Tamoghna Das

Quantum discord and its allies: a review of recent progress

We review concepts and methods associated with quantum discord and related topics. We also describe their possible connections with other aspects of quantum information and beyond, including quantum communication, quantum computation, many-body physics, and open quantum dynamics. Quantum discord in the multiparty regime and its applications are also discussed.

Multipartite dense coding versus quantum correlation: Noise inverts relative capability of information transfer

A highly entangled bipartite quantum state is more advantageous for the quantum dense coding protocol than states with low entanglement. Such a correspondence, however, does not exist even for pure quantum states in the multipartite domain. We establish a connection between the multiparty capacity of classical information transmission in quantum dense coding and several multipartite quantum correlation measures of the shared state, used in the dense coding protocol. In particular, we show that for the noiseless channel, if multipartite quantum correlations of an arbitrary multipartite state of arbitrary number of qubits is the same as that of the corresponding generalized Greenberger-Horne-Zeilinger state, then the multipartite dense coding capability of former is the same or better than that of the generalized Greenberger-Horne-Zeilinger state. Interestingly, in a noisy channel scenario, where we consider both uncorrelated and correlated noise models, the relative abilities of the quantum channels to transfer classical information can get inverted by administering a sufficient amount of noise. When the shared state is an arbitrary multipartite mixed state, we also establish a link between the classical capacity for the noiseless case and multipartite quantum correlation measures.

Distributed quantum dense coding with two receivers in noisy environments

We investigate the effect of noisy channels in a classical information transfer through a multipartite state which acts as a substrate for the distributed quantum dense coding protocol between several senders and two receivers. The situation is qualitatively different from the case with one or more senders and a single receiver. We obtain an upper bound on the multipartite capacity which is tightened in case of the covariant noisy channel. We also establish a relation between the genuine multipartite entanglement of the shared state and the capacity of distributed dense coding using that state, both in the noiseless and the noisy scenarios. Specifically, we find that in the case of multiple senders and two receivers, the corresponding generalized Greenberger-Horne-Zeilinger states possess higher dense coding capacities as compared to a significant fraction of pure states having the same multipartite entanglement.

Reducing computational complexity of quantum correlations

We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures such as quantum discord and quantum work deficit in two qubits and higher-dimensional systems. We show that determination of the quantum correlation measure is possible even if we utilize a restricted set of local measurements. We find that the determination allows us to obtain a closed form of quantum discord and quantum work deficit for several classes of states, with a low error. We show that the computational error caused by the constraint over the complete set of local measurements reduces fast with an increase in the size of the restricted set, implying usefulness of constrained optimization, especially with the increase of dimensions. We perform quantitative analysis to investigate how the error scales with the system size, taking into account a set of plausible constructions of the constrained set. Carrying out a comparative study, we show that the resource required to optimize quantum work deficit is usually higher than that required for quantum discord. We also demonstrate that minimization of quantum discord and quantum work deficit is easier in the case of two-qubit mixed states of fixed ranks and with positive partial transpose in comparison to the corresponding states having nonpositive partial transpose. Applying the methodology to quantum spin models, we show that the constrained optimization can be used with advantage in analyzing such systems in quantum information-theoretic language. For bound entangled states, we show that the error is significantly low when the measurements correspond to the spin observables along the three Cartesian coordinates, and thereby we obtain expressions of quantum discord and quantum work deficit for these bound entangled states.

Canonical distillation of entanglement

Abstract Distilling highly entangled quantum states from weaker ones is a process that is crucial for efficient and long-distance quantum communication, and has implications for several other quantum information protocols. We introduce the notion of distillation under limited resources, and specifically focus on the energy constraint. The corresponding protocol, which we call the canonical distillation of entanglement, naturally leads to the set of canonically distillable states. We show that for non-interacting Hamiltonians, almost no states are canonically distillable, while the situation can be drastically different for interacting ones. Several paradigmatic Hamiltonians are considered for bipartite as well as multipartite canonical distillability. The results have potential applications for practical quantum communication devices.

