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Random access coding is an information task that has been extensively studied and found many applications in quantum information. In this scenario, Alice receives an n-bit string x, and wishes to encode x into a quantum state x , such that Bob, when receiving the state x , can choose any bit i [ n ] and recover the input bit xi with high probability. Here we study two variants: parity-oblivious random access codes (RACs), where we impose the cryptographic property that Bob cannot infer any information about the parity of any subset of bits of the input apart from the single bits xi; and even-parity-oblivious RACs, where Bob cannot infer any information about the parity of any even-size subset of bits of the input. In this paper, we provide the optimal bounds for parity-oblivious quantum RACs and show that they are asymptotically better than the optimal classical ones. Our results provide a large non-contextuality inequality violation and resolve the main open problem in a work of Spekkens et al (2009 Phys. Rev. Lett.102 010401). Second, we provide the optimal bounds for even-parity-oblivious RACs by proving their equivalence to a non-local game and by providing tight bounds for the success probability of the non-local game via semidefinite programming. In the case of even-parity-oblivious RACs, the cryptographic property holds also in the device independent model.

A random access code (RAC), corresponding to a communication primitive with various applications in quantum information theory, is an instance of a preparation-and-measurement scenario. In this work, we consider ( n ,  d )-RACs constituting an n -length string, constructed from a d size set of letters, and send an encoding of the string in a single d -level physical system and present their quantum advantages. We first characterize optimal classical RACs and prove that a known classical strategy, called majority-encoding-identity-decoding , is optimal. We then construct a quantum protocol by exploiting only two incompatible measurements (the minimal requirement) and show the advantages beyond the classical one. We also discuss the generality of our results and whether quantum advantages are valid for all types of ( n , d ) ↦ 1 RACs.

Quantum random access codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.

A random access code (RAC), corresponding to a communication primitive with various applications in quantum information theory, is an instance of a preparation-and-measurement scenario. In this work, we consider ( n ,  d )-RACs constituting an n -length string, constructed from a d size set of letters, and send an encoding of the string in a single d -level physical system and present their quantum advantages. We first characterize optimal classical RACs and prove that a known classical strategy, called majority-encoding-identity-decoding , is optimal. We then construct a quantum protocol by exploiting only two incompatible measurements (the minimal requirement) and show the advantages beyond the classical one. We also discuss the generality of our results and whether quantum advantages are valid for all types of$(n, d) \\!\\mapsto\\! 1$RACs.

We consider two classes of quantum generalisations of random access code (RAC) and study the bounds for probabilities of success for such tasks. It provides a useful framework for the study of certain information processing tasks with constrained resources. The first class is based on a RAC with quantum inputs and output known as the no-signalling quantum RAC (NS-QRAC) box (Grudka et al 2015 Phys. Rev. A 92 052312), where unbounded entanglement and constrained classical communication are allowed. We show that it can be seen as quantum teleportation with constrained classical communication and provide a lower quantum bound for the success probability. We consider two modifications to the NS-QRAC scenario: the first, where unbounded entanglement and constrained quantum communication is allowed and the second, where bounded entanglement and unconstrained classical communication is allowed. We find a monogamy relation for the transmission fidelities, which—in contrast to the usual communication schemes—involves multiple senders and a single receiver. We provide an upper bounds for the latter and a lower one for the former. The second class is based on a RAC with a quantum channel and shared entanglement (Tavakoli et al 2021 PRX Quantum 2 040357). We study the set of tasks where two inputs made of two digits of d -base are encoded over a qudit and a maximally entangled state. We show that such tasks can be seen as quantum dense-coding with constrained quantum communication and explicit protocols, which give lower quantum bounds for the tasks’ efficiency, in dimensions d = 2 , 3 , 4 . The employed encoding utilises Gray codes.

Unsharp measurements play an increasingly important role in quantum information theory. In this paper, we study a three-party prepare-transform-measure experiment with unsharp measurements based on 3 → 1 sequential random access codes (RACs). We derive optimal trade-off between the two correlation witnesses in 3 → 1 sequential quantum random access codes (QRACs), and use the result to complete the self-testing of quantum preparations, instruments and measurements for three sequential parties. We also give the upper and lower bounds of the sharpness parameter to complete the robustness analysis of the self-testing scheme. In addition, we find that classical correlation witness violation based on 3 → 1 sequential RACs cannot be obtained by both correlation witnesses simultaneously. This means that if the second party uses strong unsharp measurements to overcome the classical upper bound, the third party cannot do so even with sharp measurements. Finally, we give the analysis and comparison of the random number generation efficiency under different sharpness parameters based on the determinant value, 2 → 1 and 3 → 1 QRACs separately. This letter sheds new light on generating random numbers among multi-party in semi-device independent framework.

