This deposit contains the manuscript and complete supplementary material supporting the hardware realization of binary Clifford quantum random access codes for the sectors n=4 and n=5 on the IBM Heron r2 processor ibm_kingston. A quantum random access code encodes n classical bits into a single quantum carrier so that any one bit can later be recovered with bias above one half. The sectors n=2 and n=3 are realized natively in the qubit Bloch sphere; the sectors with n greater than or equal to four require Hilbert-space dimension at least four and are realized here using mutually anticommuting Hermitian generators of the Clifford algebra. For n=4 and n=5 this places the encoding in dimension four, implemented on two physical qubits. The experiment covers all 64 input-query configurations of the n=4 sector and all 160 configurations of the n=5 sector, with 8192 shots per configuration and no error mitigation applied. The measured per-sector biases are 0.469 plus or minus 0.002 for n=4, against the predicted value of 0.500, and 0.432 plus or minus 0.002 for n=5, against the predicted value of approximately 0.447
This deposit contains the manuscript and complete supplementary material supporting the hardware realization of binary Clifford quantum random access codes for the sectors n=4 and n=5 on the IBM Heron r2 processor ibm_kingston. A quantum random access code encodes n classical bits into a single quantum carrier so that any one bit can later be recovered with bias above one half. The sectors n=2 and n=3 are realized natively in the qubit Bloch sphere; the sectors with n greater than or equal to four require Hilbert-space dimension at least four and are realized here using mutually anticommuting Hermitian generators of the Clifford algebra. For n=4 and n=5 this places the encoding in dimension four, implemented on two physical qubits. The experiment covers all 64 input-query configurations of the n=4 sector and all 160 configurations of the n=5 sector, with 8192 shots per configuration and no error mitigation applied. The measured per-sector biases are 0.469 plus or minus 0.002 for n=4, against the predicted value of 0.500, and 0.432 plus or minus 0.002 for n=5, against the predicted value of approximately 0.447
A (Quantum) Random Access Code ((Q)RAC) is a scheme that encodes n bits into m (qu)bits such that any of the n bits can be recovered with a worst case probability p>21. Such a code is denoted by the triple (n,m,p). It is known that n<4m for all QRACs and n<2m for classical RACs. These bounds are also known to be tight, as explicit constructions exist for n=4m−1 and n=2m−1 for quantum and classical codes respectively. We generalize (Q)RACs to a scheme encoding nd-levels into m (qu)-d-levels such that any d-level can be recovered with the probability for every wrong outcome value being less than d1. We construct explicit solutions for all n≤d−1d2m−1. For d=2, the constructions coincide with those previously known. We show that the (Q)RACs are d-parity-oblivious, generalizing ordinary parity-obliviousness. We further investigate optimization of the success probabilities. For d=2, we use the measure operators of the previously best known solutions, but improve the encoding states to give a higher success probability. We conjecture that for maximal (n=4m−1,m,p) QRACs, p=21+(3+1)m−11 is possible and show that it is an upper bound for the measure operators that we use. When we compare (n,m,pq) QRACs with classical (n,2m,pc) RACs, we can always find pq≥pc, but the classical code gives information about every input bit simultaneously, while the QRAC only gives information about a subset. For several different (n,2,p) QRACs, we see the same trade-off, as the best p values are obtained when the number of bits that can be obtained simultaneously is as small as possible. The trade-off is connected to parity-obliviousness, since high certainty information about several bits can be used to calculate probabilities for parities of subsets.
