Quantum state and circuit distinguishability with single-qubit measurements

We show that the Quantum State Distinguishability (QSD), which is a QSZK-complete problem, and the Quantum Circuit Distinguishability (QCD), which is a QIP-complete problem, can be solved by the verifier who can perform only single-qubit measurements. To show these results, we use measurement-based quantum computing: the honest prover sends a graph state to the verifier, and the verifier can perform universal quantum computing on it with only single-qubit measurements. If the prover is malicious, he does not necessarily generate the correct graph state, but the verifier can verify the correctness of the graph state by measuring the stabilizer operators.Comment: 17 pages, 5 figure

Superposition of macroscopically distinct states means large multipartite entanglement

We show relations between superposition of macroscopically distinct states and entanglement. These relations lead to the important conclusion that if a state contains superposition of macroscopically distinct states, the state also contains large multipartite entanglement in terms of several measures. Such multipartite entanglement property also suggests that if a state contains superposition of macroscopically distinct states, a measurement on a single particle drastically changes the state of macroscopically many other particles, as in the case of the N-qubit GHZ state.Comment: 6 pages, PRA Rapid, accepte

Acausal measurement-based quantum computing

In the measurement-based quantum computing, there is a natural "causal cone" among qubits of the resource state, since the measurement angle on a qubit has to depend on previous measurement results in order to correct the effect of byproduct operators. If we respect the no-signaling principle, byproduct operators cannot be avoided. In this paper, we study the possibility of acausal measurement-based quantum computing by using the process matrix framework [O. Oreshkov, F. Costa, and C. Brukner, Nature Communications {\bf3}, 1092 (2012)]. We construct a resource process matrix for acausal measurement-based quantum computing. The resource process matrix is an analog of the resource state of the causal measurement-based quantum computing. We find that the resource process matrix is (up to a normalization factor and trivial ancilla qubits) equivalent to the decorated graph state created from the graph state of the corresponding causal measurement-based quantum computing.Comment: 5 pages, 2 figure

Hardness of classically sampling one clean qubit model with constant total variation distance error

The one clean qubit model (or the DQC1 model) is a restricted model of quantum computing where only a single input qubit is pure and all other input qubits are maximally mixed. In spite of the severe restriction, the model can solve several problems (such as calculating Jones polynomials) whose classical efficient solutions are not known. Furthermore, it was shown that if the output probability distribution of the one clean qubit model can be classically efficiently sampled with a constant multiplicative error, then the polynomial hierarchy collapses to the second level. Is it possible to improve the multiplicative error hardness result to a constant total variation distance error one like other sub-universal quantum computing models such as the IQP model, the Boson Sampling model, and the Fourier Sampling model? In this paper, we show that it is indeed possible if we accept a modified version of the average case hardness conjecture. Interestingly, the anti-concentration lemma can be easily shown by using the special property of the one clean qubit model that each output probability is so small that no concentration occurs.Comment: 9 page

Highly-mixed measurement-based quantum computing and the one clean qubit model

We show that a highly-mixed state in terms of a large min-entropy is useless as a resource state for measurement-based quantum computation in the sense that if a classically efficiently verifiable problem is efficiently solved with such a highly-mixed measurement-based quantum computation then such a problem can also be classically efficiently solved. We derive a similar result also for the DQC1$_k$ model, which is a generalized version of the DQC1 model where $k$ output qubits are measured. We also show that the measurement-based quantum computing on a highly-mixed resource state in terms of the von Neumann entropy, and DQC1$_k$ model are useless in another sense that the mutual information between the computation results and inputs is very small.Comment: 5 pages, 2 figure

Verification for measurement-only blind quantum computing

Blind quantum computing is a new secure quantum computing protocol where a client who does not have any sophisticated quantum technlogy can delegate her quantum computing to a server without leaking any privacy. It is known that a client who has only a measurement device can perform blind quantum computing [T. Morimae and K. Fujii, Phys. Rev. A {\bf87}, 050301(R) (2013)]. It has been an open problem whether the protocol can enjoy the verification, i.e., the ability of client to check the correctness of the computing. In this paper, we propose a protocol of verification for the measurement-only blind quantum computing.Comment: 5 pages, 3 figure

Testing honesty of quantum server

Alice, who does not have any sophisticated quantum technology, delegates her quantum computing to Bob, who has a fully-fledged quantum computer. Can she check whether the computation Bob performs for her is correct? She cannot recalculate the result by herself, since she does not have any quantum computer. A recent experiment with photonic qubits suggests she can. Here, I explain the basic idea of the result, and recent developments about secure cloud quantum computing.Comment: 2 pages, 1 figure; News and Views article for Nature Physics; different from the published versio

Measurement-only verifiable blind quantum computing with quantum input verification

Verifiable blind quantum computing is a secure delegated quantum computing where a client with a limited quantum technology delegates her quantum computing to a server who has a universal quantum computer. The client's privacy is protected (blindness) and the correctness of the computation is verifiable by the client in spite of her limited quantum technology (verifiability). There are mainly two types of protocols for verifiable blind quantum computing: the protocol where the client has only to generate single-qubit states, and the protocol where the client needs only the ability of single-qubit measurements. The latter is called the measurement-only verifiable blind quantum computing. If the input of the client's quantum computing is a quantum state whose classical efficient description is not known to the client, there was no way for the measurement-only client to verify the correctness of the input. Here we introduce a new protocol of measurement-only verifiable blind quantum computing where the correctness of the quantum input is also verifiable.Comment: 7 pages, 1 figur

Necessity of macroscopic operation for the creation of superpositions of macroscopically distinct states

We consider the creation of superpositions of macroscopically distinct states by a completely-positive (CP) operation on a subsystem. We conclude that the subsystem on which the CP operation acts must be macroscopically large if the success probability of the CP operation does not vanish in the thermodynamic limit. In order to obtain this conclusion, we show two inequalities each of which represents a trade-off relation among the magnitude of an indicator for superpositions of macroscopically distinct states, the success probability of a CP operation, and the volume of the subsystem on which the CP operation acts.Comment: 9 pages, no figur

Minimum heat dissipation in measurement-based quantum computation

We show that at least 2kTln2 of heat dissipation per qubit occurs in measurement-based quantum computation according to Landauer's principle. This result is derived by using only the fundamental fact that quantum physics respects the no-signaling principle.Comment: 6 pages, 4 figure