Vaibhav Madhok

Interpreting quantum discord through quantum state merging

We present an operational interpretation of quantum discord based on the quantum state merging protocol. Quantum discord is the markup in the cost of quantum communication in the process of quantum state merging, if one discards relevant prior information. Our interpretation has an intuitive explanation based on the strong subadditivity of von Neumann entropy. We use our result to provide operational interpretations of other quantities like the local purity and quantum deficit. Finally, we discuss in brief some instances where our interpretation is valid in the single-copy scenario.

Quantum discord as a resource in quantum communication

As quantum technologies move from the issues of principle to those of practice, it is important to understand the limitations on attaining tangible quantum advantages. In the realm of quantum communication, quantum discord captures the damaging effects of a decoherent environment. This is a consequence of quantum discord quantifying the advantage of quantum coherence in quantum communication. This establishes quantum discord as a resource for quantum communication processes. We discuss this progress, which derives a quantitative relation between the yield of the fully quantum Slepian–Wolf (FQSW) protocol in the presence of noise and the quantum discord of the state involved. The significance of quantum discord in noisy versions of teleportation, super-dense coding, entanglement distillation and quantum state merging are discussed. These results lead to open questions regarding the tradeoff between quantum entanglement and discord in choosing the optimal quantum states for attaining palpable quantum advantages in noisy quantum protocols.

Entanglement and the generation of random states in the quantum chaotic dynamics of kicked coupled tops.

We study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time averaged entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section – it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudo-random states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. For a map with global chaos, we derive that value based on new analytic results for the typical entanglement in a subspace defined by the symmetries of the system. For a mixed phase space, we use the Percival conjecture to identify a “chaotic subspace” of the Hilbert space. The typical entanglement, averaged over the unitarily invariant Haar measure in this subspace, agrees with the long-time averaged entanglement for initial states in the chaotic sea. In all cases the dynamically generated entanglement is predicted by a unitary ensemble of random states, even though the system is time-reversal invariant, and the Floquet operator is a member of the circular orthogonal ensemble.

Signatures of chaos in the dynamics of quantum discord

We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time-averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behavior of two-qubit discord versus entanglement of the two qubits as measured by the concurrence. Our results provide evidence of signatures of chaos in dynamically generated discord.

Information gain in tomography - A quantum signature of chaos

We find quantum signatures of chaos in various metrics of information gain in quantum tomography. We employ a quantum state estimator based on weak collective measurements of an ensemble of identically prepared systems. The tomographic measurement record consists of a sequence of expectation values of a Hermitian operator that evolves under repeated application of the Floquet map of the quantum kicked top. We find an increase in information gain and, hence, higher fidelities in the reconstruction algorithm when the chaoticity parameter map increases. The results are well predicted by random matrix theory.

Quantum Discord in Quantum Information Theory From Strong Subadditivity to the Mother Protocol

Positivity of quantum discord is shown to be equivalent to the strong sub additivity of the von Neumann entropy. This leads to a connection between the mother protocol of quantum information theorya[ 17 ] and quantum discord. We exploit this to show that discord is a measure coherence in the performance of the mother protocol. Since the mother protocol is a unification of an important class of problems (those that are bipartite, unidirectional and memoryless), we show discord to be a measure of coherence in these protocols. Our work generalizes an earlier operational interpretation of discord provided in terms of quantum state merginga[ 10 ].

Quantum correlations as probes of chaos and ergodicity

Abstract Long-time average behavior of quantum correlations in a multi-qubit system, collectively modeled as a kicked top, is addressed here. The behavior of dynamical generation of quantum correlations such as entanglement, discord, concurrence, as previously studied, and Bell correlation function and tangle, as identified in this study, is a function of initially localized coherent states. Their long-time average reproduces coarse-grained classical phase space structures of the kicked top which contrast, often starkly, chaotic and regular regions. Apart from providing numerical evidence of such correspondence in the semiclassical regime of a large number of qubits, we use data from a recent transmons based experiment to explore this in the deep quantum regime of a 3-qubit kicked top. The degree to which quantum correlations can be regarded as a quantum signature of chaos, and in what ways the various correlation measures are similar or distinct are discussed.

Quantum Discord in Quantum Communication Protocols

We review an operational interpretation of quantum discord by quantifying it as the difference in the yield of the noisy and noiseless fully quantum Slepian-Wolf (FQSW) protocol and the closely related Mother protocol. The fully quantum Slepian-Wolf protocol is the most general form of unidirectional and bipartite quantum communication protocols and hence we provided an operational interpretation of discord for the entire spectrum of such protocols. We discuss examples giving specific scenarios for the role of discord in quantum communication. We provide examples of how the properties of discord can be derived intuitively from our operational view point.