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

It has been suggested that there may exist quantum correlations that go beyond entanglement. The existence of such correlations can be revealed by information theoretic quantities such as quantum discord, but not by the conventional measures of entanglement. We argue that a state displays quantumness that can be of local and nonlocal origin. Information theoretic measures not only characterize the nonlocal quantumness but also the local quantumness, such as the “local superposition”. This can be a reason why such measures are nonzero 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

In a recent work, authors prove a yet another no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. In this short note, we show that in the presence of closed time like curves, one can indeed create superposition of unknown quantum states and evade the no-go result.

Abstract

We find a single parameter family of genuinely entangled three qubit pure states, called the maximally Bell inequality violating states (MBV), which exhibit maximum Bell inequality violation by the reduced bipartite system for a fixed amount of genuine tripartite entanglement quantified by the so called tangle measure. This in turn implies that there holds a complementary relation between the Bell inequality violation by the reduced bipartite systems and the tangle present in the three qubit states, not necessarily pure. The MBV states also exhibit maximum Bell inequality violation by the reduced bipartite systems of the three qubit pure states with a fixed amount of genuine tripartite correlation quantified by the generalized geometric measure, a genuine entanglement measure of multiparty pure states, and the discord monogamy score, a multipartite quantum correlation measure from information theoretic paradigm. The aforementioned complementary relation has also been established for three qubit pure states for the generalized geometric measure and the discord monogamy score respectively. The complementarity between the Bell inequality violation by the reduced bipartite systems and the genuine tripartite correlation suggests that the Bell inequality violation in the reduced two qubit system comes at the cost of the total tripartite correlation present in the entire system.

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

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

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

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 quantum correlations (QCs). This includes broadcasting of quantum entanglement as well as correlations that go beyond the notion of entanglement (QCsbE). It is quite well known from the “no-broadcasting theorem” that perfect broadcasting of QCs is not possible. However, it does not rule out the possibility of partial broadcasting of QCs where we can get lesser correlated states from a given correlated state. In order to have a holistic view of broadcasting, we investigate this problem by starting with a most general representation of two qubit mixed states in terms of the Bloch vectors. As a cloning transformation we have used universal symmetric optimal Buzek-Hillery (BH) cloner both locally and nonlocally. Unlike entanglement, we find that it is impossible to broadcast QCsbE optimally. Lastly, we generalize these results for any symmetric or asymmetric cloning machines as well. This result brings out a fundamental difference between the correlations defined from the perspective of entanglement and the correlations measure which claims to go beyond entanglement.

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.