Related papers: Quantum interactive proofs and the complexity of s…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
Suppose that a polynomial-time mixed-state quantum circuit, described as a sequence of local unitary interactions followed by a partial trace, generates a quantum state shared between two parties. One might then wonder, does this quantum…
We construct a single observable measurement of which mean value on four copies of an {\it unknown} two-qubit state is sufficient for unambiguous decision whether the state is separable or entangled. In other words, there exists a universal…
The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum…
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard. There is a highly inefficient `basic algorithm'…
Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first…
Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in…
We map the quantum entanglement problem onto the mathematically well-studied truncated moment problem. This yields a necessary and sufficient condition for separability that can be checked by a hierarchy of semi-definite programs. The…
We give a quantum interactive proof system for the local Hamiltonian problem on n qubits in which (i) the verifier has a single round of interaction with five entangled provers, (ii) the verifier sends a classical message on O(log n) bits…
Whereas quantum complexity theory has traditionally been concerned with problems arising from classical complexity theory (such as computing boolean functions), it also makes sense to study the complexity of inherently quantum operations…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
This paper presents stronger methods of achieving perfect completeness in quantum interactive proofs. First, it is proved that any problem in QMA has a two-message quantum interactive proof system of perfect completeness with constant…
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…
Quantum entanglement is essential to the development of quantum computation, communications, and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and useful test for entanglement of a…
Determining the worst-case uncertainty added by a quantum circuit is shown to be computationally intractable. This is the problem of detecting when a quantum channel implemented as a circuit is close to a linear isometry, and it is shown to…
We study the quantum separability problem by using general symmetric informationally complete measurements and present separability criteria for both $d$-dimensional bipartite and multipartite systems. The criterion for bipartite quantum…
The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing, which is known to be an NP-hard problem in general. Despite the proposed many methods such as the positive partial…
In this work we are interested the problem of testing quantum entanglement. More specifically, we study the separability problem in quantum property testing, where one is given $n$ copies of an unknown mixed quantum state $\varrho$ on…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
We present a review of the problem of finding out whether a quantum state of two or more parties is entangled or separable. After a formal definition of entangled states, we present a few criteria for identifying entangled states and…