Session R28: Distributed Quantum Computation, Networking and Information Security II

Entanglement cost of quantum state preparation and channel simulation

We study various aspects of the entanglement cost of quantum state preparation and quantum channel simulation. First, we establish that the exact entanglement cost of any bipartite quantum state under PPT-preserving operations is given by a single-letter formula, here called the κ-entanglement of a quantum state. This formula is calculable by a semidefinite program, thus allowing for an efficiently computable solution for general quantum states. Notably, this is the first time that an entanglement measure for general bipartite states has been proven not only to possess a direct operational meaning but also to be efficiently computable, thus solving a question that has remained open since the inception of entanglement theory over two decades ago. Second, we study the exact entanglement cost of quantum channel simulation in the parallel setting. In particular, the largest κ-entanglement that can be established via a quantum channel remarkably gives a single-letter formula for the exact parallel PPT-entanglement cost of simulating this channel, and it is also efficiently computable by a semidefinite program.   

Communicating via Ignorance

Communication through a sequence of two identical, noisy, depolarising channels is impossible in conventional information theory. Surprisingly, it has been shown in the paper [1] communication becomes possible if the depolarising channels are within a quantum switch, where the order of the channels is in a quantum superposition [2,3]. We experimentally demonstrate this counterintuitive result in a quantum switch that uses polarisation to coherently control the order of two depolarising channels acting on the transverse spatial mode of a photon. We send (3.41±0.15)×10^-2 bits of information through two fully depolarising channels that are in an indefinite causal order. [4]
References:
1. D. Ebler et al, ``Enhanced Communication with the Assistance of Indefinite Causal Order,'' Phys. Rev. Lett., vol. 120, 120502 (2018).
2. G. Rubino et al., "Experimental verification of an indefinite causal order," Sci. Adv., vol. 3, e16025589 (2017).
3. K. Goswami et al., ``Indefinite Causal Order in a Quantum Switch,'' Phys. Rev. Lett. Vol. 121, 090503 (2018).
4. K. Goswami, J. Romero, and A. G. White, ``Communicating via ignorance,'' arXiv:1807.07383 (2018).   

Quantum Link Prediction in Complex Networks

Predicting the existence of a link in a complex network is a non-trivial task, namely for large social and biological networks, with important applications. Experiments to map the full structure of biological networks (e.g. protein-protein interactions) are very challenging, costly and time consuming, and large amounts of data is still missing. Link prediction methods are not only a key computational tool to aid these efforts in understanding complex biological systems, but also very useful for other studies of time-varying complex networks, as for example social networks.

In this work we present a novel method for link prediction in complex networks based on continuous-time quantum walks. The control of a relative phase allows our method to be used in different types of networks (physical, biological, social, etc.). By exploiting quantum coherence we are able to outperform the state of the art classical methods, indicating that our method is also able to capture complex local patterns (such as local communities around paths of length 3) without the need to impose a specific pattern structure. Our results indicate there is a strong potential for combining quantum algorithms with complex network research to produce tools with direct and immediate experimental relevance.   

Indefinite Causal Order

Quantum mechanics allows events to happen with no definite causal order: this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement.
Here we realise a photonic quantum switch, where two operations, A and B, act in a quantum superposition of their two possible orders.
The operations are on the transverse spatial mode of the photons, while polarisation coherently controls their order. Our implementation ensures that the operations cannot be distinguished by spatial or temporal position. It also allows qudit encoding in the target. We confirm our quantum switch has no definite causal order by constructing a causal witness and measuring its value to be 18 standard deviations beyond the definite-order bound.   

Counterfactual Quantum Superdense Coding

Quantum superdense coding (QSC) ) is one of the most striking effects in quantum communication. It enables one to transmit a two-bit classical message by sending only one qubit using initially shared entanglement. In this article, we present a counterfactual QSC scheme that enables remote parties to accomplish this task without prior entanglement but no physical particle is found in the transmission channel. We consider two remote parties, namely Alice (sender) and Bob (receiver), have untangled particles---an electron and a photon. First, we generate entanglement between the electron and photon without transmitting any physical particle over the channel. Alice performs one of the four unitary operations μ ∈ {Ι, σ_x, σ_Y, σ_Z } on her entangled particle. Instead of transmitting her entangled particle to Bob, Alice and Bob perform counterfactual Bell-state analysis based on the chained quantum Zeno effect to distinguish between the four Bell-states under local operations and enable Bob to decode the two-bit classical message.   

Drone-based Quantum Key Distribution

Recent advances in quantum memories point to the future viability of quantum networking, including quantum cryptography. To be truly multi-purpose, future quantum communication networks should consist of a variety of platforms, e.g., airplanes, drones, and ships, though the motion of these platforms precludes the use of fiber-based approaches to quantum cryptography; free-space quantum key distribution (QKD) systems have historically been rather bulky. Small moving platforms, such as multirotor drones, are ideal for reconfigurable networks in both urban and rural environments but are only capable of supporting lightweight payloads (< 10 kg). Here we discuss our current progress in developing a reconfigurable network of two or more small multi-rotor drones implementing a modified BB84 quantum key distribution protocol over a free-space optical channel. This requires the development of fast and lightweight sources of polarized photons with no side channel leakage, miniaturization of time-tagging electronics and single-photon detectors, and the development of a robust signal acquisition and pointing and tracking system.   