Emergence of entanglement with temperature and time in factorization-surface states

There exist zero-temperature states in quantum many-body systems that are fully factorized, thereby possessing vanishing entanglement, and hence being of no use as resource in quantum information processing tasks. Such states can become useful for quantum protocols when the temperature of the system is increased, and when the system is allowed to evolve under either the influence of an external environment, or a closed unitary evolution driven by its own Hamiltonian due to a sudden change in the system parameters. Using the one-dimensional anisotropic XY model in a uniform and an alternating transverse magnetic field, we show that entanglement of the thermal states, corresponding to the factorization points in the space of the system parameters, revives once or twice with increasing temperature. We also study the closed unitary evolution of the quantum spin chain driven out of equilibrium when the external magnetic fields are turned off, and show that considerable entanglement is generated during the dynamics, when the initial state has vanishing entanglement. Interestingly, we find that creation of entanglement for a pair of spins is possible when the system is made open to an external heat bath, interacting through that spin-pair having a repetitive quantum interaction.

Superiority of photon subtraction to addition for entanglement in a multimode squeezed vacuum

We investigate the entanglement patterns of photon-added and -subtracted four-mode squeezed vacuum states. Entanglements in different scenarios are analyzed by varying the number of photons added or subtracted in certain modes, which are referred to as the “player” modes, the others being “spectators”. We find that the photon-subtracted state can give us higher entanglement than the photon-added state which is in contrast of the two-mode situation. We also study the logarithmic negativity of the two-mode reduced density matrix obtained from the four-mode state which again shows that the state after photon subtraction can possess higher entanglement than that of the photon-added state, and we then compare it to that of the two-mode squeezed vacuum state. Moreover, we examine the non-Gaussianity of the photon-added and -subtracted states to find that the rich features provided by entanglement cannot be captured by the measure of non-classicality.

Generalized geometric measure of entanglement for multiparty mixed states

Computing entanglement of an arbitrary bipartite or multipartite mixed state is in general not an easy task as it usually involves complex optimization. Here we show that exploiting symmetries of certain mixed states, we can compute a genuine multiparty entanglement measure, the generalized geometric measure for these classes of mixed states. The chosen states have different ranks and consist of an arbitrary number of parties.

Deterministic quantum dense coding networks

Abstract We consider the scenario of deterministic classical information transmission between multiple senders and a single receiver, when they a priori share a multipartite quantum state – an attempt towards building a deterministic dense coding network. Specifically, we prove that in the case of two or three senders and a single receiver, generalized Greenberger–Horne–Zeilinger (gGHZ) states are not beneficial for sending classical information deterministically beyond the classical limit, except when the shared state is the GHZ state itself. On the other hand, three- and four-qubit generalized W (gW) states with specific parameters as well as the four-qubit Dicke states can provide a quantum advantage of sending the information in deterministic dense coding. Interestingly however, numerical simulations in the three-qubit scenario reveal that the percentage of states from the GHZ-class that are deterministic dense codeable is higher than that of states from the W-class.

Statistics of leading digits leads to unification of quantum correlations

We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures or belong to the information-theoretic paradigm, exhibit a universal behavior. In particular, for Haar uniformly simulated arbitrary two-qubit states, we find that the first-digit distributions corresponding to a collection of chosen computable quantum correlation quantifiers tend to follow the first-digit law, known as Benfords law, when the rank of the states increases. Considering a two-qubit state which is obtained from a system governed by paradigmatic spin Hamiltonians, namely, the XY model in a transverse field, and the XXZ model, we show that entanglement as well as information-theoretic measures violate Benfords law. We quantitatively discuss the violation of Benfords law by using a violation parameter, and demonstrate that the violation parameter can signal quantum phase transitions occurring in these models. We also comment on the universality of the statistics of the first significant digits corresponding to appropriate measures of quantum correlations in the case of multipartite systems as well as systems in higher dimensions.