Quantum Random Access Codes Research Articles

Improvement in quantum communication using quantum switch

Applications of the quantum switch on quantum channels have recently become a topic of intense discussion. In the present work, we show that some useless (for communication) channels may provide useful communication under the action of quantum switch for several information-theoretic tasks: quantum random access codes, quantum steering, etc. We demonstrate that the quantum switch can also be useful in preventing the loss of coherence in a system when only coherence-breaking channels are the available channels for communication. We also show that if a useless quantum channel does not provide useful communication even after using a quantum switch, concatenating the channel with another suitable quantum channel, and subsequently using the switch, one may achieve useful communication. Finally, we discuss how the introduction of noise in the quantum switch can reduce the advantage that the switch provides.

Random access codes via quantum contextual redundancy

We propose a protocol to encode classical bits in the measurement statistics of many-body Pauli observables, leveraging quantum correlations for a random access code. Measurement contexts built with these observables yield outcomes with intrinsic redundancy, something we exploit by encoding the data into a set of convenient context eigenstates. This allows to randomly access the encoded data with few resources. The eigenstates used are highly entangled and can be generated by a discretely-parametrized quantum circuit of low depth. Applications of this protocol include algorithms requiring large-data storage with only partial retrieval, as is the case of decision trees. Using n-qubit states, this Quantum Random Access Code has greater success probability than its classical counterpart for n≥14 and than previous Quantum Random Access Codes for n≥16. Furthermore, for n≥18, it can be amplified into a nearly-lossless compression protocol with success probability 0.999 and compression ratio O(n2/2n). The data it can store is equal to Google-Drive server capacity for n=44, and to a brute-force solution for chess (what to do on any board configuration) for n=100.

Role of nonclassical temporal correlation in powering quantum random access codes

We explore the fundamental origin of the quantum advantage behind random access code. We propose new temporal inequalities compatible with noninvasive-realist models and show that any non-zero quantum advantage of n bits encoded to 1-bit random access code in the presence of shared randomness is equivalent to the violation of the corresponding temporal inequality. As an immediate consequence of this connection, we also prove that the maximal success probability of n bits encoded to 1-bit random access code can be obtained when the maximal violation of the corresponding inequality is achieved. We then show that any non-zero quantum advantage of n bits encoded to 1-bit random access code, or in other words, any non-zero violation of the corresponding temporal inequality can certify genuine randomness.

High-dimensional multi-input quantum random access codes and mutually unbiased bases

Quantum random access codes (QRACs) provide a basic tool for demonstrating the advantages of quantum resources and protocols, which have a wide range of applications in quantum information processing tasks. However, the investigation and application of high-dimensional $(d)$ multi-input $(n)$ $n^{(d)}\rightarrow1$ QRACs are still lacking. Here, we present a general method to find the maximum success probability of $n^{(d)}\rightarrow1$ QRACs. In particular, we give the analytical solution for maximum success probability of $3^{(d)}\rightarrow1$ QRACs when measurement bases are mutually unbiased bases (MUBs). Based on the analytical solution, we show the relationship between MUBs and $n^{(d)}\rightarrow1$ QRACs. First, we provide a systematic method of searching for the operational inequivalence of MUBs (OI-MUBs) when the dimension $d$ is a prime power. Second, we theoretically prove that, surprisingly, the commonly used Galois MUBs are not the optimal measurement bases to obtain the maximum success probability of $n^{(d)}\rightarrow1$ QRACs, which indicates a breakthrough according to the traditional conjecture regarding the optimal measurement bases. Furthermore, based on high-fidelity high-dimensional quantum states of orbital angular momentum, we experimentally achieve two-input and three-input QRACs up to dimension 11. We experimentally confirm the OI-MUBs when $d=5$. Our results open alternative avenues for investigating the foundational properties of quantum mechanics and quantum network coding.

