Vol.18 No.7&8, June 1, 2018

Stabiliser states are efficiently PAC-learnable (pp0541-0552)
          Andrea Rocchetto
The exponential scaling of the wave function is a fundamental property of quantum systems with far reaching implications in our ability to process quantum information. A problem where these are particularly relevant is quantum state tomography. State tomography, whose objective is to obtain an approximate description of a quantum system, can be analysed in the framework of computational learning theory. In this model, Aaronson (2007) showed that quantum states are Probably Approximately Correct (PAC)-learnable with sample complexity linear in the number of qubits. However, it is conjectured that in general quantum states require an exponential amount of computation to be learned. Here, using results from the literature on the efficient classical simulation of quantum systems, we show that stabiliser states are efficiently PAC-learnable. Our results solve an open problem formulated by Aaronson (2007) and establish a connection between classical simulation of quantum systems and efficient learnability.

Optimized CASCADE protocol for efficient information reconciliation (pp0553-0578)
          Metin Toyran, Mustafa Toyran, and Sitki Ozturk
CASCADE protocol is an error detection and correction (EDC) method proposed firstly for use in quantum key distribution (QKD) systems. It is used to detect and correct all the errors in keys transmitted over a noisy quantum channel. This is done by sending some redundant information about the key to receiver as usual. However, just as differently, this extra information is sent over another noiseless classical channel after the quantum transmission is completely finished. Briefly, all the errors in noisy quantum communication are detected and corrected by a later noiseless classical communication using CASCADE protocol. In QKD literature, this EDC process is also called as information reconciliation (IR) or secret key reconciliation (SKR). For an IR protocol in QKD, one of the main performance measures is efficiency which depends on the amount of redundant information sent to make EDC possible. Since this extra information is transmitted over public channels, everyone can get it easily. Because this can damage the secrecy of keys that must be kept secret from third parties, more efficient, that is revealing less information about keys, IR methods are needed. In this paper, we present more efficient implementations of CASCADE protocol, using some inherent information already available in the protocol, exactly known bits and already known parities. This information is used in error detection and correction steps of the protocol to decrease the redundancy in redundant information. Our experiments have shown that the resulting protocols have higher efficiency than both all the previous CASCADE versions and several other more recently proposed IR methods.

High-capacity quantum secret sharing based on orbital angular momentum (pp0579-0591)
          Huawang Qin and Raylin Tso
A high-capacity quantum secret sharing scheme based on orbital angular momentum is proposed. The dealer uses single particles in the orbital angular momentum (OAM) basis to bring the secret and encodes the secret through performing the transformation between the orbital angular momentum (OAM) basis and the angular position (ANG) basis. In the recovery, the participants perform the single-particle measurements to reconstruct the secret. The proposed scheme can use the multi-dimension of OAM to reach higher information capacity and enhanced security.

Distributed synthesis of chains with one-way biphotonic control (pp0592-0598)
          Yuri Ozhigov
An example of a one-way distributed computation is given in which the use of entangled states of two photons to synchronize processes gives a benefit. The process of assembling polymer chains at two remote points is considered; the quality of the assembly is determined when they are superimposed on each other. The effect of using entangled states is almost 14 percents.

The Delta game (pp0599-0616)
          Ken Dykema, Vern I. Paulsen, and Jitendra Prakash
We introduce a game related to the $I_{3322}$ game and analyze a constrained value function for this game over various families of synchronous quantum probability densities.

Entanglement of approximate quantum strategies in XOR games (pp0617-0631)
          Dimiter Ostrev and Thomas Vidick
We characterize the amount of entanglement that is sufficient to play any XOR game near-optimally. We show that for any XOR game $G$ and $\eps>0$ there is an $\eps$-optimal strategy for $G$ using $\lceil \eps^{-1} \rceil$ ebits of entanglement, irrespective of the number of questions in the game. By considering the family of XOR games CHSH($n$) introduced by Slofstra (Jour. Math. Phys. 2011), we show that this bound is nearly tight: for any $\eps>0$ there is an $n = \Theta(\eps^{-1/5})$ such that $\Omega(\eps^{-1/5})$ ebits are required for any strategy achieving bias that is at least a multiplicative factor $(1-\eps)$ from optimal in CHSH($n$).

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