Quantum Anonymous Voting Protocols

• Quantum Anonymous Voting (QAV) is a class of protocols that use quantum cryptography to hide the link between voters and votes while producing verifiable aggregate outcomes.
• QAV protocols employ diverse methods such as self-tallying via correlated randomness, GHZ and Bell-state encoding, and AQKD-based anonymous credentialing to secure votes.
• These schemes balance tradeoffs between anonymity, verifiability, and efficiency, with experimental implementations on platforms like IBM quantum computers and photonic GHZ systems.

Searching arXiv for recent and foundational papers on quantum anonymous voting to ground the article in published work. Quantum Anonymous Voting (QAV) denotes a class of voting protocols in which “the link between a voter and a vote is hidden,” while the protocol still outputs an authorized aggregate result such as a tally, a majority decision, or, in the anonymous-veto setting, whether at least one veto occurred (Wang et al., 2016, Khabiboulline et al., 2021, Mishra et al., 2021). In the literature, QAV includes self-tallying anonymous voting, authority-free GHZ-state protocols, anonymous-veto protocols, election schemes built from anonymous quantum key distribution (AQKD), and hybrid quantum-assisted architectures that use quantum cryptography around an otherwise classical voting workflow (Centrone et al., 2021, Zhou et al., 2011, Mishra et al., 2022).

1. Scope, lineage, and problem models

Early AQKD-based election schemes framed the core problem as follows: only eligible voters should cast one valid ballot each, anonymously and verifiably, in a way that the counter learns the ballot but not the voter identity (Zhou et al., 2011). In that line, the voting task is reduced to anonymous voter–counter key establishment followed by encrypted ballot submission. A later distributed quantum election scheme sharpened the privacy objective to post-election anonymity, namely resistance even if previously separated authorities later cooperate, provided that the administrator components do not collude during protocol execution (Zhou et al., 2013).

A different line formulates QAV directly as anonymous tallying. In “Self-tallying Quantum Anonymous Voting,” the setting is $n$ voters $V_0,\dots,V_{n-1}$, each voting for one among $m$ candidates labeled $0,1,\dots,m-1$, with the protocol hiding the link between a vote and a voter while allowing any interested party to obtain the result through simple calculation (Wang et al., 2016). In “Quantum protocol for electronic voting without election authorities,” the task is a binary anonymous vote among $N$ participants, with self-tallying and public verifiability, and support for $K>2$ candidates by repeating the binary protocol $\log_2 K$ times (Centrone et al., 2021).

Another branch targets aggregate-decision functionality rather than full tally disclosure. “Efficient Quantum Voting with Information-Theoretic Security” studies a distributed quantum voting protocol for $N$ voters that computes a majority election outcome while aiming to satisfy correctness, accountability, verifiability, and anonymity (Khabiboulline et al., 2021). Quantum anonymous veto (QAVeto) is the restricted case in which the output is only whether unanimity failed. In that setting, the functionality is the Boolean predicate

$\mathcal{V}_n = \lor_i \mathcal{W}_i,$

or equivalently $f(k)=0$ if $V_0,\dots,V_{n-1}$0 and $V_0,\dots,V_{n-1}$1 if $V_0,\dots,V_{n-1}$2, where $V_0,\dots,V_{n-1}$3 is the number of vetoes (Mishra et al., 2021, Sangwan et al., 19 Sep 2025). This suggests that the term QAV covers both full anonymous tallying and anonymous collective predicates.

2. Core protocol mechanisms

One central mechanism is self-tallying through correlated randomness and hidden ordering. In the self-tallying protocol of Wang et al., two multipartite entangled states distribute, among all voters, a set of secret correlated random numbers that function as “ballot boxes” and a secret random permutation that assigns each voter to exactly one ballot box anonymously. Each voter adds the vote only to the ballot box indicated by the private index; when everyone simultaneously publishes the updated ballot numbers, the row sums reveal the multiset of votes as a random permutation of the individual ballots, while hiding which voter cast which vote (Wang et al., 2016).

A second mechanism is GHZ-parity encoding with a hidden voting schedule. In the authority-free protocol of Centrone, Diamanti, and Kerenidis, voters anonymously assign themselves a secret random permutation of the round numbers via UniqueIndex. In each round, all parties measure an $V_0,\dots,V_{n-1}$4-qubit GHZ state in the Hadamard basis, for which the raw outcomes have even parity,

$V_0,\dots,V_{n-1}$5

The unique voting agent in that round flips the announced bit by XORing with the vote $V_0,\dots,V_{n-1}$6, so the row parity becomes

$V_0,\dots,V_{n-1}$7

The public bulletin board is therefore an $V_0,\dots,V_{n-1}$8 binary matrix whose row parities give the anonymous votes (Centrone et al., 2021).

A third mechanism is AQKD-based anonymous credentialing. In the 2011 election scheme, a voter first anonymously establishes a key $V_0,\dots,V_{n-1}$9 with the counter Charlie by means of authority-certified AQKD, and then anonymously submits

$m$0

where $m$1 is a valid candidate string (Zhou et al., 2011). The distributed election scheme of 2013 generalizes this idea by splitting the administrator into more than one part so that privacy is intended to survive post-election collusion (Zhou et al., 2013). In both cases, the anonymous ballot is an encrypted classical payload, while the quantum part is the anonymous key-establishment channel.

A fourth mechanism is distributed additive masking protected by quantum cryptographic subroutines. “A Simple Voting Protocol on Quantum Blockchain” uses integers $m$2 satisfying

$m$3

and masked ballots

$m$4

The masking values are exchanged by quantum secure communication, the masked ballots are committed using cheat-sensitive quantum bit commitment, and the opening/tally phase is recorded on a quantum blockchain (Sun et al., 2018). A plausible implication is that QAV research includes both fully entanglement-based anonymous ballot constructions and hybrid designs in which quantum communication protects the masking or commitment layer rather than the tally rule itself.

3. Security notions and formal guarantees

Across the literature, a recurring target set is privacy, correctness, eligibility or accountability, non-reusability, verifiability, fairness, and robustness. The 2016 self-tallying protocol explicitly claims to be the first quantum anonymous voting scheme in the literature considered by the authors that simultaneously achieves privacy, self-tallying, non-reusability, verifiability, and fairness (Wang et al., 2016). The 2021 anonymous-veto framework adopts privacy, verifiability, robustness, binding, eligibility, and correctness as the requirements of a valid QAV scheme (Mishra et al., 2021).

The most explicit formalization appears in “Efficient Quantum Voting with Information-Theoretic Security.” There, correctness is defined by

$m$5

accountability by

$m$6

and anonymity by an indistinguishability game under which malicious voters should not distinguish whether honest votes were assigned in the original or permuted order except with advantage $m$7 (Khabiboulline et al., 2021). The same work states that every voter can check that the vote is tallied and any auditor can verify the outcome by looking at the transcript, while also stressing that this is not a full modern public-verifiability framework with zero-knowledge proofs or UC security (Khabiboulline et al., 2021).

The GHZ-based authority-free protocol makes the dependence on state quality explicit. If the state used for voting has fidelity $m$8, then the probability that the protocol does not abort and yet uses an insufficiently good voting state is bounded by

$m$9

and the anonymity theorem bounds a colluding dishonest subset’s success probability by

$0,1,\dots,m-1$0

The same paper defines an approximate privacy parameter

$0,1,\dots,m-1$1

so privacy and correctness are explicitly approximate rather than exact (Centrone et al., 2021).

A more recent line replaces quantum ballots by quantum voting tokens with classical votes. “Anonymous Public-Key Quantum Money and Quantum Voting” constructs a universally verifiable quantum voting scheme with classical votes under $0,1,\dots,m-1$2 and LWE. Privacy is defined by a game $0,1,\dots,m-1$3 with

$0,1,\dots,m-1$4

and uniqueness by $0,1,\dots,m-1$5, where $0,1,\dots,m-1$6 issued tokens should not yield $0,1,\dots,m-1$7 publicly valid distinct-tag votes except with negligible probability (Cakan et al., 2024). In that construction, the quantum resource enforces one-token-one-vote, while the cast vote itself is classical and publicly verifiable.

4. Resource trade-offs and protocol classes

A useful classification divides QAV protocols into probabilistic, iterative, and deterministic schemes. In the anonymous-veto taxonomy of Mishra et al., QAV-1 through QAV-4 are probabilistic, QAV-5 and QAV-6 are iterative, and QAV-7 is deterministic (Mishra et al., 2021). The probabilistic schemes typically detect a veto with probability

$0,1,\dots,m-1$8

so increasing $0,1,\dots,m-1$9 improves logical correctness. The same paper also shows that increasing $N$0 reduces physical robustness under amplitude damping and phase damping, and explicitly identifies a correctness–robustness trade-off in probabilistic QAV (Mishra et al., 2021).

The iterative Bell-state protocol QAV-6 is a particularly important midpoint between multipartite theory and practical implementation. It uses a single Bell pair per round, a travel qubit that passes sequentially through the voters, and phase operations

$N$1

so that the number of vetoes is resolved after at most

$N$2

iterations (Mishra et al., 2021). By contrast, the deterministic dense-coding protocol QAV-7 uses multipartite entanglement and voter-specific subgroup assignments satisfying $N$3, so a single round suffices (Mishra et al., 2021).

Efficiency comparisons in that same work are unusually explicit. For 4 voters, the paper’s table gives qubit efficiencies $N$4 for RKQAV, $N$5 for WQAV, and $N$6 for both QAV-6 and QAV-7 (Mishra et al., 2021). The authors characterize QAV-7 as the most efficient among their proposed schemes, while also describing QAV-6 as an efficient and practical Bell-state-based iterative scheme (Mishra et al., 2021).

Later work pushes the Bell-state direction further. “Single-Round Deterministic Quantum Anonymous Veto Using Bell States” encodes the veto count $N$7 into relative phases on

$N$8

Bell pairs in the protocol section, although the efficiency section writes $N$9. The protocol’s determinism comes from a binary valuation hierarchy: for every nonzero $K>2$0, there exists a unique pair whose phase becomes $K>2$1, yielding a conclusive $K>2$2 outcome in a single pass (Sangwan et al., 19 Sep 2025). This suggests an implementation trend away from multipartite GHZ resources and toward Bell-state constructions that preserve anonymity, correctness, and verifiability while reducing experimental overhead.

Beyond veto, efficiency arguments also appear in majority voting. “Efficient Quantum Voting with Information-Theoretic Security” states that ballot information is encoded in quantum states that enable an exponential reduction in communication complexity compared to classical communication, and that the scheme requires modest quantum memories with size scaling logarithmically with the number of voters (Khabiboulline et al., 2021). A different hardware-oriented direction appears in “Quantum voting machine encoded with microwave photons,” where the tally is stored in a target-qubit phase

$K>2$3

that depends only on the total number $K>2$4 of affirmative votes (Zhang et al., 2024). In that model, anonymity is output-level anonymity: the prescribed readout reveals only the tally, not the ordered vote string.

5. Experimental realizations and implementation landscape

Experimental QAV has so far concentrated on small voter sets, anonymous veto, and GHZ-based proof-of-principle voting. On IBM superconducting hardware, “United Nation Security Council in Quantum World: Experimental Realization of Quantum Anonymous Veto Protocols using IBM Quantum Computer” implemented two previously proposed anonymous-veto protocols on IBMQ Casablanca. The reported fidelities were $K>2$5 to $K>2$6 for the Bell-state implementation, $K>2$7 to $K>2$8 for the cluster-state implementation, and $K>2$9 to $\log_2 K$0 for the GHZ-state implementation; the explicit performance ordering was

$\log_2 K$1

and the noise models were ordered, in ascending order based on diminishing effect on fidelity, as phase damping, amplitude damping, depolarizing, bit-flip (Kumar et al., 2021).

Photonic GHZ platforms have enabled authority-free voting demonstrations. “Experimental quantum voting using photonic GHZ states” implements a four-party election with two candidates using a modified version of the Centrone–Diamanti–Kerenidis protocol, reports a four-partite GHZ-state fidelity of approximately $\log_2 K$2, and states that voters’ intentions were successfully recorded approximately $\log_2 K$3 of the time (Marcellino et al., 3 Dec 2025). A closely related experiment, “Experimental Quantum Electronic Voting,” reports a 4-photon GHZ source with tomography fidelity $\log_2 K$4, a 4-voter 2-candidate configuration with privacy enhancement $\log_2 K$5, and a second demonstration with 8 voters split into two pools of 4 supporting up to 16 candidates, although privacy enhancement was omitted in the latter due to runtime impracticality (Laurent-Puig et al., 3 Dec 2025).

