Mixed-State Entanglement from Local Randomized Measurements

Physical Review A, 2015

We describe a direct method to determine the negativity of an arbitrary two-qubit state in experiments. The method is derived by analyzing the relation between the purity, negativity, and a universal entanglement witness for two-qubit entanglement. We show how the negativity of a twoqubit state can be calculated from just three experimentally-accessible moments of the partiallytransposed density matrix of a two-photon state. Moreover, we show that the negativity can be given as a function of only six invariants, which are linear combinations of nine invariants from the complete set of 21 fundamental and independent two-qubit invariants. We analyze the relation between these moments and the concurrence for some classes of two-qubit states (including the X states, as well as pure states affected by the amplitude-damping and phase-damping channels). We also discuss the possibility of using the universal entanglement witness as an entanglement measure for various classes of two-qubit states. Moreover, we analyze how noise affects the estimation of entanglement via this witness.

Physical Review A, 2012

npj Quantum Information

We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The k-th condition involves comparing moments of the partially transposed density operator up to order k. Remarkably, the union of all moment inequalities reproduces the Peres-Horodecki criterion for detecting entanglement. Our empirical studies highlight that the first four conditions already detect mixed state entanglement reliably in a variety of quantum architectures. Exploiting symmetries can help to further improve their detection capabilities. We also show how to estimate moment inequalities based on local random measurements of single state copies (classical shadows) and derive statistically sound confidence intervals as a function of the number of performed measurements. Our analysis includes the experimentally relevant situation of drifting sources, i.e. non-identical, but independent, state copies.

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.

Physical Review A

It is very crucial to know that whether the quantum state generated in the experiment is entangled or not. In the literature, this topic was studied extensively and researchers proposed different approaches for the detection of mixed bipartite entangled state in arbitrary dimension. Proceeding in this line of research, we also propose three different criteria for the detection of mixed bipartite negative partial transpose (NPT) entangled state in arbitrary dimension. Our criteria is based on the method of structural physical approximation (SPA) of partial transposition (PT). We have shown that the proposed criteria for the detection of NPT entangled state can be realized experimentally. Two of the proposed criteria is given in terms of the concurrence of the given state in arbitrary dimension so it is essential to find out the concurrence. Thus, we provide new lower and upper bound of concurrence of the quantum state under investigation in terms of average fidelity of two quantum states and hence these bounds can be realized experimentally. Moreover, we have shown how to perform SPA map on qutrit-qubit system and then explicitly calculated the matrix elements of the density matrix describing the SPA-PT of the qutrit-qubit system. We then illustrate our criteria for the detection of entanglement by considering a class of qubit-qubit system and a class of qutrit-qubit system.

Physical Review A

Experimental detection of entanglement of an arbitrary state of a given bipartite system is crucial for exploring many areas of quantum information processing. But such a detection should be made in a device-independent way if the preparation process of the state is considered to be faithful, in order to avoid detection of a separable state as an entangled one. The recently developed scheme of detecting bipartite entanglement in a measurement-deviceindependent way [Phys. Rev. Lett. 110, 060405 (2013)] does require information about the state. Here, by using Auguisiak et al.'s universal entanglement witness scheme for two-qubit states [Phys. Rev. A 77, 030301 (2008)], we provide a universal entanglement detection scheme for two-qubit states in a measurement-device-independent way. We also provide a set of universal witness operators for detecting NPT-ness (negative under partial transpose) of two-qudit states in a measurement-device-independent way. We conjecture that no such universal entanglement witness scheme exists for PPT (positive under partial transpose) entangled states. We also analyze the robustness of some of the experimental schemes-for detecting entanglement in a measurement-device-independent wayunder the influence of noise in the inputs (from the referee) as well as in the measurement operator.

arXiv (Cornell University), 2023

It is shown that a fixed measurement setting, e.g., a measurement in the computational basis, can detect all entangled states by preparing multipartite quantum states, called network states. We present network states for both cases to construct decomposable entanglement witnesses (EWs) equivalent to the partial transpose criteria and also non-decomposable EWs that detect undistillable entangled states beyond the partial transpose criteria. Entanglement detection by state preparation can be extended to multipartite states such as graph states, a resource for measurement-based quantum computing. Our results readily apply to a realistic scenario, for instance, an array of superconducting qubits. neutral atoms, or photons, in which the preparation of a multipartite state and a fixed measurement are experimentally feasible.

Scientific Reports, 2015

2017

Experimental detection of entanglement of an arbitrary state of a given bipartite system is crucial for exploring many areas of quantum information. But such a detection should be made in a device independent way if the preparation process of the state is considered to be faithful, in order to avoid detection of a separable state as entangled one. The recently developed scheme of detecting bipartite entanglement in a measurement device independent way [Phys. Rev. Lett 110, 060405 (2013)] does require information about the state. Here by using Auguisiak et al.'s universal entanglement witness scheme for two-qubit states [Phys. Rev. A 77, 030301 (2008)], we provide a universal detection scheme for two-qubit states in a measurement device independent way. We provide a set of universal witness operators for detecting NPT-ness(negative under partial transpose) of states in a measurement device independent way. We conjecture that no such universal entanglement witness exists for PPT(p...

Physical Review A, 2009

We explore procedures to detect entanglement of unknown mixed states, which can be experimentally viable. The heart of the method is a hierarchy of simple feasibility problems, which provides sufficient conditions to entanglement. Our numerical investigations indicate that the entanglement is detected with a cost which is much lower than full state tomography. The procedure is applicable to both free and bound entanglement, and involves only single copy measurements.