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Register a new userHomomorphic encryption of linear optics quantum computation on almost arbitrary states of light with asymptotically perfect security
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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 clients 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.
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We present a scheme for implementing homomorphic encryption on coherent states encoded using phase-shift keys. The encryption operations require only rotations in phase space, which commute with computations in the codespace performed via passive linear optics, and with generalized non-linear phase operations that are polynomials of the photon-number operator in the codespace. This encoding scheme can thus be applied to any computation with coherent state inputs, and the computation proceeds via a combination of passive linear optics and generalized non-linear phase operations. An example of such a computation is matrix multiplication, whereby a vector representing coherent state amplitudes is multiplied by a matrix representing a linear optics network, yielding a new vector of coherent state amplitudes. By finding an orthogonal partitioning of the support of our encoded states, we quantify the security of our scheme via the indistinguishability of the encrypted codewords. Whilst we focus on coherent state encodings, we expect that this phase-key encoding technique could apply to any continuous-variable computation scheme where the phase-shift operator commutes with the computation.
Quantum computers promise not only to outperform classical machines for certain important tasks, but also to preserve privacy of computation. For example, the blind quantum computing protocol enables secure delegated quantum computation, where a client can protect the privacy of their data and algorithms from a quantum server assigned to run the computation. However, this security comes at the expense of interaction: the client and server must communicate after each step of the computation. Homomorphic encryption, on the other hand, avoids this limitation. In this scenario, the server specifies the computation to be performed, and the client provides only the input data, thus enabling secure non-interactive computation. Here we demonstrate a homomorphic-encrypted quantum random walk using single-photon states and non-birefringent integrated optics. The client encrypts their input state in the photons polarization degree of freedom, while the server performs the computation using the path degree of freedom. Our random walk computation can be generalized, suggesting a promising route toward more general homomorphic encryption protocols.
In this note, we characterize the form of an invertible quantum operation, i.e., a completely positive trace preserving linear transformation (a CPTP map) whose inverse is also a CPTP map. The precise form of such maps becomes important in contexts such as self-testing and encryption. We show that these maps correspond to applying a unitary transformation to the state along with an ancilla initialized to a fixed state, which may be mixed. The characterization of invertible quantum operations implies that one-way schemes for encrypting quantum states using a classical key may be slightly more general than the ``private quantum channels studied by Ambainis, Mosca, Tapp and de Wolf (FOCS 2000). Nonetheless, we show that their results, most notably a lower bound of 2n bits of key to encrypt n quantum bits, extend in a straightforward manner to the general case.
Quantum state teleportation of optical number states is conspicuously absent from the list of experimental milestones achieved to date. Here we demonstrate analytically a teleportation scheme with fidelity $100%$ for optical number states of arbitrary dimension using linear optical elements only. To this end, we develop an EPR source to supply Bell-type states for the teleportation, and show how the same set-up can also be used as a Bell-state analyser (BSA) when implemented in a time-reversal manner. These two aspects are then brought together to complete the teleportation protocol in a scheme that can deliver perfect fidelity, albeit with an efficiency that decays exponentially as the occupation of the number states increases stepwise. The EPR source and BSA schemes both consist of two optical axes in a symmetrical V-shape experimental layout, along which beam-splitters are placed cross-beam fashion at regular intervals, with their transmittivities treated as variables for which the values are calculated ad hoc. In particular, we show the full treatment for the case of qutrit teleportation, and calculate the transmittivity values of the beam splitters required for teleporting qubits, qutrits, qupentits, quheptits and qunits. The general case for arbitrary-dimensional number state teleportation is demonstrated through a counting argument.
The scalability of photonic implementations of fault-tolerant quantum computing based on Gottesman-Kitaev-Preskill (GKP) qubits is injured by the requirements of inline squeezing and reconfigurability of the linear optical network. In this work we propose a topologically error-corrected architecture that does away with these elements at no cost - in fact, at an advantage - to state preparation overheads. Our computer consists of three modules: a 2D array of probabilistic sources of GKP states; a depth-four circuit of static beamsplitters, phase shifters, and single-time-step delay lines; and a 2D array of homodyne detectors. The symmetry of our proposed circuit allows us to combine the effects of finite squeezing and uniform photon loss within the noise model, resulting in more comprehensive threshold estimates. These jumps over both architectural and analytical hurdles considerably expedite the construction of a photonic quantum computer.
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