Unitary gates are an interesting resource for quantum communication in part because they are always invertible and are intrinsically bidirectional. This paper explores these two symmetries: time-reversal and exchange of Alice and Bob. We will present examples of unitary gates that exhibit dramatic separations between forward and backward capacities (even when the back communication is assisted by free entanglement) and between entanglement-assisted and unassisted capacities, among many others. Along the way, we will give a general time-reversal rule for relating the capacities of a unitary gate and its inverse that will explain why previous attempts at finding asymmetric capacities failed. Finally, we will see how the ability to erase quantum information and destroy entanglement can be a valuable resource for quantum communication.
In this article we consider flagged extensions of convex combination of quantum channels, and find general sufficient conditions for the degradability of the flagged extension. An immediate application is a bound on the quantum $Q$ and private $P$ capacities of any channel being a mixture of a unitary map and another channel, with the probability associated to the unitary component being larger than $1/2$. We then specialize our sufficient conditions to flagged Pauli channels, obtaining a family of upper bounds on quantum and private capacities of Pauli channels. In particular, we establish ne…
Time Reversal and n-qubit Canonical Decompositions
对于n是偶数个量子比特和v是酉演化，酉群的矩阵分解v=k1 a k2是明确可计算的，并且允许研究并发纠缠单调的动力学。该并发正则分解（CCD）的边因子k1和k2是并发对称的，因此动力学问题归结为对因子a的考虑。在这项工作中，我们提供了一个显式的数值算法计算v=k1 k2为n奇数。此外，在奇数情况下，我们将单调性提升为双参数函数，从而允许奇数量子比特中的并发动力学理论。一般化也可以使用CCD来研究，再次导致大多数酉的最大并发能力。关键的技术是考虑自旋翻转作为一个时间反演对称运营商在维格纳的公理化，原来的CCD推导可以重述完全在这个时间反演。在途中，我们观察到Kramers的非简并性：任何时间反演对称n-量子比特哈密顿量的非简并本征态的存在要求（i）n偶数和（ii）所述本征态的最大并发。我们提供了如何应用这项工作的例子来研究自旋链哈密顿纠缠的运动学和动力学。
Quantum metrology enhanced by effective time reversal
Joint Center for Quantum Information and Computer Science, NIST and University of Maryland（马里兰大学量子信息与计算联合中心）；University of Cambridge（剑桥大学）；Hitachi Cambridge Laboratory（日立剑桥实验室）；Department of Electrical Engineering and Computer Science（加州大学伯克利分校电气工程和计算机科学系）；University of California, Berkeley（加州大学伯克利分校物理系）；Department of Physics, University of California, Berkeley（马里兰大学物理科学与技术研究所）；Institute for Physical Science and Technology, University of Maryland
Passive environment assisted communication takes place via a quantum channel modeled as a unitary interaction between the information carrying system and an environment, where the latter is controlled by a passive helper, who can set its initial state such as to assist sender and receiver, but not help actively by adjusting her behaviour depending on the message. Here we investigate the information transmission capabilities in this framework by considering Gaussian unitaries acting on Bosonic systems. We consider both quantum communication and classical communication with helper, as well as cl…
Current theories of massless free particle assume {\sl unitary} space inversion and {\sl anti-unitary} time reversal operators. In so doing robust classes of possible theories are discarded. In the present work theories of massless systems are derived through a strictly deductive development from the principle of relativistic invariance, so that a kind of space inversion or time reversal operator is ruled out only if it causes inconsistencies. As results, new classes of consistent theories for massless isolated systems are explicitly determined. On the other hand, the approach determines defin…
Efficient certification of time-reversal symmetry requires entanglement
Technology Innovation Institute (TII)（技术创新研究所）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Dahlem Center for Complex Quantum Systems, Freie Universität Berlin（柏林自由大学达勒姆复杂量子系统中心）；Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）；Helmholtz-Zentrum Berlin für Materialien und Energie（赫尔霍兹柏林材料与能源中心）
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the Harper-Hofstadter, the Haldane models, demonstrating one-way waveguides and topologically protected edge states. Central to these discoveries is the chirality induced by time-symmetry breaking. In quantum walk algorithms, recent work has discovered implications time-reversal symmetry breaking has on the transport of quantum states which has enabled a host of new ex…
In this work, we study quantum many-body teleportation, where a single qubit is teleported through a strongly-interacting quantum system, as a result of a scrambling unitary and local measurements on a few qubits. Usual many-body teleportation protocols require a double copy of the system, and backward time evolution, we demonstrate that teleportation is possible in the 2D spin-$1/2$ XY model, without these constraints. The necessary long-range entanglement for teleportation is generated from the model hosting special eigenstates known as rainbow scars. We outline a specific protocol for prepa…
Bogoliubov excitations of Bose-Einstein condensates in optical lattices may possess band topology in analogous to topological insulators in class AII of fermions. Using the language of the Krein-space theory, this topological property is shown to be protected by a pseudo-time-reversal symmetry that is pseudo-antiunitary and squares to $-1$, with the associated bulk topological invariant also being a $\mathbb Z_2$ index. We construct three equivalent expressions for it, relating to the Pfaffian, the pseudo-time-reversal polarization, and most practically, the Wannier center flow, all adopted fr…
We consider a time reversal symmetry (TRS) broken Kane-Mele model superimposed with Haldane model and chart out the phase diagram using spin Chern number to investigate the fate of quantum anomalous Hall insulator (QAHI) and quantum spin Hall insulator (QSHI) phases. Interestingly, in addition to QSHI and QAHI phase, the phase diagram unveils quantum anomalous spin Hall insulator (QASHI) phase where only one spin sector is topological. We also find multicritical points where three / four topological phase boundaries coalesce. These topological phases are protected by an effective TRS and a com…
We calculate the hybrid entanglement entropy between coin and walker degrees of freedom in a non-unitary quantum walk. The model possesses a joint parity and time-reversal symmetry or PT-symmetry and supports topological phases when this symmetry is unbroken by its eigenstates. An asymptotic analysis at long times reveals that the quantum walk can indefinitely sustain hybrid entanglement in the unbroken symmetry phase even when gain and loss mechanisms are present. However, when the gain-loss strength is too large, the PT-symmetry of the model is spontaneously broken and entanglement vanishes.…