Quantum Internet Applications

In this talk, we will discuss the application layer of a quantum internet. In such a network, the nodes are connected by quantum communication links, and can altogether be in an arbitrary entangled state. This allows the network to run a wide range of application, much beyond quantum key distribution, the main application of current quantum communication networks.
We will first review the roadmap to develop such a network, and present the efforts to identify, classify and develop applications that could be implemented while the capabilities of the network are improving.
We will then focus on two specific application domains. The first ones are on authentication mechanisms. It is well known that quantum key distribution requires authenticated classical channels in order to avoid basic attacks from eavesdropper. We will show that the common solution adopted by quantum key distribution systems becomes impractical when the complexity of networks increases. We will then review alternative solutions, and discuss their security.
The second type of applications is for multiparty computation. In this setting, some parties want to compute a distributed function of distributed inputs while revealing as little information as possible. This problem is impossible to solve in full generality, even using quantum ressources. There are, however, several restricted settings which admit solutions. We will review some of these settings, and the main techniques used to make the protocols secure.   

Quantum-Assisted Telescope Arrays

Quantum networks provide a platform for astronomical interferometers capable of imaging faint stellar objects. We present a protocol with efficient use of quantum resources and modest quantum memories. In our approach, the quantum state of incoming photons along with an arrival time index is stored in a binary qubit code at each receiver. Nonlocal retrieval of the quantum state via entanglement-assisted parity checks at the expected photon arrival rate allows for direct extraction of phase difference, effectively circumventing transmission losses between nodes. Compared to prior proposals, our scheme, based on efficient quantum data compression, offers an exponential decrease in required entanglement bandwidth. We show that it can be operated as a broadband interferometer and generalized to multiple nodes. We also analyze how imaging based on the quantum Fourier transform provides improved signal-to-noise ratio compared to classical processing. Finally, we discuss physical realizations including photon detection-based quantum state transfer. Experimental implementation is then feasible with near-term technology, enabling optical imaging of astronomical objects akin to well-established radio interferometers and pushing resolution beyond what is practically achievable classically.   

Long distance measurement-device-independent quantum key distribution without reference calibration

Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) can reduce the complexity of practical systems caused by the alignment of the reference frame. Lengthening the transmission distance and improving the system clock rate are essential in practical applications of QKD. Herein, in an asymptotic case, we report the results of RFI-MDI-QKD over a distance of 160 km at a clock rate of 50 MHz. By considering the statistical fluctuation of a finite key, we experimentally implemented a four-intensity decoy-state RFI-MDI-QKD protocol with biased bases at transmission distances of 100 km and 120 km. In addition, we compare the RFI-MDI-QKD protocol with the original MDI-QKD protocol when different isalignments of the reference frame are deployed. The results demonstrate the robustness of our scheme and that the key rate of RFI-MDI-QKD can be improved for a large misalignment of the reference frame.

Please see the Referece [H.-W. Liu,et al., Optica 5, 902 (2018)] for mor information about the results of our paper.   

Entangled-pulse generation inside coherent Ising machines using entanglement swapping

Coherent Ising machines (CIMs) have been proposed and demonstrated as heuristic solvers of hard combinatorial optimization problems. In current measurement-feedback-based CIMs (P.L. McMahon 2016), interactions between pulses (spins) are mediated via a classical feedback mechanism, and consequently no entanglement among pulses is generated. In this research, we investigate the use of entanglement swapping to introduce inter-pulse entanglement into such CIM-like architectures, using an external source of independently squeezed pulses. We develop models to describe the resulting intracavity dynamics as a function of system parameters, which can be numerically simulated to characterize the quantum noise and correlations in the pulse train. We also introduce and employ several measures of inseparability to quantify the nonclassical correlations that are realized. Analyzing these measures reveal trade-offs between system parameters and produce metrics useful for optimizing them. We present the requirements necessary to realize experimentally desirable levels of non-classical correlations.   

Maximal LELM Distinguishability of Qubit and Qutrit Bell States using Projective and Non-Projective Measurements

Numerous quantum information protocols make use of maximally entangled two-particle states, or Bell states, in which information is stored in the correlations between the two particles rather than their individual properties. Retrieving information stored in this way means distinguishing between different Bell states, yet the well known no-go theorem establishes that projective linear evolution and local measurement (LELM) detection schemes can only reliably distinguish three of the four qubit Bell states. We present newly-established maximum distinguishability bounds for the qutrit Bell states of bosons via projective LELM measurements; only three of the nine Bell states can be distinguished. Next, we extend to the case of non-projective measurements. We present a strengthened no-go theorem, which shows that general LELM measurements cannot reliably distinguish all four qubit Bell states. We also establish that at most five qutrit Bell states can be distinguished with generalized LELM measurements.   

Generating accessible entanglement in bosons via pair-correlated tunneling

We consider an extended Bose-Hubbard model that includes pair-correlated tunneling. We demonstrate that a minimal four-mode implementation of this model exhibits a pair-correlated regime in addition to Mott insulator and superfluid regimes. We propose a low complexity variational subspace for the ground state of the system in the pair-correlated regime, which we find to be numerically exact in pure pair-tunneling limit. Additionally, we propose a parameter-free high fidelity model wave function that qualitatively captures the features of the ground state in the pair-correlated regime. Due to particle number conservation, the operationally accessible entanglement vanishes deep inside the Mott insulator and superfluid regimes, however in the pure pair-correlated tunneling limit we find that the accessible entanglement entropy grows logarithmically with the number of particles. Additionally, we demonstrate that upon application of a unitary beamsplitter operation, the pair-correlated ground state is transformed into a state with completely accessible entanglement that is not limited by super-selection rules.