We introduce encoding strategy of k -symbol embeddings within a d -dimensional Hilbert space, validate using d = 25 experimental data and determine optimum at k = 5. These findings pave the way for error-correction and modulation for quantum cryptography.
Encoding in a high-dimensional Hilbert space improves noise resilience in quantum information processing. This approach, however, may result in cross-mode coupling and detection complexities, thereby reducing quantum cryptography performance. This fundamental trade-off between correctness and secrecy motivates the search for quantum high-dimensional encoding approaches for cryptography. Here, we introduce state embeddings that use a k -symbol subset within a d -dimensional Hilbert space, tailored to the channel's error structure. We demonstrate the advantage of our scheme in realistic quantum channels, producing a higher secure key rate. We validate our approach using d = 25 quantum key distribution (QKD) experimental data, derive closed-form expressions for the key rate and threshold, and determine the optimum at k = 5 . These findings advance high-dimensional QKD and pave the way for error correction and modulation for quantum cryptography.
The standard four-state (BB84) protocol of key distribution in quantum cryptography, Slutsky, Rao, Sun, and Fainman performed an eavesdropping probe optimization, which an average yields the most information to the eavesdropper for a given error rate caused by the probe. The most general possible probe consistent with unitary was considered, in which each individual transmitted bit is made to interact with the probe so that the carrier and the probe are left in an endangered state, and measurement by the probe, made subsequent to measurement by the legitimate receiver, yield information about the carrier state. The probe optimization is based on maximizing the Renyi information gain by the probe on corrected data for a given error rate induced by the probe in a legitimate receiver. The results were obtained for the standard protocol with an angle of 45 degrees between the signal bases. In more recent work, a larger set of optimum probe parameters was found than was known previously, and although they all yield the same maximum Renyi information gain by the probe, alternative options are made available for optimum probe design. In the present work, the corresponding optimized unitary transformation, representing the action of the probe on the signal, are calculated. I have determined three classes of unitary transformations yielding the same maximum information to the probe. The simplest one corresponds to a probe having a two-dimensional Hilbert space of states, and is uniquely determined by the error rate. The second class corresponds to a probe having a four-dimensional Hilbert space of states, and is determined by the error rate and two continuous angle parameters, which are mutually constrained by the error rate. The third class corresponds to a probe having a four-dimensional Hilbert space, and is determined by the error rate and two continuous angle parameters, one of which is constrained by the error rate. This work will be useful in the design of an optimum-entangling probe.
Decoherence-induced leakage errors can potentially damage physical or logical qubits embedded in a subspace of the entire Hilbert space by coupling them to other system levels. Here we report the first experimental implementation of Leakage Elimination Operators (LEOs) that aims to reduce this undermining. LEOs are a type of dynamical decoupling control that have been previously introduced to counteract leakage from a chosen subspace into the rest of a Hilbert space, and have been widely explored theoretically. Different from other error correction strategies, LEOs are compatible with any gate sequence in a code space, and thus, compatible with universal quantum computation. Using IBM's cloud quantum computer (QC), we design three potentially applicable examples of subspaces in two- and three-qubit Hilbert spaces and derive the explicit forms of the corresponding LEOs for these subspaces. For the first time, we experimentally demonstrate that these LEOs significantly suppress leakage. The results also show that the LEO time-scale condition can be satisfied with noise in the IBM's cloud QC and pave a way for quantum setups to get rid of leakage trouble.