We present a construction of one-time memories (OTMs) using classical-accessible stateless hardware, building upon the work of Broadbent et al. and Behera et al.. Unlike the aforementioned work, our approach leverages quantum random access codes (QRACs) to encode two classical bits, $b_0$ and $b_1$, into a single qubit state $\mathcal{E}(b_0 b_1)$ where the receiver can retrieve one of the bits with a certain probability of error. To prove soundness, we define a nonconvex optimization problem over POVMs on $\mathbb{C}^2$. This optimization gives an upper bound on the probability of distinguishing bit $b_{1-α}$ given that the probability that the receiver recovers bit $b_α$ is high. Assuming the optimization is sufficiently accurate, we then prove soundness against a polynomial number of classical queries to the hardware.
We present a construction of one-time memories (OTMs) using classical-accessible stateless hardware, building upon the work of Broadbent et al. and Behera et al.. Unlike the aforementioned work, our approach leverages quantum random access codes (QRACs) to encode two classical bits, b0 and b1, into a single qubit state E(b0b1) where the receiver can retrieve one of the bits with a certain probability of error. To prove soundness, we define a nonconvex optimization problem over POVMs on C2. This optimization gives an upper bound on the probability of distinguishing bit b1−α given that the probability that the receiver recovers bit bα is high. Assuming the optimization is sufficiently accurate, we then prove soundness against a polynomial number of classical queries to the hardware.
We construct simulation-secure one-time memories (OTM) in the random oracle model, and present a plausible argument for their security against quantum adversaries with bounded and adaptive depth. Our contributions include: (1) A simple scheme where we use only single-qubit Wiesner states and conjunction obfuscation (constructible from LPN): no complex entanglement or quantum cryptography is required. (2) A new POVM bound where e prove that any measurement achieving (1−ε) success on one basis has conjugate-basis guessing probability at most 2m1+O(ε41). (3) Simultation-secure OTMs in the quantum random oracle model where an adversary can only query the random oracle classically. (4) Adaptive depth security where, via an informal application of a lifting theorem from Arora et al., we conjecture security against adversaries with polynomial quantum circuit depth between random oracle queries.
Security against adaptive, depth-bounded, quantum adversaries captures many realistic attacks on OTMs built from single-qubit states; our work thus paves the way for practical and truly secure one-time programs. Moreover, depth bounded adaptive adversarial models may allow for encoding one-time memories into error corrected memory states, opening the door to implementations of one-time programs which persist for long periods of time.
A central tenet of theoretical cryptography is the study of the minimal assumptions required to implement a given cryptographic primitive. One such primitive is the one-time memory (OTM), introduced by Goldwasser, Kalai, and Rothblum [CRYPTO 2008], which is a classical functionality modeled after a non-interactive 1-out-of-2 oblivious transfer, and which is complete for one-time classical and quantum programs. It is known that secure OTMs do not exist in the standard model in both the classical and quantum settings. Here, we propose a scheme for using quantum information, together with the assumption of stateless ( i.e. , reusable) hardware tokens, to build statistically secure OTMs. Via the semidefinite programming-based quantum games framework of Gutoski and Watrous [STOC 2007], we prove security for a malicious receiver making at most 0.114 n adaptive queries to the token (for n the key size), in the quantum universal composability framework, but leave open the question of security against a polynomial amount of queries. Compared to alternative schemes derived from the literature on quantum money, our scheme is technologically simple since it is of the "prepare-and-measure" type. We also give two impossibility results showing certain assumptions in our scheme cannot be relaxed.
