Entanglement-Separability Boundary Within a Quantum State
- URL: http://arxiv.org/abs/2003.00607v1
- Date: Sun, 1 Mar 2020 23:06:53 GMT
- Title: Entanglement-Separability Boundary Within a Quantum State
- Authors: Bang-Hai Wang
- Abstract summary: We show that an arbitrary quantum state can be divided into a unique purely entangled structure and a purely unique separable structure.
We provide a general algorithm for the purely entangled structure and the purely separable structure, and a general algorithm for the best separable approximation (BSA) decomposition.
Our result implies that quantum states exist as families in theory, and that the entanglement (separability) of family members can be determined by referring to a crucial member of the family.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum states are the key mathematical objects in quantum mechanics, and
entanglement lies at the heart of the nascent fields of quantum information
processing and computation. What determines whether an arbitrary quantum state
is entangled or separable is therefore very important for investigating both
fundamental physics and practical applications. Here we show that an arbitrary
bipartite state can be divided into a unique purely entangled structure and a
unique purely separable structure. We show that whether a quantum state is
entangled or not is determined by the ratio of its weight of the purely
entangled structure and its weight of the purely separable structure. We
provide a general algorithm for the purely entangled structure and the purely
separable structure, and a general algorithm for the best separable
approximation (BSA) decomposition, that has been a long-standing open problem.
Our result implies that quantum states exist as families in theory, and that
the entanglement (separability) of family members can be determined by
referring to a crucial member of the family.
Related papers
- Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees.
Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation.
We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
arXiv Detail & Related papers (2022-03-30T02:02:16Z) - No-signalling constrains quantum computation with indefinite causal
structure [45.279573215172285]
We develop a formalism for quantum computation with indefinite causal structures.
We characterize the computational structure of higher order quantum maps.
We prove that these rules, which have a computational and information-theoretic nature, are determined by the more physical notion of the signalling relations between the quantum systems.
arXiv Detail & Related papers (2022-02-21T13:43:50Z) - Experimental investigation of quantum uncertainty relations with
classical shadows [7.675613458661457]
We experimentally investigate quantum uncertainty relations construed with relative entropy of coherence.
We prepare a family of quantum states whose purity can be fully controlled.
Our results indicate the tightness of quantum coherence lower bounds dependents on the reference bases as well as the purity of quantum state.
arXiv Detail & Related papers (2022-02-14T00:26:31Z) - Non-standard entanglement structure of local unitary self-dual models as
a saturated situation of repeatability in general probabilistic theories [61.12008553173672]
We show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry.
We also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable.
arXiv Detail & Related papers (2021-11-29T23:37:58Z) - Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
An important problem in any quantum resource theory is to determine how quantum states can be converted into each other.
Very few results have been presented on the intermediate regime between probabilistic and approximate transformations.
We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations.
We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
arXiv Detail & Related papers (2021-11-24T17:29:43Z) - Quantum Causal Unravelling [44.356294905844834]
We develop the first efficient method for unravelling the causal structure of the interactions in a multipartite quantum process.
Our algorithms can be used to identify processes that can be characterized efficiently with the technique of quantum process tomography.
arXiv Detail & Related papers (2021-09-27T16:28:06Z) - Quantum coherence with incomplete set of pointers and corresponding
wave-particle duality [0.0]
Quantum coherence quantifies the amount of superposition in a quantum system.
We develop the corresponding resource theory, identifying the free states and operations.
We obtain a complementarity relation between the so-defined quantum coherence and the which-path information in an interferometric set-up.
arXiv Detail & Related papers (2021-08-12T16:55:40Z) - Operational Resource Theory of Imaginarity [48.7576911714538]
We show that quantum states are easier to create and manipulate if they only have real elements.
As an application, we show that imaginarity plays a crucial role for state discrimination.
arXiv Detail & Related papers (2020-07-29T14:03:38Z) - Resource theory of quantum coherence with probabilistically
non-distinguishable pointers and corresponding wave-particle duality [0.6882042556551611]
We study the resource theory of quantum coherence with respect to an arbitrary set of quantum state vectors.
We identify a class of measures of the quantum coherence, and in particular establish a monotonicity property of the measures.
We report a relation between quantum coherence and path complementary distinguishability in a double-slit set-up.
arXiv Detail & Related papers (2020-05-17T16:56:31Z) - Characterization of quantum states based on creation complexity [0.0]
The creation complexity of a quantum state is the minimum number of elementary gates required to create it from a basic initial state.
We show for an entirely general quantum state it is exponentially hard (requires a number of steps that scales exponentially with the number of qubits) to determine if the creation complexity is.
We then show it is possible for a large class of quantum states with creation complexity to have common coefficient features such that given any candidate quantum state we can design an efficient coefficient sampling procedure to determine if it belongs to the class or not with arbitrarily high success probability.
arXiv Detail & Related papers (2020-04-28T21:12:45Z) - Quantifying the unextendibility of entanglement [13.718093420358827]
Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility.
We present a framework for quantifying and investigating the unextendibility of general bipartite quantum states.
arXiv Detail & Related papers (2019-11-18T05:22:36Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.