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Register a new userGeneralized coherence vector applied to coherence transformations and quantifiers
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Added by
Gustavo Martin Bosyk
Publication date
2020
fields
Physics
and research's language is
English
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One of the main problems in any quantum resource theory is the characterization of the
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We investigate the single qubit transformations under several typical coherence-free operations, such as, incoherent operation (IO), strictly incoherent operation (SIO), physically incoherent operation (PIO), and coherence preserving operation (CPO). Quantitative connection has been built between IO and SIO in single qubit systems. Moreover, these coherence-free operations have a clear hierarchical relationship in single qubit systems: CPO $subset$ PIO $subset$ SIO=IO. A new and explicit proof for the necessary and sufficient condition of single qubit transformation via IO or SIO has been provided, which indicates that SIO with only two Kraus operators are enough to realize this transformation. The transformation regions of single qubits via CPO and PIO are also given. Our method provides a geometric illustration to analyze single qubit coherence transformations by introducing the Bloch sphere depiction of the transformation regions, and tells us how to construct the corresponding coherence-free operations.
The resource theories of quantum coherence attract a lot of attention in recent years. Especially, the monotonicity property plays a crucial role here. In this paper we investigate the monotonicity property for the coherence measures induced by the R{e}nyi $alpha$-relative entropy which present in [Phys. Rev. A 94, 052336, 2016]. We show that the R{e}nyi $alpha$-relative entropy of coherence does not in general satisfy the monotonicity requirement under the subselection of measurements condition and it also does not satisfy the extension of monotonicity requirement which presents in [Phys. Rev. A 93, 032136, 2016]. Due to the R{e}nyi $alpha$-relative entropy of coherence can act as a coherence monotone quantifier, we examine the trade-off relations between coherence and mixedness. Finally, some properties for the single qubit of R{e}nyi $2$-relative entropy of coherence are derived.
The definition of accessible coherence is proposed. Through local measurement on the other subsystem and one way classical communication, a subsystem can access more coherence than the coherence of its density matrix. Based on the local accessible coherence, the part that can not be locally accessed is also studied, which we call it remaining coherence. We study how the bipartite coherence is distributed by partition for both l1 norm coherence and relative entropy coherence, and the expressions for local accessible coherence and remaining coherence are derived. we also study some examples to illustrate the distribution.
Known experiments with the path entangled photon pairs are considered here under more general conditions widely broadening the domain of used bases. Starting from symmetric beam splitters and equally weighted superposition in the initial setup, we allow arbitrary beam splitters and in addition insert the new elements: absorptive plates. The first innovation allows one to vary the amplitudes of local interferences. The second one enables the experimenter to monitor the nonlocal superposition amplitudes, thus varying the entanglement strength from maximal to zero. The generalized scheme reveals an interesting effect: the local coherence observed for independent photons disappears already at infinitesimally weak entanglement between them. Mathematically, local coherence turns out to be a discontinuous function of entanglement strength. The same features are unveiled for a quite different system, spin entangled fermion pair. We can thus conjecture a general rule of total mutual intolerance between local coherence and entanglement: any local coherence must vanish completely not only at maximal, but even at arbitrarily weak entanglement between members of studied pair. Altogether, the generalized thought experiment shows that coherence transfer is a complicated phenomenon with common features for various bipartite systems and different types of observables. Key words: Bi-photon, bi-fermion, entanglement, correlations, coherence transfer
Quantum coherence, like entanglement, is a fundamental resource in quantum information. In recent years, remarkable progress has been made in formulating resource theory of coherence from a broader perspective. The notions of block-coherence and POVM-based coherence have been established. Certain challenges, however, remain to be addressed. It is difficult to define incoherent operations directly, without requiring incoherent states, which proves a major obstacle in establishing the resource theory of dynamical coherence. In this paper, we overcome this limitation by introducing an alternate definition of incoherent operations, induced via coherence measures, and quantify dynamical coherence based on this definition. Finally, we apply our proposed definition to quantify POVM-based dynamical coherence.
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