Quantum computing on encrypted data allows a client who has limited quantum capacity to delegate his or her private computation to an untrusted quantum server, meanwhile the input and output are encrypted by the quantum one-time pad and only the client can correctly decrypt them. Generally, the client is required to have ability to prepare some single qubits and perform some basic gates. In this work, we consider a further restricted situation where the client can only prepare one single qubit and perform one basic gate. Specifically, we show that as long as the client can prepare a fixed qubit |+〉 and perform a fixed phase gate P, then he or she can still achieve the secure delegated quantum computation. Besides, our protocol can provide a more rigorous security for any quantum computation. For example, even if some encryption keys about the computation are leaked, it can still guarantee the privacy of the input and output. Finally, our protocol experimentally has a great significance in reducing the device complexity of the client’s side.
We design forward and backward fault-tolerant conversion circuits, which convert between the Steane code and the 15-qubit Reed-Muller quantum code so as to provide a universal transversal gate set. In our method, only 7 out of total 14 code stabilizers need to be measured, and we further enhance the circuit by simplifying some stabilizers; thus, we need only to measure eight weight-4 stabilizers for one round of forward conversion and seven weight-4 stabilizers for one round of backward conversion. For conversion, we treat random single-qubit errors and their influence on syndromes of gauge operators, and our novel single-step process enables more efficient fault-tolerant conversion between these two codes. We make our method quite general by showing how to convert between any two adjacent Reed-Muller quantum codes RM(1, m) and RM (1, m + 1), for which we need only measure stabilizers whose number scales linearly with m rather than exponentially with m obtained in previous work. We provide the explicit mathematical expression for the necessary stabilizers and the concomitant resources required.Quantum information technology, with applications such as secure quantum communication or universal quantum computing, is extremely powerful but challenging due to the fragility of quantum information in the presence of noise, loss and decoherence. Fault-tolerant quantum error correction [1][2][3] ameliorates this problem of fragility by encoding plain-text quantum information into cipher text, processing this encoded information while also measuring error syndromes and correcting, and finally turning back to plain text. For fault-tolerant error correction, transversal gates are especially valuable as qubits in each code block act bitwise between corresponding qubits in each code block, thereby naturally preventing error propagation [4]. Unfortunately, no code can simply enable a universal set of transversal gates [4-6] without invoking a technique involving ancillary qubits; thus, complicated strategies are employed to produce universal transversal gate sets. One strategy to circumvent the non-universal gate set problem is to employ magic-state distillation [7][8][9][10][11][12]. Although magic-state distillation has the advantage of a higher fault-tolerant threshold, the overhead in preparation and distillation is a major bottleneck for scalable quantum computing [13][14][15][16].Alternative techniques can provide a universal fault-tolerant gate set. The Steane code [17] provides transversal Clifford gates but not the transversal T := diag(1, exp{iπ/4}) gate whereas the 15-qubit Reed-Muller quantum code (RMQC) [18] is transversal for T, controlled-NOT (CNOT), controlled-S (CS), controlled-Z (CZ), and controlledcontrolled-Z (CCZ) gates, but not for the Hadamard (H) gate. One approach to achieving a universal set of gates employs just one code such as the Steane code or the 15-qubit RMQC and does not invoke code conversion. For example, for the Steane code, the fault-tolerant T gate can be realized with the help of an ancil...
A new scheme of quantum key distribution (QKD) using frequency and time coding is proposed, in which the security is based on the frequency-time uncertainty relation. In this scheme, the binary information sequence is encoded randomly on either the central frequency or the time delay of the optical pulse at the sender. The central frequency of the single photon pulse is set as 1 ω for bit "0" and set as 2 ω for bit "1" when frequency coding is selected. While, the single photon pulse is not delayed for bit "0" and is delayed in τ for "1" when time coding is selected.At the receiver, either the frequency or the time delay of the pulse is measured randomly, and the final key is obtained after basis comparison, data reconciliation and privacy amplification. With the proposed method, the effect of the noise in the fiber channel and environment on QKD system can be reduced effectively. PACS:03.67.Dd, 42.50. Dv In 1984, a quantum key distribution (QKD) protocol based on Hisenberg uncertainty principle and the no-cloning theorem is proposed by Charles H. Bennett and Gilles Brassard[1]. This protocol, known as BB84, can really provide unconditional security. Since then, the theory and experiments of QKD have got rapid development[2]. Various QKD schemes based on polarization coding[1][3]-[5], phase coding[6]-[10], *
In this paper, two novel schemes for deterministic joint remote state preparation (JRSP) of arbitrary single- and two-qubit states are proposed. A set of ingenious four-particle partially entangled states are constructed to serve as the quantum channels. In our schemes, two senders and one receiver are involved. Participants collaborate with each other and perform projective measurements on their own particles under an elaborate measurement basis. Based on their measurement results, the receiver can reestablish the target state by means of appropriate local unitary operations deterministically. Unit success probability can be achieved independent of the channel’s entanglement degree.
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