Related papers: The Entangled Quantum Polynomial Hierarchy Collaps…
We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and…
The Polynomial-Time Hierarchy ($\mathsf{PH}$) is a staple of classical complexity theory, with applications spanning randomized computation to circuit lower bounds to ''quantum advantage'' analyses for near-term quantum computers.…
The polynomial-time hierarchy ($\mathrm{PH}$) has proven to be a powerful tool for providing separations in computational complexity theory (modulo standard conjectures such as $\mathrm{PH}$ does not collapse). Here, we study whether two…
We study the quantum-classical polynomial hierarchy, QCPH, which is the class of languages solvable by a constant number of alternating classical quantifiers followed by a quantum verifier. Our main result is that QCPH is infinite relative…
We prove several new results concerning the pure quantum polynomial hierarchy (pureQPH). First, we show that QMA(2) is contained in pureQSigma2, that is, two unentangled existential provers can be simulated by competing existential and…
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with…
We prove that given the ability to make entangled measurements on at most $k$ replicas of an $n$-qubit state $\rho$ simultaneously, there is a property of $\rho$ which requires at least order $2^n$ measurements to learn. However, the same…
The polynomial hierarchy is a grading of problems by difficulty, including P, NP and coNP as the best known classes. The promise polynomial hierarchy is similar, but extended to include promise problems. It turns out that the promise…
The polynomial hierarchy has been widely studied in classical complexity theory. In this paper, we will generalize some commonly known results about the polynomial hierarchy to a version of the hierarchy extended to promise problems. This…
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
Quantum entanglement is a fundamental property of quantum mechanics and plays a crucial role in quantum computation and information. We study entanglement via the lens of computational complexity by considering quantum generalizations of…
We show that the value of a general two-prover quantum game cannot be computed by a semi-definite program ofvpolynomial size (unless P=NP), a method that has been successful in more restricted quantum games. More precisely, we show that…
This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. In the first area, we demonstrate a polynomial-time…
While there exist theories that have states "more strongly entangled" than quantum theory, in the sense that they show CHSH values above Tsirelson's bound, all known examples of such theories have a strictly smaller set of measurements.…
The arithmetical hierarchy (AH) is similar to the polynomial hierarchy (PH). Unlike the PH, the AH does not collapse relative to any oracle. A language in the (k + 1)-st level of the AH is computable enumerable (c.e.) relative to the kth…
A fundamental pursuit in complexity theory concerns reducing worst-case problems to average-case problems. There exist complexity classes such as PSPACE that admit worst-case to average-case reductions. However, for many other classes such…
This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two…
We establish the first hardness results for the problem of computing the value of one-round games played by a verifier and a team of provers who can share quantum entanglement. In particular, we show that it is NP-hard to approximate within…
Quantum correlations have fundamental and technological interest, and hence many measures have been introduced to quantify them. Some hierarchical orderings of these measures have been established, e.g., discord is bigger than entanglement,…