We consider the problem of implementing two-party interactive quantum

communication over noisy channels, a necessary endeavor if we wish to

fully reap quantum advantages for communication.\ \

\

For an arbitrary protocol with n messages, designed for

noiseless qudit channels, our main result is a simulation method that fails with probability less than

$2^{-\Theta(n\epsilon)}$ and uses a qudit channel $n(1 + \Theta

(\sqrt{\epsilon}))$ times, of which an $\epsilon$ fraction can be

corrupted adversarially.

\

The simulation is thus capacity achieving to leading order, and

we conjecture that it is optimal up to a constant factor in\

the $\sqrt{\epsilon}$ term.\ \

\

Furthermore, the simulation is in a model that does not require

pre-shared resources such as randomness or entanglement between the

communicating parties.

\

Surprisingly, this outperforms the best-known overhead of $1 +

O(\sqrt{\epsilon \log \log 1/\epsilon})$ in the corresponding

\emph{classical} model, which is also conjectured to be optimal

\ \ \ [Haeupler, FOCS\&$\#$39;14].

\

Our work also improves over the best previously known quantum result

where the overhead is a non-explicit large constant [Brassard \emph{et

\ \ al.}, FOCS\&$\#$39;14] for low $\epsilon$.

},
url = {http://acm-stoc.org/stoc2018/STOC-2018-Accepted.html},
author = {Debbie Leung and Ashwin Nayak and Ala Shayeghi and Dave Touchette and Penghui Yao and Nengkun Yu}
}
@article {1787,
title = {Quantum state tomography via reduced density matrices},
journal = {Physical Review Letters},
volume = {118},
year = {2017},
month = {2017/01/09},
pages = {020401},
abstract = {Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results advance the project of performing efficient and accurate quantum state tomography in practice.

}, doi = {10.1103/PhysRevLett.118.020401}, url = {http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.020401}, author = {Tao Xin and Dawei Lu and Joel Klassen and Nengkun Yu and Zhengfeng Ji and Jianxin Chen and Xian Ma and Guilu Long and Bei Zeng and Raymond Laflamme} } @article {1452, title = {Detecting Consistency of Overlapping Quantum Marginals by Separability}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/03/03}, pages = {032105}, abstract = { The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the $k$-symmetric extension problem in general, and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-known $k$-symmetric extension criterion for separability. }, doi = {10.1103/PhysRevA.93.032105}, url = {http://arxiv.org/abs/1509.06591}, author = {Jianxin Chen and Zhengfeng Ji and Nengkun Yu and Bei Zeng} } @conference {1903, title = {Exponential Separation of Quantum Communication and Classical Information}, booktitle = {20th Annual Conference on Quantum Information Processing (QIP)}, year = {2016}, month = {2016/11/28}, abstract = {We exhibit a Boolean function for which the quantum communication complexity is exponentially larger than the classical information complexity. An exponential separation in the other direction was already known from the work of Kerenidis et. al. [SICOMP 44, pp. 1550-1572], hence our work implies that these two complexity measures are incomparable. As classical information complexity is an upper bound on quantum information complexity, which in turn is equal to amortized quantum communication complexity, our work implies that a tight direct sum result for distributional quantum communication complexity cannot hold. The function we use to present such a separation is the Symmetric k-ary Pointer Jumping function introduced by Rao and Sinha [ECCC TR15-057], whose classical communication complexity is exponentially larger than its classical information complexity. In this paper, we show that the quantum communication complexity of this function is polynomially equivalent to its classical communication complexity. The high-level idea behind our proof is arguably the simplest so far for such an exponential separation between information and communication, driven by a sequence of round-elimination arguments, allowing us to simplify further the approach of Rao and Sinha.\

As another application of the techniques that we develop, we give a simple proof for an optimal trade-off between Alice\&$\#$39;s and Bob\&$\#$39;s communication while computing the related Greater-Than function on n bits: say Bob communicates at most b bits, then Alice must send n/exp(O(b)) bits to Bob. This holds even when allowing pre-shared entanglement. We also present a classical protocol achieving this bound.

\

},
url = {https://arxiv.org/abs/1611.08946},
author = {Anurag Anshu and Dave Touchette and Penghui Yao and Nengkun Yu}
}
@article {1783,
title = {Joint product numerical range and geometry of reduced density matrices},
year = {2016},
month = {2016/06/23},
abstract = {The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection Θ is convex in R3. The boundary ∂Θ of Θ may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti{\textquoteright}s theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range Π of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that ruled surface emerge naturally when taking a convex hull of Π. We show that, a ruled surface on ∂Θ sitting in Π has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of Θ, with two boundary pieces of symmetry breaking origin separated by two gapless lines.},
url = {http://arxiv.org/abs/1606.07422},
author = {Jianxin Chen and Cheng Guo and Zhengfeng Ji and Yiu-Tung Poon and Nengkun Yu and Bei Zeng and Jie Zhou}
}
@article {1689,
title = {Tomography is necessary for universal entanglement detection with single-copy observables},
journal = {Physical Review Letters},
volume = {116},
year = {2016},
month = {2016/06/07},
pages = {230501},
abstract = {Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal entanglement detection is possible without full state tomography. In this work, we prove a no-go theorem that rules out this possibility for any non-adaptive schemes that employ single-copy measurements only. We also examine in detail a previously implemented experiment, which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. By performing the experiment and analyzing the data, we demonstrate that the information gathered is indeed sufficient to reconstruct the state. These results reveal a fundamental limit for single-copy measurements in entanglement detection, and provides a general framework to study the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.},
doi = {10.1103/PhysRevLett.116.230501},
url = {http://arxiv.org/abs/1511.00581},
author = {Dawei Lu and Tao Xin and Nengkun Yu and Zhengfeng Ji and Jianxin Chen and Guilu Long and Jonathan Baugh and Xinhua Peng and Bei Zeng and Raymond Laflamme}
}
@article {1462,
title = {Discontinuity of Maximum Entropy Inference and Quantum Phase Transitions},
journal = {New Journal of Physics},
volume = {17},
year = {2015},
month = {2015/08/10},
pages = {083019},
abstract = { In this paper, we discuss the connection between two genuinely quantum
phenomena --- the discontinuity of quantum maximum entropy inference and
quantum phase transitions at zero temperature. It is shown that the
discontinuity of the maximum entropy inference of local observable measurements
signals the non-local type of transitions, where local density matrices of the
ground state change smoothly at the transition point. We then propose to use
the quantum conditional mutual information of the ground state as an indicator
to detect the discontinuity and the non-local type of quantum phase transitions
in the thermodynamic limit.
},
doi = {10.1088/1367-2630/17/8/083019},
url = {http://arxiv.org/abs/1406.5046v2},
author = {Jianxin Chen and Zhengfeng Ji and Chi-Kwong Li and Yiu-Tung Poon and Yi Shen and Nengkun Yu and Bei Zeng and Duanlu Zhou}
}