A complete characterisation of All-versus-Nothing arguments for stabiliser states
نویسندگان
چکیده
An important class of contextuality arguments in quantum foundations are the All-versus-Nothing (AvN) proofs, generalising a construction originally due to Mermin. We present a general formulation of All-versus-Nothing arguments, and a complete characterisation of all such arguments which arise from stabiliser states. We show that every AvN argument for an n-qubit stabiliser state can be reduced to an AvN proof for a three-qubit state which is local Clifford-equivalent to the tripartite GHZ state. This is achieved through a combinatorial characterisation of AvN arguments, the AvN triple Theorem,whose proof makes use of the theory of graph states. This result enables the development of a computational method to generate all the AvN arguments in Z2 on n-qubit stabiliser states. We also present new insights into the stabiliser formalism and its connections with logic.
منابع مشابه
Identifying All-vs-Nothing Arguments in Stabiliser Theory
All-vs-Nothing arguments represent a powerful method for the detection of strong contextuality in quantum theory. The original formulation by Mermin [15] has been recently formalised and generalised using stabiliser quantum mechanics [2, 9]. In the present paper, we take advantage of this framework to introduce a computational technique to identify a large amount of strongly contextual empirica...
متن کاملAll-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering
Einstein-Podolsky-Rosen steering is a form of quantum nonlocality intermediate between entanglement and Bell nonlocality. Although Schrödinger already mooted the idea in 1935, steering still defies a complete understanding. In analogy to "all-versus-nothing" proofs of Bell nonlocality, here we present a proof of steering without inequalities rendering the detection of correlations leading to a ...
متن کامل0 Local symmetry properties of pure 3 - qubit states
Entanglement types of pure states of three spin-12 particles are classified by means of their stabilisers in the group of local unitary transformations. It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a stationary value for some local invariant. We describe all the exceptional states with enlarged stabilisers.
متن کاملLocal symmetry properties of pure 3 - qubit states
Entanglement types of pure states of three spin-12 particles are classified by means of their stabilisers in the group of local unitary transformations. It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a stationary value for some local invariant. We describe all the exceptional states with enlarged stabilisers.
متن کاملThe Quantum Entropy Cone of Stabiliser States
We investigate the universal linear inequalities that hold for the von Neumann entropies in a multi-party system, prepared in a stabiliser state. We demonstrate here that entropy vectors for stabiliser states satisfy, in addition to the classic inequalities, a type of linear rank inequalities associated with the combinatorial structure of normal subgroups of certain matrix groups. In the 4-part...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1705.08459 شماره
صفحات -
تاریخ انتشار 2017