Direct method for measuring and witnessing quantum entanglement of arbitrary two-qubit states through Hong-Ou-Mandel interference
arXiv:1612.00782 · doi:10.1103/PhysRevA.95.022331
Abstract
We describe a direct method for experimental determination of the negativity of an arbitrary two-qubit state with 11 measurements performed on multiple copies of the two-qubit system. Our method is based on the experimentally accessible sequences of singlet projections performed on up to four qubit pairs. In particular, our method permits the application of the Peres-Horodecki separability criterion to an arbitrary two-qubit state. We explicitly demonstrate that measuring entanglement in terms of negativity requires three measurements more than detecting two-qubit entanglement. The reported minimal set of interferometric measurements provides a complete description of bipartite quantum entanglement in terms of two-photon interference. This set is smaller than the set of 15 measurements needed to perform a complete quantum state tomography of an arbitrary two-qubit system. Finally, we demonstrate that the set of 9 Makhlin's invariants needed to express the negativity can be measured by performing 13 multicopy projections. We demonstrate that these invariants are both a useful theoretical concept for designing specialized quantum interferometers and that their direct measurement within the framework of linear optics does not require performing complete quantum state tomography.
arXiv comment8 pages, 3 figures, 1 table
References in corpus (49)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Separability of Mixed States: Necessary and Sufficient Conditions
- Entanglement detection
- The classical-quantum boundary for correlations: discord and related measures
- Multi-photon entanglement and interferometry
- On the volume of the set of mixed entangled states
- Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations
- The entanglement cost under operations preserving the positivity of partial transpose
- Computing quantum discord is NP-complete
- Multi-particle entanglement and its applications to cryptography
- Direct detection of quantum entanglement
- Quantum inseparability as local pseudomixture
- Long distance quantum teleportation in a quantum relay configuration
- A comparison of the entanglement measures negativity and concurrence
- Estimating entanglement measures in experiments
- Computing Local Invariants of Qubit Systems
- Direct measurement of non-linear properties of bipartite quantum states
- Measuring Multipartite Concurrence with a Single Factorizable Observable
- Ordering two-qubit states with concurrence and negativity
- Universal observable detecting all two-qubit entanglement and determinant based separability tests
- Negative eigenvalues of partial transposition of arbitrary bipartite states
- Statistical mixtures of states can be more quantum than their superpositions: Comparison of nonclassicality measures for single-qubit states
- Negativity as a counter of entangled dimensions
- Noiseless Quantum Circuits for the Peres Separability Criterion
- Optimal two-qubit tomography based on local and global measurements: Maximal robustness against errors as described by condition numbers
- Tomography is necessary for universal entanglement detection with single-copy observables
- Binegativity and geometry of entangled states in two qubits
- Weaving quantum optical frequency combs into continuous-variable hypercubic cluster states
- Bell nonlocality and fully-entangled fraction measured in an entanglement-swapping device without quantum state tomography
- Some Open Problems in Quantum Information Theory
- Method for universal detection of two-photon polarization entanglement
- Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix
- Collective Uncertainty Entanglement Test
- Direct method for measuring of purity, superfidelity, and subfidelity of photonic two-qubit mixed states
- Determining eigenvalues of a density matrix with minimal information in a single experimental setting
- Construction of optimal witness for unknown two-qubit entanglement
- Direct scheme for measuring the geometric quantum discord
- Experimental measurement of the collectibility of two-qubit states
- Local Unitary Invariants of Generic Multi-qubit States
- Invariant-based entanglement monotones as expectation values and their experimental detection
- Measuring nonclassical correlations of two-photon states
- Entanglement measures as physical observables
- Viable entanglement detection of unknown mixed states in low dimensions
- Reexamination of determinant-based separability test for two qubits
- Exact interferometers for the concurrence and residual 3-tangle
- Optimal observables to determine entanglement of a two qubit state
Cited by in corpus (9)
- Bell nonlocality and fully-entangled fraction measured in an entanglement-swapping device without quantum state tomography
- Entanglement Witness : Compressed/Mirrored Entanglement Witnesses
- Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise
- Universal detection of entanglement in two-qubit states using only two copies
- Experimental measurement of nonlinear entanglement witness by hyper-entangling two-qubit states
- Two methods for measuring Bell nonlocality via local unitary invariants of two-qubit systems in Hong-Ou-Mandel interferometers
- Quantification of Quantum Correlations in Two-Beam Gaussian States Using Photon-Number Measurements
- Entanglement Meter: Estimation of entanglement with single copy in Interferometer
- Resource-efficient quantum correlation measurements via multicopy neural network methods