Those photonic experiments also make the present bottlenecks explicit. In the 2025 authority-free implementation, the raw source repetition rate is approximately $\log_2 K$6, the effective protocol rate is approximately $\log_2 K$7, and the full protocol still requires quantum memories even though the experiment itself did not include them (Laurent-Puig et al., 3 Dec 2025). The 2025 photonic GHZ-state implementation similarly attributes the gap between state fidelity and protocol success to passive basis-choice architecture, phase drift, polarization drift, and low fourfold coincidence rate $\log_2 K$8 (Marcellino et al., 3 Dec 2025).

A hardware-specific but conceptually distinct implementation path is circuit QED. The microwave-photon voting machine of 2024 uses multiple microwave cavities and a coupled superconducting flux qutrit, relies on a multi-control single-target quantum phase gate, and reports numerical fidelities above $\log_2 K$9 for some 2-voter cases, above $N$0 for $N$1, and below $N$2 for the most loss-sensitive $N$3 case at $N$4 and $N$5 (Zhang et al., 2024). This line demonstrates physical feasibility of anonymous tally extraction, though not a full end-to-end election system.

6. Limitations, adjacent approaches, and open directions

Several limitations recur across the literature. First, many protocols rely on strong trust assumptions. The AQKD-based election of 2011 assumes Bob and Charlie are semi-honest and non-colluding; if they collude, anonymity collapses (Zhou et al., 2011). The distributed election of 2013 improves post-election privacy but still assumes that the administrator components do not collude during the election period and that an overseeing body can prevent such collusion while the protocol runs (Zhou et al., 2013). The GHZ-based authority-free line removes election authorities from the tallying logic, but privacy and correctness remain approximate and depend directly on the fidelity of the shared multipartite state (Centrone et al., 2021).

Second, not every quantum voting proposal is a “true QAV protocol” in the strong sense. “Anonymous voting scheme using quantum assisted blockchain” is explicitly a classical remote e-voting architecture built on a permissioned blockchain, with QRNG, QKD, and QSS used as auxiliary security layers. Its privacy is “public anonymity / unlinkability from blockchain observers” and “conditional anonymity against insiders,” but full authority-independent anonymity is not achieved because the Voting Authority creates and stores the identity mappings (Mishra et al., 2022). “Quantum-Enhanced Secure Approval Voting Protocol” similarly relies on a hashed voter identifier and role separation between Bob and Charlie$N$6, and its anonymity mechanism is characterized as much weaker and more classical than a formal anonymous-ballot primitive (Sakhuja et al., 2024).

Third, hybrid simplicity often comes with underanalyzed anonymity under collusion. The quantum-blockchain protocol of 2018 uses additive masking, quantum secure communication, cheat-sensitive quantum bit commitment, and quantum blockchain to claim anonymity, binding, non-reusability, verifiability, eligibility, fairness, and self-tallying, yet its own technical analysis emphasizes that anonymity under collusion, metadata leakage, malicious abort, and coercion resistance are not formally addressed (Sun et al., 2018). The anonymous-veto taxonomy of 2021 likewise states that full unconditional proofs against collective or coherent attacks are left for future work, and that verifiability in anonymous-veto settings remains limited (Mishra et al., 2021).

Fourth, several recent constructions shift the quantum burden from ballots to credentials. “Anonymous Quantum Tokens with Classical Verification” is not itself a voting protocol, but it provides a primitive-level building block for anonymous single-use voting credentials: one token per voter, classical verification at redemption time, and swap-test-based detection if the issuing authority makes tokens distinguishable (Gavinsky et al., 7 Oct 2025). “Anonymous Public-Key Quantum Money and Quantum Voting” develops this direction into a voting scheme with quantum voting tokens and classical votes, aiming to combine privacy against the issuer, universal verifiability, and uniqueness under $N$7 and LWE (Cakan et al., 2024). A plausible implication is that future QAV may increasingly separate anonymous eligibility tokens from the final ballot representation.

Finally, the field continues to face the usual hard problems of voting theory in a quantum setting: coercion resistance, receipt-freeness, malicious tallying authorities, large-scale deployment, side-channel leakage, and realistic finite-noise analyses. The published record repeatedly distinguishes anonymity from these stronger notions. In current QAV research, the most mature results are therefore best read as precise advances on particular subproblems—self-tallying, authority-free binary voting, anonymous veto, anonymous credentialing, or public verifiability with quantum tokens—rather than as a single protocol family that simultaneously solves all standard election-security requirements (Wang et al., 2016, Centrone et al., 2021, Cakan et al., 2024).