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Register a new userMonogamy relations of quantum coherence between multiple subspaces
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Quantum coherence plays an important role in quantum information protocols that provide an advantage over classical information processing. The amount of coherence that can exist between two orthogonal subspaces is limited by the positivity constraint on the density matrix. On the level of multipartite systems, this gives rise to what is known as monogamy of entanglement. On the level of single systems this leads to a bound, and hence, a trade-off in coherence that can exist between different orthogonal subspaces. In this work we derive trade-off relations for the amount of coherence that can be shared between a given subspace and all other subspaces based on trace norm, Hilbert-Schmidt norm and von Neumann relative entropy. From this we derive criteria detecting genuine multisubspace coherence.
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We investigate the monogamy relations related to the concurrence and the entanglement of formation. General monogamy inequalities given by the {alpha}th power of concurrence and entanglement of formation are presented for N-qubit states. The monogamy relation for entanglement of assistance is also established. Based on these general monogamy relations, the residual entanglement of concurrence and entanglement of formation are studied. Some relations among the residual entanglement, entanglement of assistance, and three tangle are also presented.
The set of all qubit states that can be steered to by measurements on a correlated qubit is predicted to form an ellipsoid---called the quantum steering ellipsoid---in the Bloch ball. This ellipsoid provides a simple visual characterisation of the initial 2-qubit state, and various aspects of entanglement are reflected in its geometric properties. We experimentally verify these properties via measurements on many different polarisation-entangled photonic qubit states. Moreover, for pure 3-qubit states, the volumes of the two quantum steering ellipsoids generated by measurements on the first qubit are predicted to satisfy a tight monogamy relation, which is strictly stronger than the well-known monogamy of entanglement for concurrence. We experimentally verify these predictions, using polarisation and path entanglement. We also show experimentally that this monogamy relation can be violated by a mixed entangled state, which nevertheless satisfies a weaker monogamy relation.
In Newtonian mechanics, any closed-system dynamics of a composite system in a microstate will leave all its individual subsystems in distinct microstates, however this fails dramatically in quantum mechanics due to the existence of quantum entanglement. Here we introduce the notion of a `coherent work process, and show that it is the direct extension of a work process in classical mechanics into quantum theory. This leads to the notion of `decomposable and `non-decomposable quantum coherence and gives a new perspective on recent results in the theory of asymmetry as well as early analysis in the theory of classical random variables. Within the context of recent fluctuation relations, originally framed in terms of quantum channels, we show that coherent work processes play the same role as their classical counterparts, and so provide a simple physical primitive for quantum coherence in such systems. We also introduce a pure state effective potential as a tool with which to analyze the coherent component of these fluctuation relations, and which leads to a notion of temperature-dependent mean coherence, provides connections with multi-partite entanglement, and gives a hierarchy of quantum corrections to the classical Crooks relation in powers of inverse temperature.
The time evolution of the distribution and shareability of quantum coherence of a tripartite system in a non-Markovian environment is examined. The total coherence can be decomposed into various contributions, ranging from local, global bipartite and global tripartite, which characterize the type of state. We identify coherence revivals for non-Markovian systems for all the contributions of coherence. The local coherence is found to be much more robust under the environmental coupling due to an effective smaller coupling to the reservoir. This allows us to devise a characterization of a quantum state in terms of a coherence tuple on a multipartite state simply by examining various combinations of reservoir couplings. The effect of the environment on the shareability of quantum coherence, as defined using the monogamy of coherence, is investigated and found that the sign of the monogamy is a preserved quantity under the decoherence. We conjecture that the monogamy of coherence is a conserved property under local incoherent processes.
The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is expressed in terms of the entropic measures. Uncertainty bound can be altered by considering a particle as a quantum memory correlating with the primary particle. In this work, we provide a method for converting the entropic uncertainty relation in the absence of quantum memory to that in its presence. It is shown that the lower bounds obtained through the method are tighter than those having been achieved so far. The method is also used to obtain the uncertainty relations for multiple measurements in the presence of quantum memory. Also for a given state, the lower bounds on the sum of the relative entropies of unilateral coherences are provided using the uncertainty relations in the presence of quantum memory, and it is shown which one is tighter.
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