Related papers: The Power of Unentanglement
We construct a classically verifiable succinct interactive argument for quantum computation (BQP) with communication complexity and verifier runtime that are poly-logarithmic in the runtime of the BQP computation (and polynomial in the…
We study the advantages of quantum communication models over classical communication models that are equipped with a limited number of qubits of entanglement. In this direction, we give explicit partial functions on $n$ bits for which…
A protocol of quantum dense coding protection of two qubits is proposed in amplitude damping (AD) channel using weak measurement and reversal measurement. It is found that the capacity of quantum dense coding under the weak measurement and…
The intrinsic non-locality of correlations in Quantum Mechanics allow us to certify the behaviour of a quantum mechanism in a device independent way. In particular, we present a new protocol that allows an unbounded amount of randomness to…
Quantum mechanics dictates the band-structure of materials that is essential for functional electronic components. With increased miniaturization of devices, it becomes possible to exploit the full potential of quantum mechanics through the…
We prove a query complexity lower bound for $\mathsf{QMA}$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $\mathsf{SBP}^A \not\subset…
Encoding schemes and error-correcting codes are widely used in information technology to improve the reliability of data transmission over real-world communication channels. Quantum information protocols can further enhance the performance…
The most trivial way to simulate classically the communication of a quantum state is to transmit the classical description of the quantum state itself. However, this requires an infinite amount of classical communication if the simulation…
Testing quantum theory on macroscopic scales is a longstanding challenge that might help to revolutionise physics. For example, laboratory tests (such as those anticipated in nanomechanical or biological systems) may look to rule out…
The position of a device or agent is an important security credential in today's society, both online and in the real world. Unless in direct proximity, however, the secure verification of a position is impossible without further…
We show that any quantum algorithm to decide whether a function f:[n]->[n] is a permutation or far from a permutation must make Omega(n^{1/3}/w) queries to f, even if the algorithm is given a w-qubit quantum witness in support of f being a…
We show two results about the relationship between quantum and classical messages. Our first contribution is to show how to replace a quantum message in a one-way communication protocol by a deterministic message, establishing that for all…
In this paper we consider a quantum computational variant of nondeterminism based on the notion of a quantum proof, which is a quantum state that plays a role similar to a certificate in an NP-type proof. Specifically, we consider quantum…
Quantum k-SAT is the problem of deciding whether there is a n-qubit state which is perpendicular to a set of vectors, each of which lies in the Hilbert space of k qubits. Equivalently, the problem is to decide whether a particular type of…
Sequences of commuting quantum operators can be parallelized using entanglement. This transformation is behind some optimal quantum metrology protocols and recent results on quantum circuit complexity. We show that dephasing quantum maps in…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…
We prove the security of a high-capacity quantum key distribution protocol over noisy channels. By using entanglement purification protocol, we construct a modified version of the protocol in which we separate it into two consecutive…
We initiate the study of parameterized complexity of $\textsf{QMA}$ problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists…
As far as I know, at the time that I originally devised this result (1998), this was the first constructive proof that, for any integer $k$, there is a language in $\Sigma_2^P$ that cannot be simulated by a family of logic circuits of size…
We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive…