Since the introduction of the complexity class QMA as a quantum-verifier analogue of NP (Kitaev, 1997), many have wondered whether quantum proofs are necessary or classical proofs suffice - that is, whether QMA = QCMA or QCMA != QMA (Aharonov and Naveh, 2002; Aaronson and Kuperberg, CCC '07). This longstanding question was recently answered by works of Bostanci, Haferkamp, Nirkhe, and Zhandry (STOC '26) and Bostanci, Huang, and Vaikuntanathan (FOCS '26), which showed that quantum proofs are more powerful than classical ones in the classical-oracle setting.
However, it remains unclear what exactly makes quantum proofs more powerful than classical ones. In the information-theoretic setting, a family of quantum states is not classicalizable if and only if it is unclonable. Indeed, these recent works also explicitly highlight the unclonability of their quantum proofs as a key mechanism behind their separations, and their arguments crucially rely on this property. This raises the question of whether unclonability is necessary for quantum proofs to be more powerful than classical ones.
In this work, we show that even clonable quantum proofs can be more powerful than classical ones relative to a classical oracle by constructing a classical oracle O such that QCMA^O != ClonableQMA^O. This resolves the open question of Nehoran and Zhandry (ITCS '24), who established the analogous separation relative to a quantum oracle. We also show a classical-oracle separation between BQP/clonableqpoly and BQP/poly, and give applications of our results to quantum cryptography.
The famous no-cloning principle has been shown recently to enable a number of uncloneable cryptographic primitives, including the copy-protection of certain functionalities. Here we address for the first time unkeyed quantum uncloneablity, via the study of a complexity-theoretic tool that enables a computation, but that is natively unkeyed: quantum advice. Remarkably, this is an application of the no-cloning principle in a context where the quantum states of interest are not chosen by a random process. We establish unconditional constructions for promise problems admitting uncloneable quantum advice and, assuming the feasibility of quantum copy-protecting certain functions, for languages with uncloneable advice. Along the way, we note that state complexity classes, introduced by Rosenthal and Yuen (ITCS 2022) — which concern the computational difficulty of synthesizing sequences of quantum states — can be naturally generalized to obtain state cloning complexity classes. We make initial observations on these classes, notably obtaining a result analogous to the existence of undecidable problems. Our proof technique defines and constructs ingenerable sequences of finite bit strings, essentially meaning that they cannot be generated by any uniform circuit family with non-negligible probability. We then prove a generic result showing that the difficulty of accomplishing a computational task on uniformly random inputs implies its difficulty on any fixed, ingenerable sequence. We use this result to derandomize quantum cryptographic games that relate to cloning, and then incorporate a result of Kundu and Tan (arXiv 2022) to obtain uncloneable advice. Applying this two-step process to a monogamy-of-entanglement game yields a promise problem with uncloneable advice, and applying it to the quantum copy-protection of pseudorandom functions with super-logarithmic output lengths yields a language with uncloneable advice.
Secret sharing is ubiquitous throughout cryptography. All possible access structures are classically feasible, and in the case of threshold access structures, the protocols are even very efficient. However, when moving to the quantum setting, the no-cloning theorem shows that many access structures are impossible. In fact, no-cloning exactly characterizes feasibility: for thresholds, quantum secret sharing is possible if and only if the threshold
t is strictly more than
n/2.
In this work, we propose a variant of quantum secret sharing (QSS) where two or more identical copies of the input state are provided, but the output is only required to recover one copy. This notion circumvents the simple one-copy no-cloning obstruction, though the natural
k-copy generalization still gives much milder obstructions. For thresholds using
k copies, no-cloning implies that QSS is impossible whenever
t≤n/(k+1).
It is tempting to hypothesize that no-cloning continues to exactly characterize the many-copy case. However, we show that this is not the case. We give positive results showing that multiple copies allow for going slightly beyond the single-copy obstruction: for thresholds, we construct QSS whenever
t>(n−k+1)/2. On the other hand, we give a novel obstruction we call the Clique Path obstruction, which applies to arbitrary access structures. For thresholds, it shows that QSS is impossible whenever
t≤(n−1)/k. Our upper and lower bounds exactly match for
k=2. Both our results leverage connections to the
k-colorability of certain graphs derived from the access structure. We leave closing the gap for
k≥3 copies as a fascinating direction for future work.
Secret sharing is closely related to error correction, which can also be considered in the many-copy setting. Our results imply similar obstructions for quantum error correction for erasure channels.
Abstract In modern quantum information science, the no-cloning theorem constitutes a fundamental principle stating that it is impossible to create an exact copy of an arbitrary unknown quantum state. This intrinsic limitation forms the basis of quantum security mechanisms and gives rise to unique phenomena such as quantum teleportation and superdense coding, which enable the transmission of quantum information without physically transferring the quantum state itself. Within the broader framework of quantum computation, algorithms such as Grover's algorithm provide quadratic speedup for unstructured search problems, though they do not always achieve optimal query complexity for certain classes of tasks. In such scenarios, quantum random walks offer an alternative paradigm capable of further reducing query complexity and enhancing search efficiency. This study examines the theoretical foundations and practical implications of the no-cloning theorem, quantum teleportation, superdense coding, and quantum random walks in the context of information security. Special attention is given to their role in designing countermeasure systems against information theft, destruction, and modification. Practical demonstrations are conducted using Qiskit on IBM quantum hardware, highlighting the applied significance and future potential of these quantum security mechanisms.
Quantum fire is a recently introduced cryptographic primitive consisting of efficiently preparable quantum states, called \emph{flames}, that admit efficient cloning but resist efficient telegraphing, namely reconstruction via classical communication without preshared entanglement. In all prior constructions of quantum fire, cloning is a public operation that requires no separate key and every holder of a flame state can clone it. For applications to access control, however, an issuer may wish to delegate cloning to designated quantum servers while withholding this capability from other flame holders. To address this, we introduce \emph{delegatable quantum fire}, in which cloning requires a separate key.
We give two constructions in the classical-oracle model. Our first construction uses a classical secret key which enables cloning, and any user with the entire key may clone successfully. Our second construction, which we call \emph{torch-fire}, uses quantum cloning keys, called \emph{torches}, which enable cloning while remaining unaffected in the process but cannot otherwise be split or delegated to enable additional cloning. An efficient adversary given
m torches cannot, except with negligible probability, enable more than
m noncommunicating parties to each clone a fresh, independently issued challenge flame. The adversary may jointly process its resources before separating the parties and distribute arbitrarily entangled registers among them. Both constructions are in the oracle model, relying on public classical oracles that allow queries in quantum superposition.
It is a long-standing open question in quantum complexity theory whether the definition of non−deterministic quantum computation requires quantum witnesses (QMA) or if classical witnesses suffice (QCMA). We make progress on this question by constructing a randomized classical oracle separating the respective computational complexity classes. Previous separations \cite{ak-oracle}, \cite{fefferman-kimmel} required a quantum unitary oracle. The separating problem is deciding whether a distribution supported on regular un-directed graphs either consists of multiple connected components (yes instances) or consists of one expanding connected component (no instances) where the graph is given in an adjacency-list format by the oracle. Therefore, the oracle is a distribution over n -bit boolean functions.