Abstract

Complementarity have been an intriguing feature of physical systems for a long time. In this work we establish a new kind of complimentary relations in the frame work of quantum information processing tasks. In broadcasting of entanglement we create many pairs of less entangled states from a given entangled state both by local and non local cloning operations. These entangled states can be used in various information processing tasks like teleportation and superdense coding. Since these states are less entangled states it is quite intuitive that these states are not going to be as powerful resource as the initial states. In this work we study the usefulness of these states in tasks like teleportation and super dense coding. More precisely, we found out bounds of their capabilities in terms of several complimentary relations involving fidelity of broadcasting. In principle we have considered general mixed as a resource also separately providing different examples like a) Werner like states, b) Bell diagonal states. Here we have used both local and non local cloning operations as means of broadcasting. In the later part of our work, we extend this result by obtaining bounds in form of complimentary relations in a situation where we have used 1 − N cloning transformations instead of 1 − 2 cloning transformations

Abstract

In this work we give a (n, n)-threshold protocol for sequential secret sharing of quantum information for the first time. By sequential secret sharing we refer to a situation where the dealer is not having all the secrets at the same time, at the beginning of the protocol; however if the dealer wishes to share secrets at subsequent phases she/he can realize it with the help of our protocol. First of all we present our protocol for three parties and later we generalize it for the situation where we have more (n > 3) parties. Interestingly, we show that our protocol of sequential secret sharing requires less amount of quantum as well as classical resource as compared to the situation wherein existing protocols are repeatedly used. Further in a much more realistic situation, we consider the sharing of qubits through two kinds of noisy channels, namely the phase damping channel (PDC) and the amplitude damping channel (ADC). When we carry out the sequential secret sharing in the presence of noise we observe that the fidelity of secret sharing at the kth iteration is independent of the effect of noise at the (k − 1)th iteration. In case of ADC we have seen that the average fidelity of secret sharing drops down to 1 2 which is equivalent to a random guess of the quantum secret. Interestingly, we find that by applying weak measurements one can enhance the average fidelity. This increase of the average fidelity can be achieved with certain trade off with the success probability of the weak measurements

Abstract

We introduce a new feature of no-signaling (Bell) non-local theories, namely, when a system of multiple parties manifests genuine non-local correlation, then there cannot be arbitrarily high nonlocal correlation among any subset of the parties. We call this feature, complementarity of genuine multipartite non-locality. We use Svetlichny’s criterion for genuine multipartite non-locality and nonlocal games to derive the complementarity relations under no-signaling constraints. We find that the complementarity relations are tightened for the much stricter quantum constraints. We compare this notion with the well-known notion of monogamy of non-locality. As a consequence, we obtain tighter non-trivial monogamy relations that take into account genuine multipartite non-locality. Furthermore, we provide numerical evidence showcasing this feature using a bipartite measure and several other well-known tripartite measures of non-locality.

Abstract

In extant quantum secret sharing protocols, once the secret is shared in a quantum network (qnet) it cannot be retrieved, even if the dealer wishes that his/her secret no longer be available in the network. For instance, if the dealer is part of two qnets, say Q1 and Q2 and he/she subsequently finds that Q2 is more reliable than Q1, he/she may wish to transfer all her secrets from Q1 to Q2. Known protocols are inadequate to address such a revocation. In this work we address this problem by designing a protocol that enables the source/dealer to bring back the information shared in the network, if desired. Unlike classical revocation, the no-cloning theorem automatically ensures that the secret is no longer shared in the network.

Abstract

In this work, we extensively study the problem of broadcasting of entanglement. In the first part of the work, we reconceptualize the idea of state dependent quantum cloning machine, and in that process we introduce different types of state dependent cloners like static and dynamic state dependent cloners. We derive the conditions under which we can make these cloners independent of the input state. In the broadcasting part, as our resource initial state, we start with general two qubit state and consider specific examples like, non maximally entangled state (NME), Werner like state (WS), and Bell diagonal state (BDS). We apply both state dependent/ state independent cloners, both locally and non-locally, in each of these cases. Incidentally, we find several instances where state dependent cloners outperform state independent cloners in broadcasting. This work gives us a holistic view on the broadcasting of entanglement in various two qubit states, when we have an almost exhaustive sets of cloning machines in our arsenal

Abstract

We quantify the amount of correlations generated between two different output modes in the process of imperfect cloning and deletion processes. We use three different measures of quantum correlations and investigate their role in determining the fidelity of the cloning and the deletion. We obtain a bound on the total correlation generated in the successive processes of cloning and deleting operations. This bound displays a new kind of complementary relationship between the quantum correlations required in generating a copy of a quantum state and the amount of correlations required in bringing it back to the original state by deleting and vice versa. Our result shows that the better we clone (delete) a state, the more difficult it will be to bring the state back to its original form by the process of deleting (cloning).

