Abstract
Future quantum computers are likely to be expensive and affordable outright by few, motivating client/server models for outsourced computation. However, the applications for quantum computing will often involve sensitive data, and the client would like to keep her data secret, both from eavesdroppers and the server itself. Homomorphic encryption is an approach for encrypted, outsourced quantum computation, where the client's data remains secret, even during execution of the computation. We present a scheme for the homomorphic encryption of arbitrary quantum states of light with no more than a fixed number of photons, under the evolution of both passive and adaptive linear optics, the latter of which is universal for quantum computation. The scheme uses random coherent displacements in phase-space to obfuscate client data. In the limit of large coherent displacements, the protocol exhibits asymptotically perfect information-theoretic secrecy. The experimental requirements are modest, and easily implementable using present-day technology.
Highlights
In the upcoming quantum era, it is to be expected that client/server models for quantum computing will emerge, owing to the high expected cost of quantum hardware
We present a scheme for the homomorphic encryption of arbitrary quantum states of light with no more than a fixed number of photons, under the evolution of both passive and adaptive linear optics, the latter of which is universal for quantum computation
The main result of our paper is the following theorem, which implies that our encoding scheme in the limit of large coherent displacements has weak information-theoretic security
Summary
In the upcoming quantum era, it is to be expected that client/server models for quantum computing will emerge, owing to the high expected cost of quantum hardware. We consider an alternate technique that supersedes both polarization- and phase-key encoding—displacement key encoding, whereby random coherent displacements obfuscate optically encoded quantum information. This idea has been recently explored by Marshall et al [12], where it was argued heuristically why the scheme might be secure. Based on experimental data generated, Marshall et al numerically showed that the mutual information between the encrypted and the unencrypted data can be made small as the variance of the random displacements increases This encouraging evidence suggests that a displacement key encoding might offer perfect security in the asymptotic limit. This is far more general than polarization-key encoding, which applies to singlephoton input states, or phase-key encoding, which applies to input coherent states
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