Analytical construction of (n,n−1) quantum random access codes saturating the conjectured bound
Quantum Random Access Codes (QRACs) embody the fundamental trade-off between the compressibility of information into limited quantum resources and the accessibility of that information, serving as a cornerstone of quantum communication and computation. In particular, the (n,n−1)-QRACs, which encode n bits of classical information into n−1 qubits, provides an ideal theoretical model for verifying quantum advantage in high-dimensional spaces; however, the analytical derivation of optimal codes for general n has remained an open problem. In this paper, we establish an analytical construction method for (n,n−1)-QRACs by using an explicit operator formalism. We prove that this construction strictly achieves the numerically conjectured upper bound of the average success probability, P=1/2+(n−1)/n/2, for all n. Furthermore, we present a systematic algorithm to decompose the derived optimal POVM into standard quantum gates. Since the resulting decoding circuit consists solely of interactions between adjacent qubits, it can be implemented with a circuit depth of O(n) even under linear connectivity constraints. Additionally, we analyze the high-dimensional limit and demonstrate that while the non-commutativity of measurements is suppressed, an information-theoretic gap of O(logn) from the Holevo bound inevitably arises for symmetric encoding. This study not only provides a scalable implementation method for high-dimensional quantum information processing but also offers new insights into the mathematical structure at the quantum-classical boundary.
Information Theoretic One-Time Programs from Geometrically Local QNC0 Adversaries
We show how to construct simulation secure one-time memories, and thus one-time programs, without computational assumptions in the presence of constraints on quantum hardware. Specifically, we build one-time memories from random linear codes and quantum random access codes (QRACs) when constrained to non-adaptive, constant depth, and D-dimensional geometrically-local quantum circuit for some constant D. We place no restrictions on the adversary's classical computational power, number of qubits it can use, or the coherence time of its qubits. Notably, our construction can still be secure even in the presence of fault tolerant quantum computation as long as the input qubits are encoded in a non-fault tolerant manner (e.g. encoded as high energy states in non-ideal hardware). Unfortunately though, our construction requires decoding random linear codes and thus does not run in polynomial time. We leave open the question of whether one can construct a polynomial time information theoretically secure one-time memory from geometrically local quantum circuits. Of potentially independent interest, we develop a progress bound for information leakage via collision entropy (Renyi entropy of order 2) along with a few key technical lemmas for a "mutual information" for collision entropies. We also develop new bounds on how much information a specific 2↦1 QRAC can leak about its input, which may be of independent interest as well.
We study the persistent quantum and classical memory required for exact heralded storage and retrieval of quantum measurements. Given only black-box access to the measurement channel, we construct an exact compression of the port-based program into an outcome-type record and a quantum register, with total dimension polynomial in the query count. For every universal retrieval processor we prove the bounds Q+C≥log2n and 2Q+C≥log2((n−1)d2+1) on the numbers Q of qubits and C of bits of the program, for n-outcome POVMs on Cd with d≥2. For n≥2, no finite classical memory removes the need for quantum memory: any such processor requires a quantum program of dimension at least d, at that dimension its classical alphabet must have at least n symbols, and both minima are attained by a single-query protocol with success 1/d2. Combining direct-program compression with a converse from approximate measurement programming gives logarithmic total-memory scaling in 1/(1−p) as the uniform success probability p approaches one, at fixed d,n≥2. At fixed input dimension and target success below one, the optimal total-memory scaling is logarithmic in n. We also construct self-contained programs under branch-decomposition access and compare the quantum and classical costs of all constructions, including where the outcome-type record is kept: for POVMs with n nonzero rank-one effects the direct program admits a purely quantum allocation whose register is never larger than that of the minimal-Naimark unitary program and which succeeds more often whenever n>d.
A random access code (RAC) encodes an L-bit string into a k-bit message, L>k, so that any requested bit can be recovered with high probability; a quantum RAC (QRAC) uses k qubits instead. We give a geometric characterization of optimal classical (L,k)-RACs under average and worst-case decoding criteria. The average criterion is reduced to choosing 2k representatives in {0,1}L, while the worst-case criterion is reduced to a minimax problem over 2k points in [0,1]L with a distance-like objective. This framework proves optimality for several parameter families, with many optimal constructions arising from standard infinite families of binary linear codes. It also yields two explicit classical--quantum separations. First, for every L>1, we construct a (L,1)-QRAC whose average decoding success probability strictly exceeds the optimal classical value. Second, for the family (2k−1,k), we prove worst-case optimality of a classical RAC and construct a QRAC with strictly larger worst-case success probability. For the family (L,L−1), the framework identifies a classical RAC that is average-case optimal and, under a stated conjecture, also worst-case optimal. The same viewpoint further recovers explicit (L,L−1)-QRACs attaining a previously conjectured upper-bound value.