achieved experimentally in creating entangled states . In every real experiment noise and imperfections are present so that the generated states, although intended to be entangled, may in fact be separable. Therefore, it is important to find efficient experimental methods to test whether a given imperfect state ρ is indeed entangled.

Entropic uncertainties for joint quantum measurements

Physical Review A, 2009

We investigate the uncertainty associated with a joint quantum measurement of two spin components of a spin-1/2 particle and quantify this in terms of entropy. We consider two entropic quantities: the joint entropy and the sum of the marginal entropies, and obtain lower bounds for each of these quantities. For the case of joint measurements where we measure each spin observable equally well, these lower bounds are tight.

Entanglement detection via the condition of quantum correlation

Physical Review A, 2007

We develop a necessary condition of quantum correlation. It is utilized to construct a d-level bipartite Bell-type inequality which is strongly resistant to noise and requires only analyses of O͑d͒ measurement outcomes compared to the previous result O͑d 2 ͒. Remarkably, a connection between the arbitrary highdimensional bipartite Bell-type inequality and entanglement witnesses is found. Through the necessary condition of quantum correlation, we propose that the witness operators to detect truly multipartite entanglement for a generalized Greenberger-Horne-Zeilinger ͑GHZ͒ state with two local measurement settings and a four-qubit singlet state with three settings. Moreover, we also propose a robust entanglement witness to detect a four-level tripartite GHZ state with only two local measurement settings.

Detecting Entanglement of Unknown Quantum States with Random Measurements

In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the use of random local measurements, from which entanglement witnesses are then constructed via semidefinite programming methods. We propose a scheme of successively increasing the number of measurements until the presence of entanglement can be unambiguously concluded, and investigate its performance in various examples.

Complementary relationships between entanglement and measurement

Academia Quantum, 2024

Complementary relationships exist among interference properties of particles such as pattern visibility, predictability, and distinguishability. Additionally relationships between average information gain G ̄ and measurement disturbance F for entangled spin pairs are well established. This article examines whether a similar complementary relationship exists between entanglement and measurement. For qubit systems, both measurements on a single system and measurements on a bipartite system are considered in regard to entanglement. It is proven that E ̄ + D ≤ 1 holds, where E ̄ is the average entanglement after a measurement is made and D is a measure of the measurement disturbance of a single measurement. Assuming measurements on a bipartite system shared by Alice and Bob, it is shown that E ̄ + G ̄ ≤ 1, where G ̄ is the maximum average information gain that Bob can obtain regarding Alice’s result. These results are generalized to arbitrary initial mixed states and non-Hermitian operators. In the case of maximally entangled initial states, it is found that D ≤ EL and G ̄ ≤ EL, where EL is the loss of entanglement due to measurement by Alice. We conclude that the amount of disturbance and average information gain one can achieve is strictly limited by entanglement.