Quantum Communication Secured by Choosing Measurement Basis Offers Ultimate Privacy

Scientists have developed a novel protocol for one-way quantum secure direct communication, utilising the choice of measurement basis as the secret key. Santiago Bustamante and Boris A. Rodríguez, both from Universidad de Antioquia, alongside Elizabeth Agudelo of TU Wien, demonstrate a system where information is encoded and decoded through measurements performed in either the computational or Hadamard basis. This research is significant because it establishes information-theoretic security against BB84-symmetric attacks using finite ensembles of entangled pairs and a public channel. Importantly, the protocol requires no local unitary operations by the receiver, making it particularly suitable for practical implementation in network configurations such as star networks.

This research addresses the fundamental question of distinguishing ensembles described by identical compressed density operators and introduces a method for encoding and decoding classical information through measurements in either the computational or Hadamard basis.

Employing quantum wiretap channel theory, the study rigorously assesses the secure net bit rates and certifies the information-theoretic security of various implementations against BB84-symmetric attacks. A key advantage of this model is the elimination of local unitary operations required by the receiver, making it particularly suitable for practical implementation in star network configurations.
The work builds upon the concept of finite ensembles of entangled EPR pairs, each shared between two parties, Alice and Bob, and explores how local measurements influence the transmission of a single bit of information. Researchers define a compressed density operator as the state of an average entity within an ensemble, acknowledging that this operator may not fully capture all information about the ensemble’s preparation.

By measuring qubits in either the computational or Hadamard basis, Alice and Bob induce correlated collapses in their respective qubits, creating a shared ensemble with a specific compressed density operator dependent on the measurement outcome. The study demonstrates that, as the number of entangled pairs increases, the compressed density operator converges towards a state indistinguishable from a completely mixed state, highlighting the inherent limitations in distinguishing ensembles with identical statistical mixtures.
This investigation proposes a general model for one-way quantum secure direct communication, mathematically describing the state-based communication process and proving the information-theoretic security of four distinct implementations. Security is established even in the presence of noise, utilising the principles of the quantum wiretap channel theory.

The research demonstrates that the proposed model offers a viable pathway towards secure communication without relying on pre-shared secret keys, potentially simplifying the implementation of secure communication networks. This advancement could prove valuable in scenarios demanding high security and simplified infrastructure, such as secure data transmission in star network topologies.

Schmidt coefficient parameterisation and optimisation of secure code rates

A Nelder-Mead numerical optimization method from the SciPy Python library was central to quantifying the security of this direct communication model. This technique computed achievable code rates by minimizing the difference χB −χE, before maximizing in PA, using a variable ‘t’ that governs the Schmidt coefficients λij.

These coefficients were parameterized for fixed QZ and QX values as λ00 = 1 −QX + t + QZ 2, λ01 = QX + t −QZ 2, λ10 = −QX + t + QZ 2, and λ11 = QX −t + QZ 2, allowing for precise control over the system’s entanglement properties. The resulting code rates were then used to assess information-theoretic security against BB84-symmetric attacks.

The study investigated secure net bit rates per ensemble (C) and per EPR pair (R = C/n) for four distinct implementations, varying ensemble size (n) while maintaining fixed qubit error rates of QZ = QX = 0.05. Achieved rates were plotted to reveal a trade-off between ensemble size and performance, demonstrating that while larger ensembles enable arbitrarily secure codes with higher rates, the net bit rate per EPR pair can decrease if the rate increase is outpaced by ensemble growth.

Analysis revealed that all four implementations achieved maximum rate R at n = 2, with the Parity Disclosure implementation yielding the highest value of approximately 0.052. Further analysis employed colormaps to visualize achievable secure net bit rates per EPR pair as functions of qubit error rates in the Z and X bases, fixed at an ensemble size of n = 2 and b = 0.

These colormaps identified regions of complete darkness, indicating a lack of guaranteed secrecy capacity and necessitating communication abortion. The Full Outcome Disclosure implementation consistently achieved the maximum rates, peaking at R ≈0.279 in a zero-error scenario, though still less than the R = 1 rate of the standard DL04 protocol. The colormaps also highlighted the model’s greater robustness to phase-flip errors compared to bit-flip errors, aligning with the model’s inherent asymmetry.

Entanglement-assisted classical communication achieves low error rates with finite resources

Logical error rates reached 2.914% per cycle during the study of one-way direct communication using finite ensembles of shared EPR pairs. This performance was achieved with a public authenticated classical channel and local choice of mutually-unbiased measurement bases representing the secret bit. The research focused on implementing encoding and decoding of classical information through measurements in either the computational or Hadamard basis.

The CDM06 protocol, a basis for comparison, exhibits an average error probability of 1 over 22m+1 multiplied by 2m m, where m represents a given value. This error probability diminishes with increasing values of m, but at the expense of significantly reduced secure net bit rates. Analysis revealed that the protocol’s limited resourcefulness stems from inefficiencies in entanglement distillation and ensemble balancing.

The yield, or distillable entanglement, D∞(ρ), is limited by the von Neumann entropy function, satisfying D∞(ρ) ≤ 1 − S(ρ). Researchers identified that the ensemble balancing step is inherently wasteful, with a 2/2n′ probability of requiring the discard of all n′ qubits, potentially compromising communication reliability.

By removing the entanglement distillation step and utilizing all available EPR pairs, the protocol’s resourcefulness can be improved and error rates reduced. Allowing Alice and Bob to choose a code after estimating qubit error rates in the computational and Hadamard bases enables arbitrarily secure and correct direct communication for low qubit error rates. This approach eliminates the need for receiver-side unitary operations, enhancing the protocol’s suitability for star network configurations and real-world implementation.

Entangled Qubit Ensembles Enable Information-Theoretic Security

Scientists have developed a model for one-way direct communication utilising shared entangled pairs of qubits and a public classical channel. This approach encodes and decodes classical information through measurements performed in either the computational or Hadamard basis, circumventing the need for complex local unitary operations by the receiver.

The system’s security against BB84-symmetric attacks has been certified using wiretap channel theory, demonstrating information-theoretic security. The research centres on the distinguishability of ensembles possessing identical compressed density operators, a crucial aspect of quantum communication protocols.

The model leverages finite ensembles of Einstein-Podolsky-Rosen pairs, where the state of each qubit is correlated with its entangled partner. By analysing measurements in different bases, the study establishes how these ensembles can be used for secure communication, resulting in a compressed density operator that reflects the shared state of the qubits.

The authors acknowledge that the compressed density operator does not always fully capture all information about the ensemble, requiring a full density operator for complete fidelity. This work is particularly suited for implementation in star network configurations due to its simplicity. Future research could explore optimising the number of entangled pairs required for a given level of security and investigating the performance of the model in more complex network topologies. The findings contribute to the advancement of practical quantum secure direct communication, offering a viable pathway for transmitting information with information-theoretic security guarantees.