49 research outputs found
Improving Einstein-Podolsky-Rosen Steering Inequalities with State Information
We discuss the relationship between entropic Einstein-Podolsky-Rosen
(EPR)-steering inequalities and their underlying uncertainty relations, along
with the hypothesis that improved uncertainty relations lead to tighter
EPR-steering inequalities. In particular, we discuss how the intrinsic
uncertainty in a mixed quantum state is used to improve existing uncertainty
relations and how this information affects one's ability to witness
EPR-steering. As an example, we consider the recent improvement (using a
quantum memory) to the entropic uncertainty relation between pairs of discrete
observables (Nat. Phys. 6, 659 (2010)) and show that a trivial substitution of
the tighter bound in the steering inequality leads to contradictions, due in
part to the fact that the improved bound depends explicitly on the state being
measured. By considering the assumptions that enter into the development of a
steering inequality, we derive correct steering inequalities from these
improved uncertainty relations and find that they are identical to ones already
developed (Phys. Rev. A, 87, 062103 (2013)). In addition, we consider how one
can use the information about the quantum state to improve our ability to
witness EPR-steering, and develop a new symmetric EPR-steering inequality as a
result.Comment: 6 page
Uncertainty Relation for Mutual Information
We postulate the existence of a universal uncertainty relation between the
quantum and classical mutual informations between pairs of quantum systems.
Specifically, we propose that the sum of the classical mutual information,
determined by two mutually unbiased pairs of observables, never exceeds the
quantum mutual information. We call this the complementary-quantum correlation
(CQC) relation and prove its validity for pure states, for states with one
maximally mixed subsystem, and for all states when one measurement is minimally
disturbing. We provide results of a Monte Carlo simulation suggesting the CQC
relation is generally valid. Importantly, we also show that the CQC relation
represents an improvement to an entropic uncertainty principle in the presence
of a quantum memory, and that it can be used to verify an achievable secret key
rate in the quantum one-time pad cryptographic protocol.Comment: 6 pages, 2 figure
EPR Steering Inequalities from Entropic Uncertainty Relations
We use entropic uncertainty relations to formulate inequalities that witness
Einstein-Podolsky-Rosen (EPR) steering correlations in diverse quantum systems.
We then use these inequalities to formulate symmetric EPR-steering inequalities
using the mutual information. We explore the differing natures of the
correlations captured by one-way and symmetric steering inequalities, and
examine the possibility of exclusive one-way steerability in two-qubit states.
Furthermore, we show that steering inequalities can be extended to generalized
positive operator valued measures (POVMs), and we also derive hybrid-steering
inequalities between alternate degrees of freedom.Comment: 10 pages, 2 figure
Extracting an Entanglement Signature from Only Classical Mutual Information
We introduce a quantity which is formed using classical notions of mutual information and which is computed using the results of projective measurements. This quantity constitutes a sufficient condition for entanglement and represents the amount of information that can be extracted from a bipartite system for spacelike separated observers. In addition to discussion, we provide simulations as well as experimental results for the singlet and maximally correlated mixed states
Improving Einstein–Podolsky–Rosen Steering Inequalities with State Information
We discuss the relationship between entropic Einstein–Podolsky–Rosen (EPR)-steering inequalities and their underlying uncertainty relations along with the hypothesis that improved uncertainty relations lead to tighter EPR-steering inequalities. In particular, we discuss how using information about the state of a quantum system affects oneʼs ability to witness EPR-steering. As an example, we consider the recent improvement to the entropic uncertainty relation between pairs of discrete observables (Berta et al., 2010 [10]). By considering the assumptions that enter into the development of a steering inequality, we derive correct steering inequalities from these improved uncertainty relations and find that they are identical to ones already developed (Schneeloch et al., 2013 [9]). In addition, we consider how one can use state information to improve our ability to witness EPR-steering, and develop a new continuous variable symmetric EPR-steering inequality as a result
Large-Alphabet Quantum Key Distribution Using Energy-Time Entangled Bipartite States
We present a protocol for large-alphabet quantum key distribution (QKD) using energy-time entangled biphotons. Binned, high-resolution timing measurements are used to generate a large-alphabet key with over 10 bits of information per photon pair, albeit with large noise. QKD with 5% bit error rate is demonstrated with 4 bits of information per photon pair, where the security of the quantum channel is determined by the visibility of Franson interference fringes. The protocol is easily generalizable to even larger alphabets, and utilizes energy-time entanglement which is robust to transmission over large distances in fiber
Device-Independent Quantum Key Distribution with Generalized Two-Mode Schrödinger Cat States
We show how weak nonlinearities can be used in a device-independent quantum key distribution (QKD) protocol using generalized two-mode Schrödinger cat states. The QKD protocol is therefore shown to be secure against collective attacks and for some coherent attacks. We derive analytical formulas for the optimal values of the Bell parameter, the quantum bit error rate, and the device-independent secret key rate in the noiseless lossy bosonic channel. Additionally, we give the filters and measurements which achieve these optimal values. We find that, over any distance in this channel, the quantum bit error rate is identically zero, in principle, and the states in the protocol are always able to violate a Bell inequality. The protocol is found to be superior in some regimes to a device-independent QKD protocol based on polarization entangled states in a depolarizing channel. Finally, we propose an implementation for the optimal filters and measurements
Preservation of Energy-Time Entanglement in a Slow Light Medium
We demonstrate the preservation of entanglement of an energy-time entangled biphoton through a slow light medium. Using the D1 and D2 fine structure resonances of Rubidium, we delay one photon of the 1.5 THz biphoton by ∼1.3 correlation lengths and measure the fourth order correlation fringes. After the group delay the fringe visibility is reduced from 97.0±4.4% to 80.0±4.8%, but is still sufficient to violate a Bell inequality. We show that temporal broadening is the primary mechanism for reducing the fringe visibility and that smaller bandwidths lead to greatly reduced broadening