The geometry of Bloch space in the context of quantum random access codes

We study the communication protocol known as a quantum random access code (QRAC) which encodes n classical bits into m qubits ( $$m<n$$ ) with a probability of recovering any of the initial n bits of at least $$p>\tfrac{1}{2}$$ . Such a code is denoted by (n, m, p)-QRAC. If cooperation is allowed through a shared random string, we call it a QRAC with shared randomness. We prove that for any (n, m, p)-QRAC with shared randomness the parameter p is upper bounded by $$ \tfrac{1}{2}+\tfrac{1}{2}\sqrt{\tfrac{2^{m-1}}{n}}$$ . For $$m=2$$ , this gives a new bound of $$p\le \tfrac{1}{2}+\tfrac{1}{\sqrt{2n}}$$ confirming a conjecture by Imamichi and Raymond (AQIS’18). Our bound implies that the previously known analytical constructions of $$(3,2,\tfrac{1}{2}+\tfrac{1}{\sqrt{6}})$$ - , $$(4,2,\tfrac{1}{2}+\tfrac{1}{2\sqrt{2}})$$ - and $$(6,2,\tfrac{1}{2}+\tfrac{1}{2\sqrt{3}})$$ -QRACs are optimal. To obtain our bound, we investigate the geometry of quantum states in the Bloch vector representation and make use of a geometric interpretation of the fact that any two quantum states have a nonnegative overlap.

Proof-of-principle demonstration of sequential 3 → 1 quantum random access code via cascaded measurements.

Quantum random access code (QRAC) serves the communication task to encode a long message into a quantum system and allow the receiver to decode the initial information with a higher success probability than classical random access code (RAC). Here, we present an experimental demonstration of sequential 3 → 1 QRAC in the prepare-transform-measure scenario with one sender and three independent receivers. The experimental results show that, in the 3 → 1 QRAC scenario, three receivers can independently decode the initial information with an average success probability higher than the classical RAC.

Semi-device-independent randomness certification with partially free random sources using $$4\rightarrow 1$$ quantum random access code

Semi-device-independent randomness certification with partially free random sources using $$4\rightarrow 1$$ quantum random access code

Certification of three black boxes with unsharp measurements using 3 → 1 sequential quantum random access 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.

Widening the sharpness modulation region of an entanglement-assisted sequential quantum random access code: Theory, experiment, and application

The authors provide a method to widen the sharpness modulation region of sequential entanglement-assisted quantum random access code and show its application for sequential device independent randomness expansion.

Quantum Random Access Codes for Boolean Functions

Ann↦pmrandom access code (RAC) is an encoding ofnbits intombits such that any initial bit can be recovered with probability at leastp, while in a quantum RAC (QRAC), thenbits are encoded intomqubits. Since its proposal, the idea of RACs was generalized in many different ways, e.g. allowing the use of shared entanglement (called entanglement-assisted random access code, or simply EARAC) or recovering multiple bits instead of one. In this paper we generalize the idea of RACs to recovering the value of a given Boolean functionfon any subset of fixed size of the initial bits, which we callf-random access codes. We study and give protocols forf-random access codes with classical (f-RAC) and quantum (f-QRAC) encoding, together with many different resources, e.g. private or shared randomness, shared entanglement (f-EARAC) and Popescu-Rohrlich boxes (f-PRRAC). The success probability of our protocols is characterized by thenoise stabilityof the Boolean functionf. Moreover, we give anupper boundon the success probability of anyf-QRAC with shared randomness that matches its success probability up to a multiplicative constant (andf-RACs by extension), meaning that quantum protocols can only achieve a limited advantage over their classical counterparts.

Sequential 3 → 1 quantum random access code utilizing unsharp measurements

Quantum random access codes (QRACs) are important communication tasks that are usually implemented in prepare-and-measure scenarios. The receiver tries to retrieve one arbitrarily chosen bit of the original bit-string from the code qubit sent by the sender. In this Letter, we analyze in detail the sequential version of the 3→1 QRAC with two receivers. The average successful probability for the strategy of unsharp measurement is derived. The prepare-and-measure strategy within projective measurement is also discussed. It is found that sequential 3→1 QRAC with weak measurement cannot be always superior to the one with projective measurement, as the 2→1 version can be.