An ( n ,1, p )-quantum random access (QRA) coding, introduced by Ambainis et al (1999 ACM Symp. Theory of Computing p 376), is the following communication system: the sender which has n -bit information encodes his/her information into one qubit, which is sent to the receiver. The receiver can recover any one bit of the original n bits correctly with probability at least p , through a certain decoding process based on positive operator-valued measures. Actually, Ambainis et al shows the existence of a (2,1,0.85)-QRA coding and also proves the impossibility of its classical counterpart. Chuang immediately extends it to a (3,1,0.79)-QRA coding and whether or not a (4,1, p )-QRA coding such that p > 1/2 exists has been open since then. This paper gives a negative answer to this open question. Moreover, we generalize its negative answer for one-qubit encoding to the case of multiple-qubit encoding
A (quantum) random access code ((Q)RAC) is a scheme that encodes n bits into m (qu)bits such that any of the n bits can be recovered with a worst case probability p>21. We generalize (Q)RACs to a scheme encoding nd-levels into m (quantum) d-levels such that any d-level can be recovered with the probability for every wrong outcome value being less than d1. We construct explicit solutions for all $n\ensuremath{\le}\frac{{d}^{2m}\ensuremath{-}1}{d\ensuremath{-}1}$. For d=2, the constructions coincide with those previously known. We show that the (Q)RACs are d-parity oblivious, generalizing ordinary parity obliviousness. We further investigate optimization of the success probabilities. For d=2, we use the measure operators of the previously best-known solutions, but improve the encoding states to give a higher success probability. We conjecture that for maximal $(n={4}^{m}\ensuremath{-}1,m,p)$ QRACs, $p=\frac{1}{2}{1+{[{(\sqrt{3}+1)}^{m}\ensuremath{-}1]}^{\ensuremath{-}1}}$ is possible, and show that it is an upper bound for the measure operators that we use. We then compare (n,m,pq) QRACs with classical (n,2m,pc) RACs. We can always find ${p}_{q}\ensuremath{\ge}{p}_{c}$, but the classical code gives information about every input bit simultaneously, while the QRAC only gives information about a subset. For several different (n,2,p) QRACs, we see the same trade-off, as the best p values are obtained when the number of bits that can be obtained simultaneously is as small as possible. The trade-off is connected to parity obliviousness, since high certainty information about several bits can be used to calculate probabilities for parities of subsets.
We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This procedure is called (n,1,p) quantum random access code (QRAC) where p > 1/2 is its success probability. It is known that (2,1,0.85) and (3,1,0.79) QRACs (with no classical counterparts) exist and that (4,1,p) QRAC with p > 1/2 is not possible. We extend this model with shared randomness (SR) that is accessible to both parties. Then (n,1,p) QRAC with SR and p > 1/2 exists for any n > 0. We give an upper bound on its success probability (the known (2,1,0.85) and (3,1,0.79) QRACs match this upper bound). We discuss some particular constructions for several small values of n. We also study the classical counterpart of this model where n bits are encoded into 1 bit instead of 1 qubit and SR is used. We give an optimal construction for such codes and find their success probability exactly--it is less than in the quantum case. Interactive 3D quantum random access codes are available on-line at http://home.lanet.lv/~sd20008/racs .
This preprint develops marginal information persistence as a framework in which information itself is treated as the dynamical variable under repeated protocol composition. The central question is which information measures vanish, remain marginally finite, or persist exactly as concatenation depth increases. For the canonical binary concatenated entanglement-assisted random access code, the complete pre-query quantum register is characterized in closed form for arbitrary primitive correlation bias. At the Tsirelson point, Bob's complete register retains exactly one bit of Holevo information about the full database at every concatenation depth, while every individual target correlation decays exponentially. The work further distinguishes information stored in the quantum register from information operationally extractable from a single copy. For the associated critical Clifford ensemble, the accessible-information problem reduces exactly to a global unit-vector optimization. Explicit finite-depth bounds show that the optimal single-copy accessible information decays exponentially with concatenation depth, even though the complete-register Holevo information remains exactly one bit. The task-summed random-access score remains finite at the same critical point because it combines mutually exclusive query contexts. Complete-register Holevo information, target marginals, task-summed random-access information, and single-copy accessible information therefore occupy distinct asymptotic classes under the same recursion. The analysis connects marginal information persistence with Information Causality, Clifford observables, Holevo information, accessible information, entropy optimization, and earlier Fisher-information formulations of criticality in concatenated protocols. It also clarifies the relation to previous work on persistence, random-access codes, and information-theoretic stability. Depth-two consequences are tested experimentally on IBM Marrakesh and Quantum Inspire Tuna-17. Both platforms yield positive 99.9% finite-shot lower confidence bounds on an implemented decoder gap. Full-register physical tomography provides separate reconstruction estimates of the corresponding strong information gap. This Zenodo record contains the main manuscript and the Supplementary Information.
The Clifford operators are an important and well-studied subset of quantum operations, in both the qubit and higher-dimensional qudit cases. While there are many ways to characterize this set, this paper aims to provide an ideal characterization, in the sense that it has the same characterization in every finite dimension, is characterized by a minimal set of gates, is constructive, and does not make any assumptions about non-Clifford operations or resources (such as the use of ancillas or the ability to make measurements). While most characterizations satisfy some of these properties, this appears to be the first characterization satisfying all of the above. As an application, we use these results to briefly analyze characterizations of Clifford embeddings, that is, the action of logical Clifford operations acting on qunits embedded in higher-dimensional qudits, inside the qudit Clifford framework.