It is known that a reliable geometric quantifier of discord-like correlations can be built by employing the so-called trace distance, which is used to measure how far the state under investigation is from the closest 'classical-quantum' state. To date, the explicit calculation of this indicator for two qubits has only been accomplished for states where the reduced density matrix of the measured party is maximally mixed, a class that includes Bell-diagonal states. Here, we first reduce the required optimization for a general two-qubit state to the minimization of an explicit two-variable function. Using this framework, we show that the minimum can be analytically worked out in a number of relevant cases, including quantum-classical and X states. This provides an explicit and compact expression for the trace distance discord of an arbitrary state belonging to either of these important classes of density matrices.

It is known that a reliable geometric quantifier of discord-like correlations can be built by employing the so-called trace distance, which is used to measure how far the state under investigation is from the closest ‘classical-quantum’ state. To date, the explicit calculation of this indicator for two qubits has only been accomplished for states where the reduced density matrix of the measured party is maximally mixed, a class that includes Bell-diagonal states. Here, we first reduce the required optimization for a general two-qubit state to the minimization of an explicit two-variable function. Using this framework, we show that the minimum can be analytically worked out in a number of relevant cases, including quantum-classical and X states. This provides an explicit and compact expression for the trace distance discord of an arbitrary state belonging to either of these important classes of density matrices.

Toward computability of trace distance discord

GIOVANNETTI, VITTORIO
2014

Abstract

It is known that a reliable geometric quantifier of discord-like correlations can be built by employing the so-called trace distance, which is used to measure how far the state under investigation is from the closest 'classical-quantum' state. To date, the explicit calculation of this indicator for two qubits has only been accomplished for states where the reduced density matrix of the measured party is maximally mixed, a class that includes Bell-diagonal states. Here, we first reduce the required optimization for a general two-qubit state to the minimization of an explicit two-variable function. Using this framework, we show that the minimum can be analytically worked out in a number of relevant cases, including quantum-classical and X states. This provides an explicit and compact expression for the trace distance discord of an arbitrary state belonging to either of these important classes of density matrices.
X-STATES; QUANTUM; ENTANGLEMENT; DYNAMICS
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/38620
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