All research outputs are listed in the CV.
No Quantum Advantage for Violating Fixed-Order Inequalities?
Veronika Baumann, Ämin Baumeler, and Eleftherios-Ermis Tselentis
arXiv:2412.17551
In standard quantum theory, the causal relations between operations are fixed and determined by the spacetime structure. Relaxing this notion of fixed causal order has been studied extensively over the past years. A first departure allows for dynamical arrangements, where operations can influence the causal relations of future operations, as certified by violation of fixed-order inequalities. A second non-causal departure relaxes even these limitations, and is certified by violations of causal inequalities. The quantum switch, which allows a party to coherently control the order in which operations are applied, is known to be incapable of violating causal inequalities. It was therefore believed that a device-independent certification of the causal indefiniteness in the quantum switch requires extended setups incorporating spacelike separation. Here, we show that the quantum switch violates fixed-order inequalities without exploiting its indefinite nature. Concretely, we study the k-cycle inequalities and introduce multi-party generalizations of the quantum switch tailored to these fixed-order inequalities. We further show that, when removing the dynamical aspect, k-cycle inequalities become novel, facet-defining, causal inequalities. On the one hand, this means that violating k-cycle inequalities under this restriction requires non-causal setups. On the other hand, since k-cycle inequalities are just one example of fixed-order inequalities, this reopens the possibility for a device-independent certification of the quantum switch in isolation.
The Möbius Game: A Quantum-Inspired Test of General Relativity
Eleftherios-Ermis Tselentis and Ämin Baumeler
arXiv:2407.17203
We present a tight inequality to test the dynamical nature of spacetime. A general-relativistic violation of that inequality certifies change of curvature, in the same sense as a quantum-mechanical violation of a Bell inequality certifies a source of entanglement. The inequality arises from a minimal generalization of the Bell setup. It represents a limit on the winning chance of a collaborative multi-agent game played on the Möbius graph. A long version of this Letter including other games and how these games certify the dynamical character of the celebrated quantum switch is accessible as arXiv:2309.15752 [gr-qc].
Admissible Causal Structures and Correlations
Eleftherios-Ermis Tselentis and Ämin Baumeler
PRX Quantum 4, 040307 (2023)arXiv:2210.12796
It is well-known that if one assumes quantum theory to hold locally, then processes with indefinite causal order and cyclic causal structures become feasible. Here, we study qualitative limitations on causal structures and correlations imposed by local quantum theory. For one, we find a necessary graph theoretic criterion--the "siblings-on-cycles" property--for a causal structure to be admissible: Only such causal structures admit a realization consistent with local quantum theory. We conjecture that this property is moreover sufficient. This conjecture is motivated by an explicit construction of quantum causal models, and supported by numerical calculations. We show that these causal models, in a restricted setting, are indeed consistent. For another, we identify two sets of causal structures that, in the classical-deterministic case, give rise to causal and non-causal correlations respectively.
Trading Causal Order for Locality
Ravi Kunjwal and Ämin Baumeler
Physical Review Letters 131, 120201 (2023)arXiv:2202.00440
Quantum theory admits ensembles of quantum nonlocality without entanglement (QNLWE). These ensembles consist of seemingly classical states (they are perfectly distinguishable and non-entangled) that cannot be perfectly discriminated with local operations and classical communication (LOCC). Here, we analyze QNLWE from a causal perspective, and show how to perfectly discriminate some of these ensembles using local operations and classical communication without definite causal order. Specifically, three parties with access to an instance of indefinite causal order-the AF/BW process-can perfectly discriminate the states in a QNLWE ensemble--the SHIFT ensemble--with local operations. Hence, this type of quantum nonlocality disappears at the expense of definite causal order while retaining classical communication. Our results thereby leverage the fact that LOCC is a conjunction of three constraints: local operations, classical communication, and definite causal order. Moreover, we show how multipartite generalizations of the AF/BW process are transformed into multiqubit ensembles that exhibit QNLWE. Such ensembles are of independent interest for cryptographic protocols and for the study of separable quantum operations unachievable with LOCC.
The Axiom of Choice and the No-Signaling Principle
Ämin Baumeler, Borivoje Dakić, and Flavio Del Santo
arXiv:2206.08467
We show that the axiom of choice, a basic yet controversial postulate of set theory, leads to revise the standard understanding of one of the pillars of our best physical theories, namely the no-signaling principle. While it is well known that probabilistic no-signaling resources (such as quantum non-locality) are stronger than deterministic ones, we show-by invoking the axiom of choice-the opposite: Functional (deterministic) no-signaling resources can be stronger than probabilistic ones. To prove this, we devise a Bell-like game that shows a systematic advantage of functional no-signaling with respect to any probabilistic no-signaling resource.
Free Energy of a General Computation
Ämin Baumeler and Stefan Wolf
Physical Review E 100, 052115 (2019)arXiv:1901.10290
Starting from Landauer's slogan "information is physical," we revise and modify Landauer's principle stating that the erasure of information has a minimal price in the form of a certain quantity of free energy. We establish a direct link between the erasure cost and the work value of a piece of information, and show that the former is essentially the length of the string's best compression by a reversible computation. We generalize the principle by deriving bounds on the free energy to be invested for --- or gained from, for that matter --- a general computation. We then revisit the second law of thermodynamics and compactly rephrase it (assuming the Church/Turing/Deutsch hypothesis that physical reality can be simulated by a universal Turing machine): Time evolutions are logically reversible --- "the future fully remembers the past (but not necessarily vice versa)." We link this view to previous formulations of the second law, and we argue that it has a particular feature that suggests its "logico-informational" nature, namely simulation resilience: If a computation faithfully simulates a physical process violating the law --- then that very computation procedure violates it as well.
Reversible Time Travel With Freedom of Choice
Ämin Baumeler, Fabio Costa, Timothy Ralph, Stefan Wolf, and Magdalena Zych
Classical and Quantum Gravity 36, 224002 (2019)arXiv:1703.00779
General relativity allows for the existence of closed time-like curves, along which a material object could travel back in time and interact with its past self. This possibility raises the question whether certain initial conditions, or more generally local operations, lead to inconsistencies and should thus be forbidden. Here we consider the most general deterministic dynamics connecting classical degrees of freedom defined on a set of bounded space-time regions, requiring that it is compatible with arbitrary operations performed in the local regions. We find that any such dynamics can be realised through reversible interactions. We further find that consistency with local operations is compatible with non-trivial time travel: Three parties can interact in such a way to be all both in the future and in the past of each other, while being free to perform arbitrary local operations.
The Space of Logically Consistent Classical Processes Without Causal Order
Ämin Baumeler and Stefan Wolf
New Journal of Physics 18, 013036 (2016)arXiv:1507.01714
Classical correlations without predefined causal order arise from processes where parties manipulate random variables, and where the order of these interactions is not predefined. No assumption on the causal order of the parties is made, but the processes are restricted to be logically consistent under any choice of the parties' operations. It is known that for three parties or more, this set of processes is larger than the set of processes achievable in a predefined ordering of the parties. Here, we model all classical processes without predefined causal order geometrically and find that the set of such processes forms a polytope. Additionally, we model a smaller polytope --- the deterministic-extrema polytope --- where all extremal points represent deterministic processes. This polytope excludes probabilistic processes that must be --- quite unnaturally --- fine-tuned, because any variation of the weights in a decomposition into deterministic processes leads to a logical inconsistency.
Causal Loops: Logically Consistent Correlations, Time Travel, and Computation
Ämin Baumeler
PhD Thesis, Università della Svizzera italiana (2017)