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Fluctuation and Noise Letters

Direct High-Dimensional Quantum Communication with Tunable Bases via Sequential Non-Demolition Measurements

Zhenghong Li, Shun Li, M. Al-Amri

Published Jan 10, 2026• 0 citations
Publisher

Abstract

A theoretical framework utilizing sequential non-demolition measurements to extract information from high-dimensional quantum systems is proposed. In our scheme, an unsuccessful measurement does not cause collapse of the system state but allows it to revert to its pre-measurement state for subsequent measurements. Compared with conventional schemes, our approach enables flexible switching of the bases used for encoding and transmitting signals, making it particularly suitable for high-dimensional quantum-secure communication protocols based on mutually unbiased bases (MUBs). Moreover, our scheme does not strictly require orthogonality of the signal states, which relaxes the precision requirements for the information encoding processes while supporting more flexible signal state selection strategies. Our work opens a new pathway for the practical design of high-dimensional quantum communication systems.

DOI
10.1142/s0219477525400346

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•Dec 23, 2012•1 citation
A theoretical framework utilizing sequential non-demolition measurements to extract information from high-dimensional quantum systems is proposed. In our scheme, an unsuccessful measurement does not cause collapse of the system state but allows it to revert to its pre-measurement state for subsequent measurements. Compared with conventional schemes, our approach enables flexible switching of the bases used for encoding and transmitting signals, making it particularly suitable for high-dimensional quantum-secure communication protocols based on mutually unbiased bases (MUBs). Moreover, our scheme does not strictly require orthogonality of the signal states, which relaxes the precision requirements for the information encoding processes while supporting more flexible signal state selection strategies. Our work opens a new pathway for the practical design of high-dimensional quantum communication systems.
Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corresponding rank-1 projective measurements are ubiquitous in quantum information theory. In this work, we study a recently introduced generalisation of MUBs called mutually unbiased measurements (MUMs). These measurements inherit the essential property of complementarity from MUBs, but the Hilbert space dimension is no longer required to match the number of outcomes. This operational complementarity property renders MUMs highly useful for device-independent quantum information processing. It has been shown that MUMs are strictly more general than MUBs. In this work we provide a complete proof of the characterisation of MUMs that are direct sums of MUBs. We then construct new examples of MUMs that are not direct sums of MUBs. A crucial technical tool for this construction is a correspondence with quaternionic Hadamard matrices, which allows us to map known examples of such matrices to MUMs that are not direct sums of MUBs. Furthermore, we show that—in stark contrast with MUBs—the number of MUMs for a fixed outcome number is unbounded. Next, we focus on the use of MUMs in quantum communication. We demonstrate how any pair of MUMs withdddoutcomes defines addd-dimensional superdense coding protocol. Using MUMs that are not direct sums of MUBs, we disprove a recent conjecture due to Nayak and Yuen on the rigidity of superdense coding, for infinitely many dimensions. The superdense coding protocols arising in the refutation reveal how shared entanglement may be used in a manner heretofore unknown.
Certifying entanglement is an important step in the development of many quantum technologies, especially for higher-dimensional systems, where entanglement promises increased capabilities for quantum communication and computation. A key feature distinguishing entanglement from classical correlations is the occurrence of correlations for complementary measurement bases. In particular, mutually unbiased bases (MUBs) are a paradigmatic example that is well-understood and routinely employed for entanglement certification. However, implementing unbiased measurements exactly is challenging and not generically possible for all physical platforms. Here, we extend the entanglement-certification toolbox from correlations in MUBs to arbitrary bases. This practically significant simplification paves the way for efficient characterizations of high-dimensional entanglement in a wide range of physical systems. Furthermore, we introduce a simple three-MUBs construction for all dimensions without using the Wootters-Fields construction, potentially simplifying experimental requirements when measurements in more than two MUBs are needed, especially in high-dimensional settings.
Mutually unbiased bases (MUBs) play a key role in many protocols in quantum science, such as quantum key distribution. However, defining MUBs for arbitrary high-dimensional systems is theoretically difficult, and measurements in such bases can be hard to implement. We show experimentally that efficient quantum state reconstruction of a high-dimensional multipartite quantum system can be performed by considering only the MUBs of the individual parts. The state spaces of the individual subsystems are always smaller than the state space of the composite system. Thus, the benefit of this method is that MUBs need to be defined for the small Hilbert spaces of the subsystems rather than for the large space of the overall system. This becomes especially relevant where the definition or measurement of MUBs for the overall system is challenging. We illustrate this approach by implementing measurements for a high-dimensional system consisting of two photons entangled in the orbital angular momentum degree of freedom, and we reconstruct the state of this system for dimensions of the individual photons from d = 2 to 5.
Abstract Transverse spatial mode of light is crucial in high-dimensional quantum key distribution (QKD). However, applications in realistic scenarios suffer from mode-dependent loss and the complexity of system, making it impractical to achieve higher-dimensional, longer-distance and low-cost communications. A mutually partially unbiased bases (MPUBs) protocol has been proposed to fundamentally eliminate the effects induced by mode-dependent loss for long propagation distances and limited sizes of apertures. Here, we demonstrate the first implementation of the MPUBs protocol in dimensions of d = 2 , 4 , 5 and 6. By performing a controlled unitary transformation, we can actively switch the measurement basis and enable a compact measurement system. In consequence, a higher encoding dimension is available under finite system resources, resulting in higher key rates and stronger noise resistance. Our work enhances the practicability of MPUBs protocol, and may promote the applications of high-dimensional QKD in quantum networks.
We propose a feasible high-dimensional two-step quantum secure direct communication scheme by using the Einstein-Podolsky-Rosen entangled beam pair. Accoding to the quality of the two superposition forms of the EPR entangled state (two-mode squeezed vacuum state), we select the mutually unbiased bases for quantum measurement. With the unitary operation, we can subtly encode the confidential information in the quantum state. We also conducted a more detailed analysis of the security of this protocol.
Measurements in mutually unbiased bases (MUBs) are integral to quantum science. An underlying principle of a set of MUBs is that a measurement in one such basis provides no information about a measurement in one of the others. This feature is especially relevant for quantum key distribution. We perform a complete set of mutually unbiased measurements for high-dimensional orbital angular momentum (OAM) states of light. For a two-photon entangled state we show that specific joint measurements provide the minimum number of experimental settings required to characterize the quantum state. From these measurements we reconstruct the density matrix describing the high-dimensional two-photon entangled state. The experimental procedure that we outline can be applied to many different multipartite and high-dimensional systems.