| 1. |
- Ahrens, Johan, et al.
(author)
-
Experimental device independent tests of classical and quantum dimensions
- 2012
-
In: Nature Physics. - 1745-2473 .- 1745-2481. ; 8:8, s. 592-595
-
Journal article (peer-reviewed)abstract
- A fundamental resource in any communication and computation task is the amount of information that can be transmitted and processed. The classical information encoded in a set of states is limited by the number of distinguishable states or classical dimension d(c) of the set. The sets used in quantum communication and information processing contain states that are neither identical nor distinguishable, and the quantum dimension d(q) of the set is the dimension of the Hilbert space spanned by these states. An important challenge is to assess the (classical or quantum) dimension of a set of states in a device-independent way, that is, without referring to the internal working of the device generating the states. Here we experimentally test dimension witnesses designed to efficiently determine the minimum dimension of sets of (three or four) photonic states from the correlations originated from measurements on them, and distinguish between classical and quantum sets of states.
|
|
| 2. |
- Ahrens, Johan, et al.
(author)
-
Experimental Tests of Classical and Quantum Dimensionality
- 2014
-
In: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 112:14
-
Journal article (peer-reviewed)abstract
- We report on an experimental test of classical and quantum dimension. We have used a dimension witness that can distinguish between quantum and classical systems of dimensions two, three, and four and performed the experiment for all five cases. The witness we have chosen is a base of semi-device-independent cryptographic and randomness expansion protocols. Therefore, the part of the experiment in which qubits were used is a realization of these protocols. In our work we also present an analytic method for finding the maximum quantum value of the witness along with corresponding measurements and preparations. This method is quite general and can be applied to any linear dimension witness.
|
|
| 3. |
- Andersson, Ole, et al.
(author)
-
Device-independent certification of two bits of randomness from one entangled bit and Gisin's elegant Bell inequality
- 2018
-
In: Physical Review A. Atomic, Molecular, and Optical Physics. - : American Physical Society. - 1050-2947 .- 1094-1622. ; 97:1
-
Journal article (peer-reviewed)abstract
- We prove that as conjectured by Acín et al. [Phys. Rev. A 93, 040102(R) (2016)], two bits of randomness can be certified in a device-independent way from one bit of entanglement using the maximal quantum violation of Gisin's elegant Bell inequality. This suggests a surprising connection between maximal entanglement, complete sets of mutually unbiased bases, and elements of symmetric informationally complete positive operator-valued measures, on one side, and the optimal way of certifying maximal randomness, on the other.
|
|
| 4. |
- Andersson, Ole, et al.
(author)
-
Self-testing properties of Gisin's elegant Bell inequality
- 2017
-
In: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : American Physical Society. - 2469-9926 .- 2469-9934. ; 96:3
-
Journal article (peer-reviewed)abstract
- An experiment in which the Clauser-Horne-Shimony-Holt inequality is maximally violated is self-testing (i.e., it certifies in a device-independent way both the state and the measurements). We prove that an experiment maximally violating Gisin's elegant Bell inequality is not similarly self-testing. The reason can be traced back to the problem of distinguishing an operator from its complex conjugate. We provide a complete and explicit characterization of all scenarios in which the elegant Bell inequality is maximally violated. This enables us to see exactly how the problem plays out.
|
|
| 5. |
- Badziag, Piotr, et al.
(author)
-
Bound entangled states with extremal properties
- 2014
-
In: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 90:1, s. 012301-
-
Journal article (peer-reviewed)abstract
- Following recent work of Beigi and Shor, we investigate positive partial transpose (PPT) states that are heavily entangled. We first exploit volumetric methods to show that in a randomly chosen direction, there are PPT states whose distance in trace norm from separable states is (asymptotically) at least 1/4. We then provide explicit examples of PPT states which are nearly as far from separable ones as possible. To obtain a distance of 2 - c from the separable states, we need a dimension of 2(poly[log(1/epsilon)]), as opposed to 2(poly(1/epsilon)) given by the construction of Beigi and Shor [J. Math. Phys. 51, 042202 (2010)]. We do so by exploiting the so-called private states, introduced earlier in the context of quantum cryptography. We also provide a lower bound for the distance between private states and PPT states and investigate the distance between pure states and the set of PPT states.
|
|
| 6. |
- Badziag, Piotr, et al.
(author)
-
Experimentally friendly geometrical criteria for entanglement
- 2008
-
In: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 100:14, s. 140403-
-
Journal article (peer-reviewed)abstract
- A simple geometrical criterion gives experimentally friendly sufficient conditions for entanglement. Its generalization gives a necessary and sufficient condition. It is linked with a family of entanglement identifiers, which is strictly richer than the family of entanglement witnesses.
|
|
| 7. |
- Badziag, Piotr, et al.
(author)
-
Pentagrams and Paradoxes
- 2011
-
In: FOUNDATIONS OF PHYSICS. - : Springer Science Business Media. - 0015-9018 .- 1572-9516. ; 41:3, s. 414-423
-
Journal article (peer-reviewed)abstract
- Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a magical choice of basis, into SO(N) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and then show how the pentagram underlies a number of other quantum "paradoxes", such as that of Hardy.
|
|
| 8. |
- Badziag, Piotr, et al.
(author)
-
Separability in terms of a single entanglement witness
- 2013
-
In: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 88:1, s. 010301-
-
Journal article (peer-reviewed)abstract
- The separability problem is formulated in terms of a characterization of a single entanglement witness. More specifically, we show that any (in general multipartite) state rho is separable if and only if a specially constructed entanglement witness W-rho is weakly optimal, i.e., its expectation value vanishes on at least one product vector. Interestingly, the witness can always be chosen to be decomposable. Our result changes the conceptual aspect of the separability problem and raises some questions about the properties of positive maps.
|
|
| 9. |
- Bengtsson, Ingemar, et al.
(author)
-
Pentagrams and paradoxes
- 2011
-
In: Foundations of Physics. ; 41, s. 414-
-
Journal article (peer-reviewed)
|
|
| 10. |
- Bengtsson, Ingemar, et al.
(author)
-
Universality of State-Independent Violation of Correlation Inequalities for Non-Contextual Theories
- 2009
-
In: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 103:5, s. 050401-
-
Journal article (peer-reviewed)abstract
- We show that the state-independent violation of inequalities for noncontextual hidden variable theories introduced in [Phys. Rev. Lett. 101, 210401 (2008)] is universal, i.e., occurs for any quantum mechanical system in which noncontextuality is meaningful. We describe a method to obtain state-independent violations for any system of dimension d >= 3. This universality proves that, according to quantum mechanics, there are no "classical'' states.
|
|