Abstract

The basic motivation behind this work is to raise the question that whether post selection can be considered a valid physical transformation (on probability space) or not. We study the consequences of both answers set in a device (theory) independent framework, based only on observed statistics. We start with taking up post-selection as an assumption (if the answer is YES) and model the same using independent devices governed by Boolean functions. We establish analogy between the post selection functions and the general probabilistic games in a two party binary input-output scenario. As an observation, we categorize all possible post-selection functions based on the effect on a uniform input probability distribution. We find that post-selection can transform simple no signaling probability distributions to signaling. Similarly, solving NP (nondeterministic polynomial time) complete problems is easy independent of classical or quantum computation (in particular we prove that Post RP (Randomized Polynomial Time) = NP). Finally, we demonstrate an instance of the violation of the pigeon hole principle independent of underlying theory. As result of our theory independent modeling we conclude that post-selection as an assumption adds power to the underlying theory. In particular, quantum mechanics benefits more with the post-selection assumption, only because it admits a more general set of allowed probabilities as compared to the local hidden variable model. Without the assumption (if the answer is NO) we associate a device independent efficiency factor to quantify the cost of post selection. Our study shows that in the real world post-selection is not efficient enough to be of any advantage. But from an adversarial perspective it is still of significance. As an application, we obtain robust bounds on faking the bell violation (correlation in general) in terms of minimum efficiency required using post selection. Here in this work we argue that post-selection as an assumption is not physical. In the real world post-selection is simply dropping trials based on a pre-decided rule. It makes physical reality appear surprising. However, we suggest the use of post-selection with an device independent trial efficiency to avoid anomalous effects.

Abstract

It has been suggested that there may exist quantum correlations that go beyond entanglement. The existence of such correlations can be revealed by quantum discord, but not by the conventional measure of entanglement. We argue that a state displays quantumness that can be of local and nonlocal origin. The physical quantity such as the quantum discord probes not only the nonlocal quantumness but also the local quantumness, such as the “local superposition”. This can be a reason why such measures are non-zero when there is no entanglement. We consider a generalized version of the Werner state to demonstrate the interplay of local quantumness, nonlocal quantumness, and classical mixedness of a state.

Abstract

We find a single parameter family of genuinely entangled three qubit pure states, called maximally Bell inequality violating states, which exhibits maximum Bell inequality violation by the reduced bipartite system for a fixed amount of genuine tripartite correlation. This in turn implies that there holds a complementary relation between the Bell inequality violation by the reduced bipartite systems and the genuine tripartite correlation present in the tripartite pure states. Tangle, generalized geometric measure and discord monogamy score have been considered to quantify the genuine quantum correlation of the tripartite pure states. The complementarity suggests the Bell violation in the reduced two qubit system comes at the price of the total tripartite correlations present in the entire system.

Abstract

We study the dynamics of quantum dissension for three qubit states in various dissipative channels such as amplitude damping, dephasing and depolarizing. Our study is solely based on Markovian environments where quantum channels are without memory and each qubit is coupled to its own environment. We start with mixed GHZ, mixed W, mixture of separable states, a mixed biseparable state, as the initial states and mostly observe that the decay of quantum dissension is asymptotic in contrast to sudden death of quantum entanglement in similar environments. This is a clear indication of the fact that quantum correlation in general is more robust against the effect of noise. However, for a given class of initial mixed states we find a temporary leap in quantum dissension for a certain interval of time. More precisely, we observe the revival of quantum correlation to happen for certain time period. This signifies that the measure of quantum correlation such as quantum discord, quantum dissension, defined from the information theoretic perspective is different from the correlation defined from the entanglement-separability paradigm and can increase under the effect of the local noise. We also study the effects of these channels on the monogamy score of each of these initial states. Interestingly, we find that for certain class of states and channels, there is change from negative values to positive values of the monogamy score with classical randomness as well as with time. This gives us an important insight in obtaining states which are freely sharable (polygamous state) from the states which are not freely sharable (monogamous). This is indeed a remarkable feature, as we can create monogamous states from polygamous states Monogamous states are considered to have more signatures of quantum ness and can be used for security purpose.