Controlling the entropic uncertainty lower bound in two-qubit systems under decoherence (original) (raw)
Related papers
arXiv (Cornell University), 2012
The uncertainty of measurement on a quantum system can be reduced in present of quantum memory [M. Berta et. al. Nature Phys. {\bf 6}, 659 (2010)]. By measurement on quantum memory, some information (non-classical information) is inaccessible, hence, it limits the lower bound of entropic uncertainty relation. In the present work, we improve the lower bound of entropic uncertainty relation in presence of quantum memory by considering inaccessibility of non classical correlation at Bob side and also compare the lower bound given by M. Berta et. al. and our prescription for two different kind of shared bipartite state.
The uncertainty of measurement on a quantum system can be reduced in presence of quantum memory [M. Berta et. al. Nature Phys. {\bf 6}, 659 (2010)]. By measurement on quantum memory, some information (non-classical information) is inaccessible, hence, it limits the lower bound of entropic uncertainty relation. In the present work, we improve the lower bound of entropic uncertainty relation in presence of quantum memory by considering inaccessibility of non classical correlation at Bob side and also compare the lower bound given by M. Berta et. al. and our prescription for two different kind of shared bipartite state.
Tightening the tripartite quantum-memory-assisted entropic uncertainty relation
Physical Review A
The uncertainty principle determines the distinction between the classical and the quantum world. This principle states that it is not possible to measure two incompatible observables with the desired accuracy simultaneously. In quantum information theory, the Shannon entropy is used as an appropriate measure to express the uncertainty relation. Improving the bound of the entropic uncertainty relation is of great importance. The bound can be varied by considering an extra quantum system as the quantum memory which is correlated with the measured quantum system. One can extend the bipartite quantum-memory-assisted entropic uncertainty relation to the tripartite one in which the memory is split into two parts. Here, a lower bound is obtained for the tripartite quantum-memory-assisted entropic uncertainty relation. This lower bound has two extra terms compared with the lower bound in Renes and Boileau [J. M. Renes and J.-C. Boileau, Phys. Rev. Lett. 110, 020402 (2013)] which depends on the conditional von Neumann entropy, the Holevo quantity, and the mutual information. It is shown that the bound is tighter than other bounds derived earlier. It also leads to a lower bound for the quantum secret key rate. In addition, it is applied to obtain the states for which both the strong subadditivity and the Koashi-Winter inequalities turn into equalities.
A universal, memory-assisted entropic uncertainty relation
arXiv (Cornell University), 2013
We derive a new memory-assisted entropic uncertainty relation for non-degenerate Hermitian observables where both quantum correlations, in the form of conditional von Neumann entropy, and quantum discord between system and memory play an explicit role. Our relation is 'universal', in the sense that it does not depend on the specific observable, but only on properties of the quantum state. We contrast such an uncertainty relation with previously known memory-assisted relations based on entanglement and correlations. Further, we present a detailed comparative study of entanglement-and discord-assisted entropic uncertainty relations for systems of two qubits-one of which plays the role of the memory-subject to several forms of independent quantum noise, in both Markovian and non-Markovian regimes. We thus show explicitly that, partly due to the ubiquity and inherent resilience of quantum discord, discord-tightened entropic uncertainty relations often offer a better estimate of the uncertainties in play.
Uncertainty equality with quantum memory and its experimental verification
npj Quantum Information, 2019
As a very fundamental principle in quantum physics, uncertainty principle has been studied intensively via various uncertainty inequalities. A natural and fundamental question is whether an equality exists for the uncertainty principle. Here we derive an entropic uncertainty equality relation for a bipartite system consisting of a quantum system and a coupled quantum memory, based on the information measure introduced by Brukner and Zeilinger (Phys. Rev. Lett. 83:3354, 1999). The equality indicates that the sum of measurement uncertainties over a complete set of mutually unbiased bases on a subsystem is equal to a total, fixed uncertainty determined by the initial bipartite state. For the special case where the system and the memory are the maximally entangled, all of the uncertainties related to each mutually unbiased base measurement are zero, which is substantially different from the uncertainty inequality relation. The results are meaningful for fundamental reasons and give rise to operational applications such as in quantum random number generation and quantum guessing games. Moreover, we experimentally verify the measurement uncertainty relation in the presence of quantum memory on a five-qubit spin system by directly measuring the corresponding quantum mechanical observables, rather than quantum state tomography in all the previous experiments of testing entropic uncertainty relations.
Information-theoretic approach to quantum error correction and reversible measurement
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998
Quantum operations provide a general description of the state changes allowed by quantum mechanics. The reversal of quantum operations is important for quantum error-correcting codes, teleportation, and reversing quantum measurements. We derive information-theoretic conditions and equivalent algebraic conditions that are necessary and sufficient for a general quantum operation to be reversible. We analyze the thermodynamic cost of error correction and show that error correction can be regarded as a kind of "Maxwell demon," for which there is an entropy cost associated with information obtained from measurements performed during error correction. A prescription for thermodynamically efficient error correction is given.
Quantum measurements and entropic bounds on information transmission
2005
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the monotonicity theorem for relative entropies many bounds on the classical information extracted in a quantum measurement are obtained in a unified manner. In particular, it is shown that such bounds can all be stated as inequalities between mutual entropies. This approach based on channels gives rise to a unified picture of known and new bounds on the classical information (Holevo's, Shumacher-Westmoreland-Wootters', Hall's, Scutaru's bounds, a new upper bound and a new lower one). Some examples clarify the mutual relationships among the various bounds.
2016
We discuss some applications of various versions of uncertainty relations for both discrete and continuous variables in the context of quantum information theory. The Heisenberg uncertainty relation enables demonstration of the EPR paradox. Entropic uncertainty relations are used to reveal quantum steering for non-Gaussian continuous variable states. Entropic uncertainty relations for discrete variables are studied in the context of quantum memory where fine-graining yields the optimum lower bound of uncertainty. The fine-grained uncertainty relation is used to obtain connections between uncertainty and the nonlocality of retrieval games for bipartite and tipartite systems. The Robertson-Schrodinger uncertainty relation is applied for distinguishing pure and mixed states of discrete variables.
Fine-grained lower limit of entropic uncertainty in the presence of quantum memory
Phys. Rev. Lett. 110, 020402 (2013)
The limitation on obtaining precise outcomes of measurements performed on two non-commuting observables of a particle as set by the uncertainty principle in its entropic form, can be reduced in the presence of quantum memory. We derive a new entropic uncertainty relation based on fine- graining, which leads to an ultimate limit on the precision achievable in measurements performed on two incompatible observables in the presence of quantum memory. We show that our derived uncertainty relation tightens the lower bound set by entropic uncertainty for members of the class of two-qubit states with maximally mixed marginals, while accounting for the recent experimental results using maximally entangled pure states and mixed Bell-diagonal states. An implication of our uncertainty relation on the security of quantum key generation protocols is pointed out.
Quantum Information Processing, 2019
We derive the analytical expression of local quantum uncertainty for three qubit X-states. We give also the expressions of quantum discord and the negativity. A comparison of these three quantum correlations quantifiers is discussed in the special cases of mixed GHZ states and Bell-type states. We find that local quantum uncertainty gives the same amount of non-classical correlations as are measured by entropic quantum discord and goes beyond negativity. We also discuss the dynamics of non-classical correlations under the effect of phase damping, depolarizing and phase reversal channels. We find the local quantum uncertainty shows more robustness and exhibits, under phase reversal effect, revival and frozen phenomena. The monogamy property of local quantum uncertainty is also discussed. It is shown that it is monogamous for three qubit states.