It is very common in the literature to write a Markovian quantum master equation Lindblad form describe system with multiple degrees of freedom and weakly connected thermal baths which can, general, be at different temperatures chemical potentials. However, microscopically derived up leading order system-bath coupling so-called Redfield form, known not preserve complete positivity most cases. Additional approximations are required obtain form. We lay down some fundamental requirements for...

We investigate the possibility of a Markovian quantum master equation (QME) that consistently describes finite-dimensional system, part which is weakly coupled to thermal bath. To preserve complete positivity and trace, such QME must be Lindblad form. For physical consistency, it should additionally local conservation laws able show thermalization. search for equations satisfying these additional criteria. First, we microscopically derived Bloch-Redfield violates unless in extremely special...

We present a finite-size security proof for generic quantum key distribution protocols against independent and identically distributed collective attacks extend it to coherent using the postselection technique. This work introduces two significant improvements over previous results. First, we achieve tighter rates by employing refined concentration inequalities in acceptance testing phase. Second, improve second-order correction terms rate expression, reducing them scale with number of...

We discuss the status of security proofs for practical decoy-state Quantum Key Distribution using BB84 protocol, pertaining to optical implementations weak coherent pulses and threshold photo-detectors. Our focus is on gaps in existing literature. Gaps might result, example, from a mismatch protocol detail choices proof technique elements, relying earlier results that made different assumptions, or do not consider real-world requirements. While substantial progress has been made, our...

We present a security proof for variable-length QKD in the Renner framework against IID collective attacks. Our can be lifted to coherent attacks using postselection technique. first main result is theorem convert sequence of proofs fixed-length protocols satisfying certain conditions protocol. This conversion requires no new calculations, does not require any changes final key lengths or amount error-correction information, and at most doubles parameter. second description more general...

The postselection technique is an important proof for proving the security of quantum key distribution protocols against coherent attacks. In this work, we go through multiple steps to rigorously apply optical protocols. First, place on a rigorous mathematical foundation by fixing technical flaw in original paper. Second, extend applicability prepare-and-measure using de Finetti reduction with fixed marginal. Third, show how can be used decoy-state tagging source. Finally, realistic setups...

We point out a critical flaw in the analysis of quantum key distribution protocols that employ two-way error-correction protocol Cascade. Specifically, this stems from an incomplete consideration all communication occurs during Cascade protocol. present straightforward and elegant alternative approach addresses produces valid rates. exemplify our new by comparing its rates with those generated using older, incorrect approaches, for qubit BB84 decoy-state protocols. show that, many...

The postselection technique is an important proof for proving the security of quantum key distribution protocols against coherent attacks via uplift any independent identically distributed collective attacks. In this work, we go through multiple steps to rigorously apply optical protocols. First, place on a rigorous mathematical foundation by fixing technical flaw in original paper. Second, extend applicability prepare-and-measure using de Finetti reduction with fixed marginal. Third, show...

We present a finite-size security proof of the BB84 QKD protocol against coherent attacks, using entropic uncertainty relations, in presence imperfectly characterized basis-efficiency mismatch. Our requires no new modifications to steps or hardware, and works by obtaining suitable bound on phase error rate. It is applicable detectors, only maximum relative difference detection efficiencies dark count rates detectors be characterized. Moreover, our allows Eve use any spatio-temporal degree...

We investigate the possibility of a Markovian quantum master equation (QME) that consistently describes finite-dimensional system, part which is weakly coupled to thermal bath. In order preserve complete positivity and trace, such QME must be Lindblad form. For physical consistency, it should additionally local conservation laws able show thermalization. First, we microscopically derived Redfield (RE) violates unless in extremely special cases. then prove imposing demanding preservation...

We point out a critical flaw in the analysis of Quantum Key Distribution (QKD) protocols that employ two-way error correction protocol Cascade. Specifically, this stems from an incom-plete consideration all communication occurs during Cascade protocol. present straightforward and elegant alternative approach addresses produces valid key rates. exemplify our new by comparing its rates with those generated using older, incorrect approaches, for Qubit BB84 Decoy-State protocols. show many...

We present a security proof for variable-length QKD in the Renner framework against IID collective attacks. Our can be lifted to coherent attacks using postselection technique. first main result is theorem convert series of proofs fixed-length protocols satisfying certain conditions protocol. This conversion requires no new calculations, does not require any changes final key lengths or amount error-correction information, and at most doubles parameter. second description more general class...