Abstract
AbstractEntanglement is a key ingredient for quantum technologies and a fundamental signature of quantumness in a broad range of phenomena encompassing many-body physics, thermodynamics, cosmology and life sciences. For arbitrary multiparticle systems, entanglement quantification typically involves nontrivial optimisation problems, and it may require demanding tomographical techniques. Here, we develop an experimentally feasible approach to the evaluation of geometric measures of multiparticle entanglement. Our framework provides analytical results for particular classes of mixed states of N qubits, and computable lower bounds to global, partial, or genuine multiparticle entanglement of any general state. For global and partial entanglement, useful bounds are obtained with minimum effort, requiring local measurements in just three settings for any N. For genuine entanglement, a number of measurements scaling linearly with N are required. We demonstrate the power of our approach to estimate and quantify different types of multiparticle entanglement in a variety of N-qubit states useful for quantum information processing and recently engineered in laboratories with quantum optics and trapped ion setups.
Highlights
Considerable progress has been achieved in the detection of entanglement,[4,5,6,7,8,9,10,11,12] its experimentally accessible quantification remains an open problem for any real implementation of an entangled system.[13,14,15,16,17,18,19,20,21,22,23]
Quantifying entanglement is yet necessary to gauge precisely the quantum enhancement in information processing and computation,[2,3,24] and to pin down exactly how much a physical or biological system under observation departs from an essentially classical behaviour.[25]. This is especially relevant in the case of complex, multiparticle systems, for which only quite recently have notable advances been reported on the control of entanglement.[26,27,28,29]
To illustrate the power of our approach, we focus initially on a reference family of mixed states π of N qubits, that we label M3N states, which form a subset of the class of states having all maximally mixed marginals
Summary
The fascination with quantum entanglement has evolved over the last eight decades, from the realm of philosophical debate[1] to a very concrete recognition of its resource role in a range of applied sciences.[2,3] considerable progress has been achieved in the detection of entanglement,[4,5,6,7,8,9,10,11,12] its experimentally accessible quantification remains an open problem for any real implementation of an entangled system.[13,14,15,16,17,18,19,20,21,22,23] Quantifying entanglement is yet necessary to gauge precisely the quantum enhancement in information processing and computation,[2,3,24] and to pin down exactly how much a physical or biological system under observation departs from an essentially classical behaviour.[25]. We calculate exactly distancebased measures of genuine multiparticle entanglement ED2 for these states, for every valid D Once more, these analytical results mapped into this family through a fixed procedure of single- provide lower bounds to geometric measures of genuine qubit LOCC. This reference family should be simple to entanglement for any general state of N qubits, obtainable npj Quantum Information (2016) 16030. Compared with some recent complementary approaches to the quantification of multiparticle entanglement,[13,14,15,16,17,18,19,20,21,22,23] we find that our results, obtained via the general quantitative framework discussed above, fare surprisingly well in their efficiency and versatility despite the minimal experimental requirements (see Table 1 for an in-depth comparison)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
