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The characterization of multi-time correlations in open quantum systems is of fundamental importance. In this work, we investigate multi-time processes using the process matrix formalism and show that the presence of a quantum non-Markovian environment plays a significant role in enhancing the communication capacity in sequential prepare-transform-measure Quantum Random Access Codes (QRAC). The correlated environment enables a quantum advantage to multiple parties, even with projective measurements. In particular, we show that the Markovian and classical non-Markovian processes, i.e. quantum processes with classical feedback from the environment, do not yield sequential quantum advantage. In contrast, it is possible to achieve an advantage in the presence of a quantum non-Markovian environment. Therefore this approach allows a semi-device-independent certification of quantum non-Markovianity. As opposed to entanglement-detection criteria which require the knowledge of the complete process, this method allows to certify the presence of a quantum non-Markovian environment from the observed measurement statistics. Moreover, quantum memory ameliorates the unambiguous certifiable region of unsharp instruments in a semi-device-independent manner., Comment: 16 Pages, 9 figures

Xie and Eberly introduced a genuine multipartite entanglement (GME) measure `concurrence fill'(\textit{Phys. Rev. Lett., \textbf{127}, 040403} (2021)) for three-party systems. It is defined as the area of a triangle whose side lengths represent squared concurrence in each bi-partition. However, it has been recently shown that concurrence fill is not monotonic under LOCC, hence not a faithful measure of entanglement. Though it is not a faithful entanglement measure, it encapsulates an elegant geometric interpretation of bipartite squared concurrences. There have been a few attempts to generalize GME measure to four-party settings and beyond. However, some of them are not faithful, and others simply lack an elegant geometric interpretation. The recent proposal from Xie et al. constructs a concurrence tetrahedron, whose volume gives the amount of GME for four-party systems; with generalization to more than four parties being the hypervolume of the simplex structure in that dimension. Here, we show by construction that to capture all aspects of multipartite entanglement, one does not need a more complex structure, and the four-party entanglement can be demonstrated using \textit{2D geometry only}. The subadditivity together with the Araki-Lieb inequality of linear entropy is used to construct a direct extension of the geometric GME to four-party systems resulting in quadrilateral geometry. Our measure can be geometrically interpreted as a combination of three quadrilaterals whose sides result from the concurrence in one-to-three bi-partition, and diagonal as concurrence in two-to-two bipartition., Comment: 14 pages, 3 figures

It is well known that fringe contrast is not a good quantifier of the wave nature of a quanton in multipath interference. A new interference visibility, based on the Hilbert-Schmidt coherence is introduced. It is demonstrated that this visibility is a good quantifier of wave nature, and can be experimentally measured. A generalized path predictability is introduced, which reduces to the predictability of Greenberger and Yasin, for the case of two paths. In a multipath, which-way interference experiment, the new visibility, the predictability and the I-concurrence (quantifying the entanglement between the quanton and the path-detector), are shown to follow a tight triality relation. It quantifies the essential role that entanglement plays in multipath quantum complementarity, for the first time., Comment: 8 pages, 1 figure; Revised version

We investigate the dynamical evolution of multipartite entanglement in tripartite systems with three qubits present in independent thermal reservoirs, modelled as infinite set of quantum harmonic oscillators. We show that the presence of temperature gradient between reservoirs play a significant role in robustness of multipartite correlation against environmental decoherence. Considering a bilinear form of interaction Hamiltonian, an exact expression for time evolved density matrix is presented. Interestingly, it is observed that the preservation duration of genuine multipartite concurrence for GHZ class Werner state increases as the temperature gradient between reservoirs are increased. However, this increase is non-linear and the preservation duration is shown to saturate for large temperature gradients. It is also observed that, for large temperature gradient, there are multiple intervals in which coherence and consequently the tripartite negativity shows robustness (freezing of correlation) against the environmental decoherence for W class Werner states. For the common temperature case, we show that the genuine multipartite concurrence for the GHZ class Werner state decays irreversibly, and the state experiences correlation sudden death, with a rate dependent on spectral density of the reservoirs under consideration. For the Ohmic reservoirs at low temperature, we observe that the state retains initial multipartite correlation upto a characteristic time and then sharply decays to zero with a correlation sudden death. We further investigate the dynamics of tripartite negativity and $l_{1}$ norm of coherence in the W class Werner states, and show irreversible degradation in these correlations., Comment: 19 pages, 10 figures

Establishing the correspondence of two dimensional paraxial and three dimensional non-paraxial optical beams with the qubit and qutrit systems respectively, we derive a complementary relation between Hilbert-Schmidt coherence, generalized predictability and linear entropy. The linear entropy, a measure of mixedness is shown to saturate the complementarity relation for mixed bi-partite states. For pure two qubit and qutrit systems, it quantifies the global entanglement and reduces the complementarity relation to the triality relation between coherence, predictability and entanglement. We analyze these relations in wedge-product formalism in order to investigate the innate geometry of the complex vector space. The derived complementary relations offer insights into our ability to manipulate and utilize quantum properties for practical advancements., Comment: accepted in the conference COMSNETS 2024

The wedge product of vectors has been shown to yield the generalised entanglement measure I-concurrence, wherein the separability of the multiparty qubit system arises from the parallelism of vectors in the underlying Hilbert space of the subsystems. Here, we demonstrate the geometrical conditions of the post-measurement vectors which maximize the entanglement corresponding to the bi-partitions and can yield non-identical set of maximally entangled states. The Bell states for the two qubit case, GHZ and GHZ like states with superposition of four constituents for three qubits, naturally arise as the maximally entangled states. The geometric conditions for maximally entangled two qudit systems are derived, leading to the generalised Bell states, where the reduced density matrices are maximally mixed. We further show that the reduced density matrix for an arbitrary finite dimensional subsystem of a general qudit state can be constructed from the overlap of the post-measurement vectors. Using this approach, we discuss the trade-off between the local properties namely predictability and coherence with the global property, entanglement for the non-maximally entangled two qubit state., Comment: 13 pages, 1 figure, version 2, abstract and overall text modified

We have recently proposed a Lagrangian in trace dynamics, to describe a possible unification of gravity, Yang-Mills fields, and fermions, at the Planck scale. This Lagrangian for the unified entity - called the aikyon - is invariant under global unitary transformations, and as a result possesses a novel conserved charge, known as the Adler-Millard charge. In the present paper, we derive an eigenvalue equation, analogous to the time-independent Schr\"{o}dinger equation, for the Hamiltonian of the theory. We show that in the emergent quantum theory, the energy eigenvalues of the aikyon are characterised in terms of a fundamental frequency times Planck's constant. The eigenvalues of this equation can, in principle, determine the values of the parameters of the standard model. We also report a ground state, in this theory of spontaneous quantum gravity, which could characterise a non-singular initial epoch in quantum cosmology., Comment: 18 pages, published in Mod. Phys. Lett. A

Calculations in Ising model can be cumbersome and non-intuitive. Here we provide a formulation that addresses these issues for 1-D scenario. We represent the microstates of spin interactions as a diagonal matrix. This is done using two operations: Kronecker sum and Kronecker product. The calculations thus become simple matter of manipulating diagonal matrices. We address the following problems in this work: spins in the magnetic field, open-chain 1-D Ising model, closed-chain 1-D Ising model, 1-D Ising model in an external magnetic field. We believe that this representation will help provide students as well as experts with a simple yet powerful technique to carry out calculations in this model., Comment: 15 pages, 4 figures, abstract and overall text modified, references added