Aditi Sen

Local information as a resource in distributed quantum systems

A new paradigm for distributed quantum systems where information is a valuable resource is developed. After finding a unique measure for information, we construct a scheme for its manipulation in analogy with entanglement theory. In this scheme, instead of maximally entangled states, two parties distill local states. We show that, surprisingly, the main tools of entanglement theory are general enough to work in this opposite scheme. Up to plausible assumptions, we show that the amount of information that must be lost during the protocol of concentration of local information can be expressed as the relative entropy distance from some special set of states.

Conditions for monogamy of quantum correlations: Greenberger-Horne-Zeilinger versusWstates

Quantum correlations are expected to respect all the conditions required for them to be good measures of quantumness in the bipartite scenario. In a multipartite setting, sharing entanglement between several parties is restricted by the monogamy of entanglement. We take over the concept of monogamy to an information-theoretic quantum correlation measure, and find that it violates monogamy in general. Using the notion of interaction information, we identify necessary and sufficient conditions for the measure to obey monogamy, for arbitrary pure and mixed quantum states. We show that while three-qubit generalized Greenberger-Horne-Zeilinger states follow monogamy, generalized W states do not.

Quantum Correlation without Classical Correlations

We show that genuine multiparty quantum correlations can exist on its own, without a supporting background of genuine multiparty classical correlations, even in macroscopic systems. Such possibilities can have important implications in the physics of quantum information and phase transitions.

Trapped Ion Chain as a Neural Network: Error Resistant Quantum Computation

We demonstrate the possibility of realizing a neural network in a chain of trapped ions with induced long range interactions. Such models permit one to store information distributed over the whole system. The storage capacity of such a network, which depends on the phonon spectrum of the system, can be controlled by changing the external trapping potential. We analyze the implementation of error resistant universal quantum information processing in such systems.

Entanglement swapping of noisy states: A kind of superadditivity in nonclassicality

We address the question as to whether an entangled state that satisfies local realism will give a violation of the same after entanglement swapping in a suitable scenario. We consider such a possibility as a kind of superadditivity in nonclassicality. Importantly, it will indicate that checking for violation of local realism, in the state obtained after entanglement swapping, can be a method for detecting entanglement in the input state of the swapping procedure. We investigate various entanglement swapping schemes, which involve mixed initial states. The strength of violation of local realism by the state obtained after entanglement swapping is compared with the one for the input states. We obtain a kind of superadditivity of violation of local realism for Werner states, consequent upon entanglement swapping involving Greenberger-Horne-Zeilinger-state measurements. We also discuss whether entanglement swapping of specific states may be used in quantum repeaters with a substantially reduced need to perform the entanglement distillation step.

DENSE CODING WITH MULTIPARTITE QUANTUM STATES

We consider generalizations of the dense coding protocol with an arbitrary number of senders and either one or two receivers, sharing a multiparty quantum state, and using a noiseless channel. For the case of a single receiver, the capacity of such information transfer is found exactly. It is shown that the capacity is not enhanced by allowing the senders to perform joint operations. We provide a nontrivial upper bound on the capacity in the case of two receivers. We also give a classification of the set of all multiparty states in terms of their usefulness for dense coding. We provide examples for each of these classes, and discuss some of their properties.

Unified criterion for security of secret sharing in terms of violation of Bell inequalities

In secret sharing protocols, a secret is to be distributed among several partners such that leaving out any number of them, the rest do not have the complete information. Strong multiqubit correlations in the state by which secret sharing is carried out had been proposed as a criterion for security of such protocols against individual attacks by an eavesdropper. However we show that states with weak multiqubit correlations can also be used for secure secret sharing. That our state has weak multiqubit correlations is shown from the perspective of violation of local realism, and also by showing that its higher-order correlations are described by lower ones. We then present a unified criterion for security of secret sharing in terms of violation of local realism, which works when the secret sharing state is the Greenberger-Horne-Zeilinger state (with strong multiqubit correlations), as well as states of a different class (with weak multiqubit correlations)

Benford's law detects quantum phase transitions similarly as earthquakes

A century ago, it was predicted that the first significant digit appearing in a data would be nonuniformly distributed, with the number one appearing with the highest frequency. This law goes by the name of Benfords law. It holds for data ranging from infectious-disease cases to national greenhouse gas emissions. Quantum phase transitions are cooperative phenomena where qualitative changes occur in many-body systems at zero temperature. We show that the century-old Benfords law can detect quantum phase transitions, much like it detects earthquakes. Therefore, being certainly of very different physical origins, seismic activity and quantum cooperative phenomena may be detected by similar methods. The result has immediate implications in precise measurements in experiments in general, and for realizable quantum computers in particular. It shows that estimation of the first significant digit of measured physical observables is enough to detect the presence of quantum phase transitions in macroscopic systems.

Local indistinguishability of orthogonal pure states by using a bound on distillable entanglement

We show that the four states a‖00>+b‖11>, b‖00>-a‖11>, c‖01>+d‖10>, and d‖01>-c‖10>cannot be discriminated with certainty if only local operations and classical communication (LOCC) are allowed and if only a single copy is provided, except in the case when they are simply ‖00>, ‖11>, ‖01>, and ‖10> (in which case they are trivially distinguishable with LOCC). We go on to show that there exists a continuous range of values of a, b, c, and d such that even three states among the above four are not locally distinguishable, if only a single copy is provided. The proof follows from the fact that logarithmic negativity is an upper bound of distillable entanglement.

Monotonically increasing functions of any quantum correlation can make all multiparty states monogamous

We show that arbitrary multiparty quantum states can be made to satisfy monogamy by considering increasing functions of any bipartite quantum correlation that may itself lead to a nonmonogamous feature. This is true for states of an arbitrary number of parties in arbitrary dimensions, and irrespective of whether the state is pure or mixed. The increasing function of the quantum correlation satisfies all the expected quantum correlation properties as the original one. We illustrate this by considering a thermodynamic quantum correlation measure, known as quantum work-deficit. We find that although quantum work-deficit is non-monogamous for certain three-qubit states, there exist polynomials of the measure that satisfy monogamy for those states.