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arXiv:1110.5083 · Physical Review Letters

Observable Measure of Bipartite Quantum Correlations

Davide Girolami, Gerardo Adesso

Published Apr 13, 2012• 115 citations
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Abstract

We introduce a measure Q of bipartite quantum correlations for arbitrary two-qubit states, expressed as a state-independent function of the density matrix elements. The amount of quantum correlations can be quantified experimentally by measuring the expectation value of a small set of observables on up to four copies of the state, without the need for a full tomography. We extend the measure to 2×d systems, providing its explicit form in terms of observables and applying it to the relevant class of multiqubit states employed in the deterministic quantum computation with one quantum bit model. The number of required measurements to determine Q in our scheme does not increase with d. Our results provide an experimentally friendly framework to estimate quantitatively the degree of general quantum correlations in composite systems.

DOI
10.1103/physrevlett.108.150403

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We introduce a measure Q of bipartite quantum correlations for arbitrary two-qubit states, expressed as a state-independent function of the density matrix elements. The amount of quantum correlations can be quantified experimentally by measuring the expectation value of a small set of observables on up to four copies of the state, without the need for a full tomography. We extend the measure to 2×d systems, providing its explicit form in terms of observables and applying it to the relevant class of multiqubit states employed in the deterministic quantum computation with one quantum bit model. The number of required measurements to determine Q in our scheme does not increase with d. Our results provide an experimentally friendly framework to estimate quantitatively the degree of general quantum correlations in composite systems.
We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance setup and employing geometric discord, we evaluate the quantum correlations of a state without resorting to prior knowledge of its density matrix. The method is applicable to any 2 ⊗ d system and provides, in terms of number of measurements required, an advantage over full state tomography scaling with the dimension d of the unmeasured subsystem. The negativity of quantumness is measured as well for reference. We also observe the phenomenon of sudden transition of quantum correlations when local phase and amplitude damping channels are applied to the state.
Given a quantum system on many qubits split into a few different parties, how many total correlations are there between these parties? Such a quantity, aimed to measure the deviation of the global quantum state from an uncorrelated state with the same local statistics, plays an important role in understanding multipartite correlations within complex networks of quantum states. Yet, the experimental access of this quantity remains challenging as it tends to be nonlinear, and hence often requires tomography which becomes quickly intractable as dimensions of relevant quantum systems scale. Here, we introduce a much more experimentally accessible quantifier of total correlations, which can be estimated using only single-qubit measurements. It requires far fewer measurements than state tomography, and obviates the need to coherently interfere multiple copies of a given state. Thus we provide a tool for proving multipartite correlations that can be applied to near-term quantum devices.
We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence.Our measure allows one to quantify coherence without having to perform tomography of the quantum state and can be directly calculated from measurement expectation values.This definition of coherence allows the decomposition into contributions corresponding to the nonclassical correlations between the subsystems and localized on each subsystem.The method can also be applied to cases where the full set of measurement operators is unavailable.An estimator using the truncated measurement operators can be used to obtain lower bound to the genuine value of coherence.We illustrate the method for several bipartite systems and show the singular behavior of the coherence measure in a spin-1 chain, characteristic of a quantum phase transition.
We review a recently developed theoretical approach to the experimental detection and quantification of bipartite quantum correlations (QCs) between a qubit and a d-dimensional system. Specifically, introducing a properly designed measure Q, the presented scheme allows us to quantify general QCs for arbitrary states of 2⊗d systems without the need to fully reconstruct them by tomographic techniques. We take in exam the specifics of the required experimental architecture in nuclear magnetic resonance (NMR) and optical settings. Finally we extend this approach to models of open system dynamics and discuss possible advantages and limitations in such a context.
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We derive a classification and a measure of classical- and quantum-correlation of multipartite qubit, qutrit, and in general, nnn-level systems, in terms of SU(n)(n)(n) representations of density matrices. We compare the measure for the case of bipartite correlation with concurrence and the entropy of entanglement. The characterization of correlation is in terms of the number of nonzero singular values of the correlation matrix, but that of mixed state entanglement requires additional invariant parameters in the density matrix. For the bipartite qubit case, the condition for mixed state entanglement is written explicitly in terms of the invariant paramters in the density matrix. For identical particle systems we analyze the effects of exchange symmetry on classical and quantum correlation.