It is known from Bellʼs theorem that quantum predictions for some entangled states cannot be mimicked using local hidden variable (LHV) models. From a computer science perspective, LHV models may be interpreted as classical computers operating on a potentially infinite number of correlated bits originating from a common source. As such, Bell inequality violations achieved through entangled states are able to characterize the quantum advantage of certain tasks, so long as the task itself imposes no restriction on the availability of correlated bits. However, if the number of shared bits is limited, additional constraints are placed on the possible LHV models, and separable, i.e. disentangled states may become a useful resource. Bell violations are therefore no longer necessary to achieve a quantum advantage. Here we show that, in particular, separable states improve the so-called random access codes, which is a class of communication problem wherein one party tries to read a portion of the data held by another distant party in the presence of finite shared randomness and limited classical communication. We also show how the bias of classical bits can be used to avoid wrong answers in order to achieve the optimal classical protocol and how the advantage of quantum protocols is linked to quantum discord.

With the growing interest in the Internet of Things (IoT), research on massive machine-type communication (mMTC) services is being actively promoted. Because mMTC services are required to serve a large number of devices simultaneously, a lack of resources during initial access can be a significant problem when providing mMTC services in cellular networks. Various studies on efficient preamble transmission have been conducted to solve the random access problem of mMTC services. However, supporting a large number of devices simultaneously with limited resources is a challenging problem. In this study, we investigate code-expanded random access (CeRA), which extends the limited preamble resources to the code domain to decrease the high collision rate. To solve the existing CeRA phantom codeword and physical uplink shared channel (PUSCH) resource shortage problems, we propose an optimal preamble codeword set selection algorithm based on mathematical analysis. The simulation results indicate that the proposed code-expanded random access scheme to enhance success probability (CeRA-eSP) achieves a higher random access success rate with a lower access delay compared to the existing random access schemes.

In this paper we show that a construction of Trevisan, solving the privacy amplification problem in the classical setting, also solves the problem when the adversary may keep quantum storage, thereby giving the first such construction with logarithmic seed length. The technique we use is a combination of Trevisan's approach of constructing an extractor from a black-box pseudo-random generator, together with locally list-decodable codes and previous work done on quantum random access codes. [PUBLICATION ABSTRACT]

Conventional computers operate deterministically using strings of zeros and ones called bits to represent information in binary code. Despite the evolution of conventional computers into sophisticated machines, there are many classes of problems that they cannot efficiently address, including inference, invertible logic, sampling and optimization, leading to considerable interest in alternative computing schemes. Quantum computing, which uses qubits to represent a superposition of 0 and 1, is expected to perform these tasks efficiently 1 – 3 . However, decoherence and the current requirement for cryogenic operation 4 , as well as the limited many-body interactions that can be implemented, pose considerable challenges. Probabilistic computing 1 , 5 – 7 is another unconventional computation scheme that shares similar concepts with quantum computing but is not limited by the above challenges. The key role is played by a probabilistic bit (a p-bit)—a robust, classical entity fluctuating in time between 0 and 1, which interacts with other p-bits in the same system using principles inspired by neural networks 8 . Here we present a proof-of-concept experiment for probabilistic computing using spintronics technology, and demonstrate integer factorization, an illustrative example of the optimization class of problems addressed by adiabatic 9 and gated 2 quantum computing. Nanoscale magnetic tunnel junctions showing stochastic behaviour are developed by modifying market-ready magnetoresistive random-access memory technology 10 , 11 and are used to implement three-terminal p-bits that operate at room temperature. The p-bits are electrically connected to form a functional asynchronous network, to which a modified adiabatic quantum computing algorithm that implements three- and four-body interactions is applied. Factorization of integers up to 945 is demonstrated with this rudimentary asynchronous probabilistic computer using eight correlated p-bits, and the results show good agreement with theoretical predictions, thus providing a potentially scalable hardware approach to the difficult problems of optimization and sampling. A probabilistic computer utilizing probabilistic bits, or p-bits, is implemented with stochastic nanomagnetic devices in a neural-network-inspired electrical circuit operating at room temperature and demonstrates integer factorization up to 945.