Experimental generation of asymmetric keys from the parity structure of a two-photon six-qubit entangled state

The gist The authors propose and experimentally demonstrate an asymmetric key-generation scheme in which public and private keys are derived from a six-qubit photonic entangled state.

Protocol Overview

** The protocol is based on a parity-structured six-qubit entangled state, where the public and private keys are derived from this state The protocol begins by distributing a maximally entangled pair, for example between q1 and q4 — any of the four Bell states may be used, the choice being absorbed into a known local unitary operation Within this constraint, a six-qubit state can be engineered as a superposition of a small subset of the 64 basis states, chosen so that each party’s triple forms a codeword of a classical parity code while the two codewords remain locked together through the shared pair Alice and Bob measure their respective qubits in the Z basis, obtaining the outcome triples (x1 x2 x3) and (x4 x5 x6) respectively Alice then randomly selects a position p ∈ 2, 3 and publicly announces (p, xp) over an authenticated classical channel Bob reconstructs Alice’s triple from his own measurement outcomes and the announced bit xp, using the correlations described above The secret bit x1 is obtained as x1 = x4 ⊕ 1 and the remaining private bit follows as xp′ = xp ⊕ x1 Bob reconstructs Alices private bits from his own record X4 as X1 = X¯4 and XP ⊕ X¯4 Alice encrypts a message m = (m1, m2,..., mn) of length n using her private n-bit string and sends the ciphertext together with the public bit string to Bob through an authenticated classical channel Bob decrypts the message using the reconstructed private bits of Alice, as D(mi) = E(mi) ⊕ x1 and D(mi+1) = E(mi+1) ⊕ xp′ The protocol offers two encryption bits per round, doubling the key rate The protocol is completely symmetric from both sides: Bob can likewise announce (q, xq) with q ∈ 5, 6 as the public key, from which Alice reconstructs Bob’s private pair as x4 = x1 ⊕ 1 and xq′ = xq ⊕ x4 The choice of local encoding within each triple gives flexibility in protocol design, so the six-qubit register supports a family of protocols differing in redundancy, error detection, and communication cost against one another, subject to the same entanglement budget of one ebit. The even-parity encoding adopted here spends that freedom in two ways: (i) by imposing a parity constraint on both triples, which each party can verify on its own data every round from local data alone, and (ii) by keeping one bit of each triple independent of the secret, so that it can be announced publicly to enable reconstruction of the other party’s triple. The choice of Bell state used to seed the register is immaterial to the protocol, though it fixes which strings appear in the superposition. For instance, applying the same encoders UA = CNOT2→3CNOT1→3H2 and UB = CNOT5→6CNOT4→6H5 to Φ+⟩14 in place of Ψ+⟩14 preserves the even-parity encoding on each triple. In all the above cases, the local parities are deterministic, and the key is reconstructed exactly as before. The protocol offers a key reconstruction mechanism that gives each party the other’s complete measurement record from a single publicly announced bit, second, key rate doubling due to the generation of two private bits per round for encryption, and third, the built-in self-check capability that removes the in-station faults round by round before generating the raw key, lowering its error rate. The path qubits are retained within the shielded stations of the two parties and are never exposed to an eavesdropper except for the public key bit, which is independent of the secret bits and therefore, reveals nothing. Any attempt to extract information from the polarization qubits in the channel disturbs the correlation of the entangled pair, reducing the measured S-value [7, 20] and correspondingly increasing the error rate [8]. Therefore, the security of the protocol rests on the monogamy of the shared entanglement [21, 22> The only option for eavesdropper will be to guess the random t−bit string, requiring O(2t) runs on an t-qubit quantum system to find the matching bit to decrypt. The local self-check therefore enables round by round error detection, which is a key distinguishing feature of our protocol as compared to the conventional entanglement based QKD protocols. In our implementation, both Alice and Bob verify the local parity x1 ⊕ x2 ⊕ x3 = 0 and x4 ⊕x5 ⊕x6 = 0, respectively on their own outcomes before any classical communication Any round failing to satisfy the parity constraint is discarded. This is the built-in error detection feature offered by the classical [3, 2, 2] code. It flags any odd-weight error i.e., a single or triple bit flip within a station, but cannot detect even-weight errors i.e., double bit flips that map one codeword of C onto another. Two thirds of the even-weight errors, those that alter x1 (or x4) resulting in x1 = x4, contribute to the quantum bit error rate (QBER). After a Z-basis measurement, each party independently evaluates the parity of their respective triples as sA = x1 ⊕ x2 ⊕ x3, sB = x4 ⊕ x5 ⊕ x6 A round is locally flagged as pass if s = 0 or as fail if s = 1 Over N rounds, Alice and Bob each obtain an Nbit flag string SA = s(1)A, s(2)A,..., s(N)A and SB = s(1)B, s(2)B,..., s(N)B, computed entirely from local data The parties exchange these strings with each other over an authenticated classical channel and perform a bit-wise OR operation on the two, SA ∨ SB and retain only those rounds for which s(i)A ∨ s(i)B = 0, i.e., those passing the local parity checks on both sides Consequently, for all retained rounds the announced information is identical. The local self-check therefore enables round by round error detection, which is a key distinguishing feature of our protocol as compared to the conventional entanglement based QKD protocols. The only option for eavesdropper will be to guess the random t−bit string, requiring O(2t) runs on an t-qubit quantum system to find the matching bit to decrypt. In addition, a single publicly announced bit, chosen at random from either of the path qubits, allows each party to reconstruct the other’s full triple while leaking no information to third party The security of the protocol rests on the monogamy of the shared entanglement [21, 22> The only option for eavesdropper will be to guess the random t−bit string, requiring O(2t) runs on an t-qubit quantum system to find the matching bit to decrypt. The only option for eavesdropper will be to guess the random t−bit string, requiring O(2t) runs on an t-qubit quantum system to find the matching bit to decrypt The protocol achieves a raw key rate of 130.925 ± 0.114 kbit/s at a QBER of (4.61 ± 0.02)%, with the key bit strings balanced to within 2% of unity. Beyond generating quantum-secure asymmetric keys from the quantum correlations shared through the polarization degree of freedom and the intrinsic randomness available locally to each party, the demonstration shows that six-qubit states can be engineered deterministically with quantum gate operations in a photonic system using only two photons. The distinguishing features of the protocol arise from its structure. The even-parity constraint provides a builtin self-check: each party can verify the parity of its own triple in every round from local data alone, without revealing the key Faults within a station are, therefore, removed before they enter the raw key, which lowers its error rate. The self-check also distinguishes faults within the stations from disturbances on the channel, which a single error-rate estimate cannot do.

