Purity estimation with separable measurements

Abstract

Given a large number N of copies of a qubit state of which we wish to estimate its purity, we prove that separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This shows that the optimal estimation of the entanglement of a two-qubit state can also be achieved asymptotically with fully separable measurements. Thus, quantum memories provide no advantage in this situation. The relationship between our global Bayesian approach and the quantum Cramer-Rao bound is discussed.

Abridged version of quant-ph/0505083, to appear in PRL

References in corpus (11)

• Induced measures in the space of mixed quantum states
• Estimating the spectrum of a density operator
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• Statistical properties of random density matrices
• Multiple copy 2-state discrimination with individual measurements
• Optimal parameter estimation of depolarizing channel
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• Separable Measurement Estimation of Density Matrices and its Fidelity Gap with Collective Protocols
• Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
• The Second Law of Thermodynamics under Unitary Evolution and External Operations
• Detecting mixedness of qutrit systems using the uncertainty relation
• Saturating the quantum Cramér-Rao bound using LOCC
• Discrimination between pure states and mixed states
• Relative states, quantum axes and quantum references
• Certifying the purity of quantum states with temporal correlations
• Bounds on mixed state entanglement
• Optimal estimation of quantum observables
• Estimating the spectrum of a density matrix with LOCC
• Tensorial characterization and quantum estimation of weakly entangled qubits
• Superresolving collective quantum measurements
• Efficient quantum state tomography with auxiliary Hilbert space
• Optimal estimation of an observable's expectation value for pure states for general measure of deviation