Efficient Discrete Feature Encoding for Variational Quantum Classifier

Recent days have witnessed significant interests in applying quantum-enhanced techniques for solving a variety of machine learning tasks. Variational methods that use quantum resources of imperfect quantum devices with the help of classical computing techniques are popular for supervised learning. Variational quantum classification (VQC) is one of such methods with possible quantum advantage in using quantum-enhanced features that are hard to compute by classical methods. Its performance depends on the mapping of classical features into a quantum-enhanced feature space. Although there have been many quantum-mapping functions proposed so far, there is little discussion on efficient mapping of discrete features, such as age group, zip code, and others, which are often significant for classifying datasets of interest. We first introduce the use of quantum random-access coding (QRAC) to map such discrete features efficiently into limited number of qubits for VQC. In numerical simulations, we present a range of encoding strategies and demonstrate their limitations and capabilities. We experimentally show that QRAC can help speeding up the training of VQC by reducing its parameters via saving on the number of qubits for the mapping. We confirm the effectiveness of the QRAC in VQC by experimenting on classification of real-world datasets with both simulators and real quantum devices.

Experimental Characterization of Unsharp Qubit Observables and Sequential Measurement Incompatibility via Quantum Random Access Codes.

Unsharp measurements are increasingly important for foundational insights in quantum theory and quantum information applications. Here, we report an experimental implementation of unsharp qubit measurements in a sequential communication protocol, based on a quantum random access code. The protocol involves three parties; the first party prepares a qubit system, the second party performs operations that return both a classical and quantum outcome, and the latter is measured by the third party. We demonstrate a nearly optimal sequential quantum random access code that outperforms both the best possible classical protocol and any quantum protocol that utilizes only projective measurements. Furthermore, while only assuming that the involved devices operate on qubits and that detected events constitute a fair sample, we demonstrate the noise-robust characterization of unsharp measurements based on the sequential quantum random access code. We apply this characterization towards quantifying the degree of incompatibility of two sequential pairs of quantum measurements.

Experimental demonstration of sequential quantum random access codes

A random access code (RAC) is a strategy to encode a message into a shorter one in a way that any bit of the original can still be recovered with nontrivial probability. Encoding with quantum bits rather than classical ones can improve this probability, but has an important limitation: due to the disturbance caused by standard quantum measurements, qubits cannot be used more than once. However, as recently shown by Mohan, Tavakoli, and Brunner [New J. Phys. 21 083034, (2019)], weak measurements can alleviate this problem, allowing two sequential decoders to perform better than with the best classical RAC. We use single photons to experimentally show that these weak measurements are feasible and nonclassical success probabilities are achievable by two decoders. We prove this for different values of the measurement strength and use our experimental results to put tight bounds on them, certifying the accuracy of our setting. This proves the feasibility of using sequential quantum RACs for quantum information tasks such as the self-testing of untrusted devices.

Quantum random access codes and incompatibility of measurements

It is one of the peculiar features of quantum physics that some sets of measurements are incompatible in the sense that they cannot be performed simultaneously. Incompatibility is an important quantum resource as it enables Bell nonlocality and steering. Here we show that incompatibility is crucial also in certain communication tasks; we prove that quantum random access code performs better than its classical counterpart only when incompatible quantum measurements are used in the decoding task. As a consequence, evaluating the average success probability for quantum random access code provides a semi-device-independent test for the detection of quantum incompatibility. We further demonstrate that any incompatible pair of projective measurements gives an advantage over all classical strategies. Finally, we establish a connection between the maximal average success probability for quantum random access code and earlier quantities introduced to assess incompatibility.