1. textbfKey Generation from Entanglement Structure: Improved Asymmetric Cryptography Scheme for Quantum Systems (6-Qubit Parity Code). This system can generate public and private keys derived from a parity structure of a two-photon six-qubit entangled state, offering a physics-based alternative to public-key cryptosystems built on computational hardness assumptions.

2. textbfError Detection and Key Rate Enhancement: Round-by-Round Self-Check Capability. The protocol includes built-in self-check capability that removes the in-station faults round by round before generating the raw key, which is a key distinguishing feature of our protocol as compared to the conventional entanglement based QKD protocols.

3. textbfEnhanced Security Against Eavesdropping: Monogamy of Shared Entanglement. The security rests on the monogamy of the shared entanglement, meaning any attempt to extract information from polarization qubits disturbs the correlation of the entangled pair, reducing the measured S-value [7, 20] and correspondingly increasing the error rate [8].

4. textbfIncreased Key Rate: Private Bit Generation for Encryption. The protocol achieves key rate doubling due to the generation of two private bits per round for encryption, allowing for two encryption bits per round.

5. textbfDeterministic State Engineering: Quantum Gate Operations in Photonic Systems. The system can achieve complex states by engineering them using local operations, as demonstrated by applying unitaries like UA = CNOT2→3CNOT1→3H2 and UB = CNOT5→6CNOT4→6H5.

We propose and experimentally demonstrate an asymmetric key-generation scheme in which public and private keys are derived from a six-qubit photonic entangled state. A six-qubit entangled state is generated from two photons, each carrying one polarization and two path qubits. The state is prepared in an equal superposition of eight of the sixty-four six-qubit basis states, in which each photon's three qubits form a codeword of the classical [3,2,2] even-parity code, and are distributed between the two parties, Alice and Bob. This ensures, each triple is a uniformly random codeword and the two codewords are locked together through the correlation. The parity constraint is a local stabilizer, so each party verifies it on its own data every round, and eliminates the bit flip errors arising from imperfections, detector dark counts and multiple occupancy before it enters the raw key. A single publicly announced bit, chosen at random from either of the path qubits, allows each party to reconstruct the other's full triple while leaking no information to third party. We realize the desired six-qubit state using a Sagnac-based type-II SPDC source, reporting a Bell-CHSH parameter S = 2.798 +/- 0.008, by implementing gate operation on polarization and path degree's of freedom. This approach provides a physics-based alternative to public-key cryptosystems built on computational hardness assumptions. A t-bit string generated from multiple rounds for encryption will be intrinsically random. Without the private key, one needs at least O(2 t) runs on an t-qubit quantum system to find the matching bit to decrypt.