On Quantum Chosen-Ciphertext Attacks and Learning with Errors

Large-scale quantum computing poses a major threat to classical public-key cryptography. Recently, strong “quantum access” security models have shown that numerous symmetric-key cryptosystems are also vulnerable. In this paper, we consider classical encryption in a model that grants the adversary quantum oracle access to encryption and decryption, but where we restrict the latter to non-adaptive (i.e., pre-challenge) queries only. We formalize this model using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA 1 in analogy to the classical CCA 1 security model. We show that the standard pseudorandom function ( PRF )-based encryption schemes are QCCA 1 -secure when instantiated with quantum-secure primitives. Our security proofs use a strong bound on quantum random-access codes with shared randomness. Revisiting plain IND − CPA -secure Learning with Errors ( LWE ) encryption, we show that leaking only a single quantum decryption query (and no other leakage or queries of any kind) allows the adversary to recover the full secret key with constant success probability. Information-theoretically, full recovery of the key in the classical setting requires at least a linear number of decryption queries. Our results thus challenge the notion that LWE is unconditionally “just as secure” quantumly as it is classically. The algorithm at the core of our attack is a new variant of the well-known Bernstein–Vazirani algorithm. Finally, we emphasize that our results should not be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.

Sequential random access codes and self-testing of quantum measurement instruments

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.

Superunsteerability as a quantifiable resource for random access codes assisted by Bell-diagonal states

We show how nonclassical correlations in local bipartite states can act as a resource for quantum information processing. Considering the task of quantum random access codes (RAC) through separable Bell-diagonal states, we demonstrate the advantage of superunsteerability over classical protocols assisted with two-bits of shared randomness. We propose a measure of superunsteerability, which quantifies nonclassicality beyond quantum steering, and obtain its analytical expression for Bell-diagonal states in the context of the two- and three-setting steering scenarios that are directly related to the quantum $2 \to 1$ and $3 \to 1$ RAC protocols, respectively. The maximal values of our quantifier yield the optimal quantum efficiency for both of the above protocols, thus showing that superunsteerability provides a precise characterization of the nonclassical resource for implementing RACs with separable Bell-diagonal class of states.

Self-testing mutually unbiased bases in the prepare-and-measure scenario

Mutually unbiased bases (MUBs) constitute the canonical example of incompatible quantum measurements. One standard application of MUBs is the task known as quantum random access code (QRAC), in which classical information is encoded in a quantum system, and later part of it is recovered by performing a quantum measurement. We analyse a specific class of QRACs, known as the $2^{d} \to 1$ QRAC, in which two classical dits are encoded in a $d$-dimensional quantum system. It is known that among rank-1 projective measurements MUBs give the best performance. We show (for every $d$) that this cannot be improved by employing non-projective measurements. Moreover, we show that the optimal performance can only be achieved by measurements which are rank-1 projective and mutually unbiased. In other words, the $2^{d} \to 1$ QRAC is a self-test for a pair of MUBs in the prepare-and-measure scenario. To make the self-testing statement robust we propose measures which characterise how well a pair of (not necessarily projective) measurements satisfies the MUB conditions and show how to estimate these measures from the observed performance. Similarly, we derive explicit bounds on operational quantities like the incompatibility robustness or the amount of uncertainty generated by the uncharacterised measurements. For low dimensions the robustness of our bounds is comparable to that of currently available technology, which makes them relevant for existing experiments. Lastly, our results provide essential support for a recently proposed method for solving the long-standing existence problem of MUBs.

The randomness in 2 $$\rightarrow $$ → 1 quantum random access code without a shared reference frame

The non-classical correlations presented in quantum random access code experiment are a powerful diagnostic tool for semi-device-independent random number generator protocols. The idea behind it is that if the user observes the optimal non-classical correlations, he has the guarantee that the unknown quantum states and measurements in the devices have carefully calibrated (we say have global reference frame), in a relationship which can bring to random outcomes. This means, for observing the non-classical correlations, the devices must have that calibration in previous. However, that calibration can’t always be guaranteed in reality due to unintentional flaws or failures of the quantum apparatuses, thus the devices do not always occur the wanted non-classical correlations. In this paper, we show there will always have non-classical correlations by the proper operations, when the devices have local reference. The quantity of true randomness in the observed non-classical correlations is then quantified by the violation values of some inequality. Besides we also consider the devices without local reference and show the probability of non-classical correlations occurring in 100 trials.